Continuous and discontinuous piecewise linear solutions of the linearly forced inviscid Burgers equation

We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We derive and solve ODEs governing the soliton dynamics, first for continuous solutions, and then for more general shock wave solutions with discontinuities. We show that triple collisions of solitons cannot take place for continuous solutions, but give an example of a triple collision in the presence of a shock.Comment: To appear in Journal of Nonlinear Mathematical Physics (proceedings of NEEDS 2007). 16 pages, 3 figures, LaTeX + AMS packages + pstrick

Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps

The creation of tunable open quantum systems is becoming feasible in current experiments with ultracold atoms in low-dimensional traps. In particular, the high degree of experimental control over these systems allows detailed studies of tunneling dynamics, e.g., as a function of the trapping geometry and the interparticle interaction strength. In order to address this exciting opportunity we present a theoretical framework for two-body tunneling based on the rigged Hilbert space formulation. In this approach, bound, resonant and scattering states are included on an equal footing, and we argue that the coupling of all these components is vital for a correct description of the relevant threshold phenomena. In particular, we study the tunneling mechanism for two-body systems in one-dimensional traps and different interaction regimes. We find a strong dominance of sequential tunneling of single particles for repulsive and weakly attractive systems, while there is a signature of correlated pair tunneling in the calculated many-particle flux for strongly attractive interparticle interaction.Comment: To be published in Phys. Rev. A (Rapid Communication

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

The Cauchy two-matrix model

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain biorthogonal polynomials and solutions of appropriate Riemann-Hilbert problems, thus paving the way to a steepest descent analysis and universality results. The interpretation of the formal expansion of the partition function in terms of multicolored ribbon-graphs is provided and a connection to the O(1) model. A steepest descent analysis of the partition function reveals that the model is related to a trigonal curve (three-sheeted covering of the plane) much in the same way as the Hermitean matrix model is related to a hyperelliptic curve.Comment: 34 pages, 2 figures. V2: changes only to metadat

No leader is an island : contextual antecedents to line managers’ constructive and destructive leadership during an organizational intervention

Purpose: Line managers can make or break organizational interventions, yet little is known about what makes them turn in either direction. As leadership does not occur in a vacuum it has been suggested that the organizational context plays an important role. Building on the intervention and leadership literature, we examine if span of control and employee readiness for change are related to line managers’ leadership during an organizational intervention. Design: Leadership is studied in terms of intervention-specific constructive, as well as passive and active forms of destructive, leadership behaviors. As a sample, we use employees (N = 172) from 37 groups working at a process industry plant. Multilevel analyses over two time points, with both survey and organizational register data were used to analyze the data. Findings: The results revealed that span of control was negatively related to constructive leadership and positively related to passive destructive leadership during the intervention. Employee readiness for change was positively related to constructive leadership, and negatively related to both passive and active destructive leadership. Practical implications: Our findings suggest that contextual factors need to be assessed and considered if we want line managers to engage in constructive rather than destructive leadership during interventions. Originality/value: The present study is the first to address line managers’ making or breaking of organizational interventions by examining the influence of context on both their destructive and constructive leadership

Inverse problems associated with integrable equations of Camassa-Holm type; explicit formulas on the real axis, I

The inverse problem which arises in the Camassa--Holm equation is revisited for the class of discrete densities. The method of solution relies on the use of orthogonal polynomials. The explicit formulas are obtained directly from the analysis on the real axis without any additional transformation to a "string" type boundary value problem known from prior works

Evaluating fuel switching options in the Swedish iron and steel industry under increased competition for forest biomass

Significant use of forest biomass in the iron and steel industry (ISI) to mitigate fossil CO2 emissions will affect the biomass availability for other users of the same resource. This paper explores the market effects of increased forest biomass competition when promoting the use of forest-based bio-products in the ISI, as well as the interactions between the ISI and the forest industries. We employ a soft-linking approach that combines a geographically explicit techno-economic energy system model and an economic partial equilibrium model of the forest industries and forestry sectors. This allows for iterative endogenous modelling of new equilibrium price developments for different biomass assortments, determining locational choice of bio-products and assessing optimal bio-products technology choices. The results indicate an upward pressure on biomass prices when bio-products are introduced in the ISI (up to 62%), which affects both forest industries and the ISI itself. Prudence is thus warranted not to render bio-production investments uneconomical ex-post by neglecting to include potential price effects in investment decisions. The estimated price effects can be mitigated by increased domestic biomass supply, adjustments of international trade or by revising relevant policies. Even though the results suggest that the price effects will affect the geographical preferences for individual bio-production plants, proximity to the ISI production facility and integration benefits are more important than the proximity to cheaper biomass feedstocks. Product gas production integrated at ISI sites emerges as particularly attractive, while charcoal production exhibits sensitivity to fluctuating markets, both regarding resulting cost for the ISI, and preferred production locations

A spatial-explicit price impact analysis of increased biofuel production on forest feedstock markets: A scenario analysis for Sweden

The present paper introduces an integrated spatially explicit framework for assessing price impact on forestry markets in Sweden. The framework is based on the “soft-link” of a price determination model, the SpPDM model with the BeWhere Sweden model. The aim is to analyse the impacts of increased forest-based biofuel production for transportation within the Swedish context by 2030. To that effect, we develop scenarios analyses based on the simulations of successive biofuel production targets, under different assumptions concerning the competition intensity for forest biomass and the use of industrial by-products. The results suggest marginal impacts on the prices of forest biomass. The average across spatial-explicit prices varies from 0% to 2.8% across feedstocks and scenario types. However, the distribution of the spatial-explicit price impacts displays large variation, with price impacts reaching as high as 8.5%. We find that the pattern of spatial distribution of price impacts follows relatively well the spatial distribution of demand pressure. However, locations with the highest price impacts show a tendency of mismatch with the locations of the highest demand pressure (e.g. sawlogs). This is a counterintuitive conclusion compared to results from non-spatial economic models. The spatial-explicit structure of the framework developed, and its refined scale allows such results to be reported. Hence, from a policy-making perspective, careful analysis should be devoted to the locational linkages for forestry markets of increased biofuel production in Sweden

Peakons arising as particle paths beneath small-amplitude water waves

We present a new kind of particle path in constant vorticity water of finite depth, within the framework of small-amplitude waves