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High-resolution x-ray tomography is a common technique for biomedical research using synchrotron sources. With advancements in laboratory x-ray sources, an increasing number of experiments can be performed in the lab. In this paper, the design, implementation, and verification of a laboratory setup for x-ray nano-computed tomography is presented using a nano-focus x-ray source and high geometric magnification not requiring any optical elements. Comparing a scintillator-based detector to a photon counting detector shows a clear benefit of using photon counting detectors for these applications, where the flux of the x-ray source is limited and samples have low contrast. Sample contrast is enhanced using propagation-based phase contrast. The resolution of the system is verified using 2D resolution charts and using Fourier Ring Correlation on reconstructed CT slices. Evaluating noise and contrast highlights the benefits of photon counting detectors and the contrast improvement through phase contrast. The implemented setup is capable of reaching sub-micron resolution and satisfying contrast in biological samples, like paraffin embedded tissue., Comment: 16 pages, 7 figures, including supplementary information

A central component of the European Spallation Source is the high-power proton accelerator. The accelerator aims in the future to provide 2 GeV protons to a rotating tungsten target for the production of neutrons at 5 MW of average beam power for neutron scattering studies. Extensive shielding surrounds the accelerator, in order to provide sufficient safety for the public and workers against radiation produced along it's length. This largely comprises several meters of soil, called the berm, and concrete structures located around the accelerator tunnel. However, due to the need for access to the accelerator, during maintenance and connections for other utilities, the shielding contains a number of penetrations which leads to weaknesses in localized areas. For these reasons, shielding design of such a facility must take care to address issues related to both the deep-penetration of the radiation through thick shields, while at the same time accounting for the streaming nature of the radiation through ducts and chicanes. In addition, radiation produced from activated components of the accelerator also poses risks for workers and public. For example, activated magnets will need maintenance and workers may need to access areas where activated water circulates. Thus, activation analyses are also needed in combination with the prompt-dose rate estimates for a complete analysis. In this summary, we present the results of a series of such studies carried out on various components around the ESS accelerator., Comment: 14th International Conference on Radiation Shielding and 21st Topical Meeting of the Radiation Protection and Shielding Division (ICRS 14/RPSD 2022) meeting

Peakons (peaked solitons) are particular solutions admitted by certain nonlinear PDEs, most famously the Camassa-Holm shallow water wave equation. These solutions take the form of a train of peak-shaped waves, interacting in a particle-like fashion. In this article we give an overview of the mathematics of peakons, with particular emphasis on the connections to classical problems in analysis, such as Pad\'e approximation, mixed Hermite-Pad\'e approximation, multi-point Pad\'e approximation, continued fractions of Stieltjes type and (bi)orthogonal polynomials. The exposition follows the chronological development of our understanding, exploring the peakon solutions of the Camassa-Holm, Degasperis-Procesi, Novikov, Geng-Xue and modified Camassa-Holm (FORQ) equations. All of these paradigm examples are integrable systems arising from the compatibility condition of a Lax pair, and a recurring theme in the context of peakons is the need to properly interpret these Lax pairs in the sense of Schwartz's theory of distributions. We trace out the path leading from distributional Lax pairs to explicit formulas for peakon solutions via a variety of approximation-theoretic problems, and we illustrate the peakon dynamics with graphics., Comment: 58 pages, 10 figures. Changes in version 2: A couple of remarks added. A few additions and updates to the list of references. More than 100 minor corrections (mostly trivial typos)

The aim of the present paper is to derive explicit formulas for arbitrary peakon solutions of the Geng-Xue equation, a two-component generalization of Novikov's cubically nonlinear Camassa-Holm type equation. By performing limiting procedures on the previosly known formulas for so-called interlacing peakon solutions, where the peakons in the two component occur alternatingly, we turn some of the peakons into zero-amplitude "ghostpeakons", in such a way that the remaining ordinary peakons occur in any desired configuration. We also study the large-time asymptotics of these solutions., Comment: 133 pages, 25 figures. pdfLaTeX + AMS packages + hyperref + TikZ

We derive explicit formulas for the characteristic curves associated with the multipeakon solutions of the Camassa-Holm, Degasperis-Procesi and Novikov equations. Such a curve traces the path of a fluid particle whose instantaneous velocity equals the elevation of the wave at that point (or the square of the elevation, in the Novikov case). The peakons themselves follow characteristic curves, and the remaining characteristic curves can be viewed as paths of 'ghostpeakons' with zero amplitude; hence, they can be obtained as solutions of the ODEs governing the dynamics of multipeakon solutions. The previously known solution formulas for multipeakons only cover the case when all amplitudes are nonzero, since they are based upon inverse spectral methods unable to detect the ghostpeakons. We show how to overcome this problem by taking a suitable limit in terms of spectral data, in order to force a selected peakon amplitude to become zero. Moreover, we use direct integration to compute the characteristic curves for the solution of the Degasperis-Procesi equation where a shockpeakon forms at a peakon-antipeakon collision. In addition to the theoretical interest in knowing the characteristic curves, they are also useful for plotting multipeakon solutions, as we illustrate in several examples.

