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Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in insurgency warfare we investigate coalescence-fragmentation systems. We begin with a simple model of size-biased coalescence accompanied by shattering into monomers. Depending on the parameters this model has an approximately power-law-distributed steady state or stochastic cycles of alternating gelation and shattering. We conduct stochastic simulations of this model and its generalizations to include different kernel types, accretion and erosion, and various distributions of non-shattering fragmentation. Our central aim is to explore the robustness of the steady state and gel-shatter stochastic cycles to these variations. We show that an approximate power-law steady state persists with the addition of accretion and erosion, and with partial rather than total shattering. However, broader distributions of fragment sizes typically vitiate both the power law steady state and gel-shatter cyclicity. This work clarifies features shown in coalescence/fragmentation model simulations and elucidates the relationship between the microscopic dynamics and observed phenomena in this widely applicable interdisciplinary model type. [ABSTRACT FROM AUTHOR]

We present a nested algebraic Bethe ansatz for a one-dimensional open spin chain whose boundary quantum spaces are irreducible so2n- or sp2n-representations, and the monodromy matrix satisfies the defining relations of the Olshanskii twisted Yangian Y±(gl2n). We use a generalization of the Bethe ansatz introduced by De Vega and Karowski which allows us to relate the spectral problem of a so2n- or sp2n-symmetric open spin chain to that of a gln-symmetric periodic spin chain. We explicitly derive the structure of the Bethe vectors and the nested Bethe equations. [ABSTRACT FROM AUTHOR]

We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl 2 Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a “bottom-up” approach for constructing integrable boundaries and can be applied to any spin chain model. [ABSTRACT FROM AUTHOR]

This article re-analyses the 1916 battle of Jutland (German: Skagerrak), the major naval engagement of the First World War, in the light of the understanding of dreadnought fleet tactics developed over the decade leading up to it. In particular, it considers the interaction of the calculus of Lanchester's Square Law with fleet geometry and the commanders' decisions that determined it, and with the shipbuilding decisions associated with the Lanchestrian trade-off between quality and quantity. There is a re-examination of the behaviour of the commanders in the light of this tactical analysis, and it is concluded that the outcome of Jutland, in spite of apparent British tactical and technological failings, was the culmination of a decade of consistent and professionally insightful decision-making by the Royal Navy, which built and correctly wielded its decisive weapon, the Grand Fleet, to achieve the required strategic victory. [ABSTRACT FROM AUTHOR]

The application of scientific methods to historical situations is restricted by the existence of a single outcome with no possibility of repetition. However, new computational methods make quantitative historical analysis possible. The authors apply methods of approximate Bayesian computation to simulate a naval engagement of the First World War, the Battle of the Dogger Bank. They demonstrate that the battle's outcome was highly unlikely, with significant implications both for subsequent actions and for historical understanding. Dogger Bank exemplifies the view that Bayesian methods offer historians the tool they need to grapple with the evolving probabilities of historical events, giving a sound scientific basis for counterfactual history and opening up a wealth of possibilities for analysis. [ABSTRACT FROM PUBLISHER]

We explain two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger ("MICZ") Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of well-separated solitonic ("BPS") monopoles using Taub-NUT space. Each system is characterized by the conservation of a Laplace-Runge-Lenz vector, and we use elementary vector techniques to show that each obeys a subtly different variation on Kepler's three laws for the Newton-Coulomb two-body problem, including a new modified Kepler third law for BPS monopoles. [ABSTRACT FROM AUTHOR]

The Battle of Britain (1940) is the focus of much historical controversy. We show here how the statistical technique of weighted bootstrapping can be used to create a new quantitative basis to help address such controversies. Bootstrapping facilitates the exploration of alternative campaign possibilities with different tactics. This results in comparative probabilities of "victory" for the actual and various counterfactual campaigns, providing a quantified assessment of the likelihood of German achievement of air superiority, thereby facilitating invasion. We And this more likely had the Luftwaffe targeted airfields more heavily, and greatly more likely had Germany brought forward its air campaign. [ABSTRACT FROM AUTHOR]

An introduction to our recent work (hep-th/0104212) on the ( G × G-invariant) principal chiral model with boundary is presented. We found that both classically integrable boundary conditions and quantum boundary is presented S-matrices were classified by the symmetric spaces G/H. [ABSTRACT FROM AUTHOR]

We show that, in the open Hubbard model with integrable boundary conditions, the bulk Yangian symmetry is broken to a twisted Yangian. We prove that the associated charges commute with the Hamiltonian and the reflection matrix, and that they form a coideal subalgebra. [ABSTRACT FROM AUTHOR]

This article examines the Big Wing controversy in the Battle of Britain according to the RAF’s understanding of the principle of concentration. RAF doctrine was developed from Fuller’s 1916 codification of the principles of war, which in terms of concentration rested on the work of engineer and air-power theorist F. W. Lanchester. We argue that fighter doctrine diverged from its Lanchestrian core between the wars and allowed conflicting interpretations of concentration in British air defence. We conclude that Park’s conduct of the Battle of Britain in 11 Group conformed closely to the Lanchester model in concentrating British resources and denying targets to the enemy. Conversely, the Big Wing failed to provide operational concentration and presented the enemy with a massed target it was his mission to destroy. Data suggest greater British losses relative to the enemy when more aircraft were engaged, though damagingly for future policy the mathematics of over-claiming indicated the opposite. [ABSTRACT FROM AUTHOR]