Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

A bear’s biography: hybrid warfare and the more-than-human battlespace

This paper makes an intervention highlighting the animal dimension of military geographies as an overlooked yet illuminating aspect of the hybrid nature of warfare. By bringing animal geographies into dialogue with critical military geographies and with a focus on relational ethics, the processes, performance and consequences of the more-than-human nature of the battlespace are examined through a vignette of Wojtek the bear. Wojtek was a mascot, pet and officially enlisted soldier of the Polish Army in the Second World War who travelled the desert plains, helped to fight at the Battle of Monte Cassino, before being demobbed with his fellow Polish comrades in the UK, eventually ending his civilian days in Edinburgh Zoo. Although a well-known figure Wojtek and his biography have predominately been used as a means to explore the Polish soldiers’ experience of the Second World War with the result that the bear as an animal is absent. This paper, therefore, puts the bear back into his biography in order to acknowledge the role and lived experience of animals in the military. Further, it suggests that exploring the place of animals in the military requires geographers to articulate the hybrid nature of warfare and also to explore the ethico-political relations this produces

Simulation of mixing effects in a VVER1000 reactor

International audienceThis work has been performed in the framework of the OECD-NEA thermalhydraulic benchmark V1000CT-2. This benchmark is related to fluid mixing in the reactor vessel during a MSLB accident scenario in a VVER-1000 reactor. Coolant mixing in a VVER-1000 V320 reactor was investigated in plant experiments during the commissioning of the Unit 6 of the Kozloduy nuclear power plant. Non-uniform and asymmetric loop flow mixing in the reactor vessel has been observed in the event of symmetric main coolant pump operation. For certain flow conditions, the experimental evidence of an azimuthal shift of the main loop flows with respect to the cold leg axes (swirl) was found. Such asymmetric flow distribution was analyzed with the Trio_U code. Trio_U is a CFD code developed by the CEA Grenoble, aimed to supply an efficient computational tool to simulate transient thermalhydraulic turbulent flows encountered in nuclear systems. For the presented study, a LES approach was used. Therefore a very precise tetrahedral mesh with more than 10 million control volumes has been created. The Trio_U calculation has correctly reproduced the measured rotation of the flow when the CAD data of the constructed reactor pressure vessel where used. This is also true for the comparison of cold leg to assembly mixing coefficients. Using the conception data, the calculated swirl was significantly underestimated. Due to this result, it is possible to improve the lower plenum flow mixing matrices which are usually used in system codes

3D LES of free convection from a side-heated vertical wall with cryogenic helium up to Ra ~ 1015^{15}

International audienceThe passive safety concept of Small Modular Reactors (SMR) is based on theextraction of residual heat from the reactor to a surrounding water pool. However, thelarge scale of the reactor vessel (height≈15m) can lead to a rather intensive heatexchange process mostly by natural convection (Ra $\approx 10^{15}$). Reliable heat transfer correlations exist to date only up to Ra $\approx 10^{12}$, with uncertainties in the extrapolation to higher Ra. To improve the understanding of natural convection at high Ra number and find a valid heat transfer correlation, the three-dimensional turbulent natural convection boundary layer along a side-heated vertical wall is simulated through LESwith the CEA in-house code TrioCFD. The simulation has taken into account thelocal variations of the fluid properties. Near wall mesh discretization is enough refined(y+~0.2) to resolve the thin boundary layer. Our preliminary analysis with water as aworking fluid have shown the ability of the computational model in recovering theheat transfer behaviour2 at moderate Rayleigh number (Ra $\approx 10^{12}$). As the second step, cryogenic helium is selected as a working fluid for its special physical properties (low viscosity, high β,…), which allows to reach high Ra $\approx 10^{15}$ in meter-sized experiments.The numerical results concerning the heat transport process show a good agreementwith available reference data. Moreover, the mean temperature and velocity in theboundary layer are also presented. The vortex evolution in the boundary layer isvisualized to enhance the understanding of the turbulence developing phases. Currentwork can shed more light on the understanding of the turbulent natural convectionalong a vertical wall at high Ra numbers. The numerical simulations will becomplemented by a new experiment currently under development atCEA aimed at reaching Ra $\approx 10^{15}$ using cryogenic helium to probe the boundary layer behaviour and statistics with μm-sized micro-fabricated hot & cold wires