We consider multipeakon solutions, and to some extent also multishockpeakon solutions, of a coupled two-component integrable PDE found by Geng and Xue as a generalization of Novikov's cubically nonlinear Camassa-Holm type equation. In order to make sense of such solutions, we find it necessary to assume that there are no overlaps, meaning that a peakon or shockpeakon in one component is not allowed to occupy the same position as a peakon or shockpeakon in the other component. Therefore one can distinguish many inequivalent configurations, depending on the order in which the peakons or shockpeakons in the two components appear relative to each other. Here we are in particular interested in the case of interlacing peakon solutions, where the peakons alternatingly occur in one component and in the other. Based on explicit expressions for these solutions in terms of elementary functions, we describe the general features of the dynamics, and in particular the asymptotic large-time behaviour. As far as the positions are concerned, interlacing Geng-Xue peakons display the usual scattering phenomenon where the peakons asymptotically travel with constant velocities, which are all distinct, except that the two fastest peakons will have the same velocity. However, in contrast to many other peakon equations, the amplitudes of the peakons will not in general tend to constant values; instead they grow or decay exponentially. Thus the logarithms of the amplitudes (as functions of time) will asymptotically behave like straight lines, and comparing these lines for large positive and negative times, one observes phase shifts similar to those seen for the positions of the peakons. In addition to these K+K interlacing pure peakon solutions, we also investigate 1+1 shockpeakon solutions, and collisions leading to shock formation in a 2+2 peakon-antipeakon solution., Comment: 59 pages, 6 figures. pdfLaTeX + AMS packages + hyperref + TikZ. Changes in v2: minor typos corrected, reference list updated and enhanced with hyperlinks

Few- and many-fermion systems on the verge of stability, and consisting of strongly interacting particles, appear in many areas of physics. The theoretical modeling of such systems is a very difficult problem. In this work we present a theoretical framework that is based on the rigged Hilbert space formulation. The few-body problem is solved by exact diagonalization using a basis in which bound, resonant, and non-resonant scattering states are included on an equal footing. Current experiments with ultracold atoms offer a fascinating opportunity to study universal properties of few-body systems with a high degree of control over parameters such as the external trap geometry, the number of particles, and even the interaction strength. In particular, particles can be allowed to tunnel out of the trap by applying a magnetic-field gradient that effectively lowers the potential barrier. The result is a tunable open quantum system that allows detailed studies of the tunneling mechanism. In this Contribution we introduce our method and present results for the decay rate of two distinguishable fermions in a one-dimensional trap as a function of the interaction strength. We also study the numerical convergence. Many of these results have been previously published (R. Lundmark, C. Forss\'en, and J. Rotureau, arXiv: 1412.7175). However, in this Contribution we present several technical and numerical details of our approach for the first time., Comment: 8 pages, 4 figures, contribution to the conference proceedings of the 7th International Workshop on the "Dynamics of Critically Stable Quantum Few-Body Systems"

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 ASACUSA CUSP collaboration at the Antiproton Decelerator (AD) of CERN is planning to measure the ground-state hyperfine splitting of antihydrogen using an atomic spectroscopy beamline. We describe here the latest developments on the spectroscopy apparatus developed to be coupled to the antihydrogen production setup (CUSP)., Comment: Proceedings of the 11th International Conference on Low Energy Antiproton Physics (LEAP 2013) held in Uppsala, Sweden, 10 to 15 June, 2013

We solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperis-Procesi equations. Like the spectral problems for those equations, this one is of a 'discrete cubic string' type -- a nonselfadjoint generalization of a classical inhomogeneous string -- but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacher-Krein type implying that the spectrum of the boundary value problem is positive and simple. The inverse spectral problem is solved by a method which generalizes, to a nonselfadjoint case, M. G. Krein's solution of the inverse problem for the Stieltjes string., Comment: 78 pages, 7 figures. pdfLaTeX + AMS packages + hyperref + TikZ

The Canada Day Theorem is an identity involving sums of $k \times k$ minors of an arbitrary $n \times n$ symmetric matrix. It was discovered as a by-product of the work on so-called peakon solutions of an integrable nonlinear partial differential equation proposed by V. Novikov. Here we present another proof of this theorem, which explains the underlying mechanism in terms of the orbits of a certain abelian group action on the set of all $k$-edge matchings of the complete bipartite graph $K_{n,n}$., Comment: 16 pages. pdfLaTeX + AMS packages + TikZ. Fixed a hyperlink problem and a few typos

Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation, admitting peaked soliton (peakon) solutions, which has nonlinear terms that are cubic, rather than quadratic. In this paper, the explicit formulas for multipeakon solutions of Novikov's cubically nonlinear equation are calculated, using the matrix Lax pair found by Hone and Wang. By a transformation of Liouville type, the associated spectral problem is related to a cubic string equation, which is dual to the cubic string that was previously found in the work of Lundmark and Szmigielski on the multipeakons of the Degasperis-Procesi equation., Comment: 41 pages, LaTeX + AMS packages + pstricks