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- ItemHybrid soliton dynamics in liquid-core fibres(Berlin : Nature Pulishing, 2017) Chemnitz, Mario; Gebhardt, Martin; Gaida, Christian; Stutzki, Fabian; Kobelke, Jens; Limpert, Jens; Tünnermann, Andreas; Schmidt, Markus A.The discovery of optical solitons being understood as temporally and spectrally stationary optical states has enabled numerous innovations among which, most notably, supercontinuum light sources have become widely used in both fundamental and applied sciences. Here, we report on experimental evidence for dynamics of hybrid solitons—a new type of solitary wave, which emerges as a result of a strong non-instantaneous nonlinear response in CS2-filled liquid-core optical fibres. Octave-spanning supercontinua in the mid-infrared region are observed when pumping the hybrid waveguide with a 460 fs laser (1.95 μm) in the anomalous dispersion regime at nanojoule-level pulse energies. A detailed numerical analysis well correlated with the experiment uncovers clear indicators of emerging hybrid solitons, revealing their impact on the bandwidth, onset energy and noise characteristics of the supercontinua. Our study highlights liquid-core fibres as a promising platform for fundamental optics and applications towards novel coherent and reconfigurable light sources.
- ItemPhase transition observations and discrimination of small cloud particles by light polarization in expansion chamber experiments(München : European Geopyhsical Union, 2016) Nichman, Leonid; Fuchs, Claudia; Järvinen, Emma; Ignatius, Karoliina; Höppel, Niko Florian; Dias, Antonio; Heinritzi, Martin; Simon, Mario; Tröstl, Jasmin; Wagner, Andrea Christine; Wagner, Robert; Williamson, Christina; Yan, Chao; Connolly, Paul James; Dorsey, James Robert; Duplissy, Jonathan; Ehrhart, Sebastian; Frege, Carla; Gordon, Hamish; Hoyle, Christopher Robert; Kristensen, Thomas Bjerring; Steiner, Gerhard; McPherson Donahue, Neil; Flagan, Richard; Gallagher, Martin William; Kirkby, Jasper; Möhler, Ottmar; Saathoff, Harald; Schnaiter, Martin; Stratmann, Frank; Tomé, AntónioCloud microphysical processes involving the ice phase in tropospheric clouds are among the major uncertainties in cloud formation, weather, and general circulation models. The detection of aerosol particles, liquid droplets, and ice crystals, especially in the small cloud particle-size range below 50 μm, remains challenging in mixed phase, often unstable environments. The Cloud Aerosol Spectrometer with Polarization (CASPOL) is an airborne instrument that has the ability to detect such small cloud particles and measure the variability in polarization state of their backscattered light. Here we operate the versatile Cosmics Leaving OUtdoor Droplets (CLOUD) chamber facility at the European Organization for Nuclear Research (CERN) to produce controlled mixed phase and other clouds by adiabatic expansions in an ultraclean environment, and use the CASPOL to discriminate between different aerosols, water, and ice particles. In this paper, optical property measurements of mixed-phase clouds and viscous secondary organic aerosol (SOA) are presented. We report observations of significant liquid–viscous SOA particle polarization transitions under dry conditions using CASPOL. Cluster analysis techniques were subsequently used to classify different types of particles according to their polarization ratios during phase transition. A classification map is presented for water droplets, organic aerosol (e.g., SOA and oxalic acid), crystalline substances such as ammonium sulfate, and volcanic ash. Finally, we discuss the benefits and limitations of this classification approach for atmospherically relevant concentrations and mixtures with respect to the CLOUD 8–9 campaigns and its potential contribution to tropical troposphere layer analysis.
- ItemOn the clustering property of the random intersection graphs(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Yao, Xin; Chen, Jinwen; Zhang, Changshui; Li, YandaA random intersection graph mtlmcalG_V,W,p is induced from a random bipartite graph mtlmcalG^*_V,W,p with vertices classes mtlV, mtlW and the edges incident between mtlv in V and mtlw in W with probability mtlp. Two vertices in mtlV are considered to be connected with each other if both of them connect with some common vertices in mtlW. The clustering properties of the random intersection graph are investigated completely in this article. Suppose that the vertices number be mtlN = mabsV and mtlM=mabsW and mtlM = N^alpha, p=N^-beta, where mtlalpha > 0,, beta > 0, we derive the exact expressions of the clustering coefficient mtlC_v of vertex mtlv in mtlmcalG_V,W,p. The results show that if mtlalpha < 2beta and mtlalpha neq beta, mtlC_v decreases with the increasing of the graph size; if mtlalpha = beta or mtlalpha geq 2beta, the graph has the constant clustering coefficients, in addition, if mtlalpha > 2beta, the graph connecChangshui Zhangts almost completely. Therefore, we illustrate the phase transition for the clustering property in the random intersection graphs and give the condition that mtlriG being high clustering graph.
- ItemShape optimization for a sharp interface model of distortion compensation(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Sturm, Kevin; Hintermüller, Michael; Hömberg, DietmarWe study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.
- ItemLow Mach asymptotic preserving scheme for the Euler-Korteweg model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Giesselmann, JanWe present an all speed scheme for the Euler-Korteweg model.We study a semi-implicit time-discretisation which treats the terms, which are stiff for low Mach numbers, implicitly and thereby avoids a dependence of the timestep restriction on the Mach number. Based on this we present a fully discrete finite difference scheme. In particular, the scheme is asymptotic preserving, i.e., it converges to a stable discretisation of the incompressible limit of the Euler-Korteweg model when the Mach number tends to zero.
- ItemModelling compressible electrolytes with phase transition(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Dreyer, Wolfgang; Giesselmann, Jan; Kraus, ChristianeA novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist. In addition, all constituents may consist of polarizable and magnetizable matter. Our introduced thermodynamically consistent diffuse interface model may be regarded as a generalized model of Allen-Cahn/Navier-Stokes/Poisson type for multi-component flows with phase transitions and electrochemical reactions. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. We consider two scaling regimes, i.e. a non-coupled and a coupled regime, where the coupling takes place between the smallness parameter in the Poisson equation and the width of the interface. We recover in the sharp interface limit a generalized Allen-Cahn/Euler/Poisson system for mixtures with electrochemical reactions in the bulk phases equipped with admissible interfacial conditions. The interfacial conditions satisfy, for instance, a generalized Gibbs-Thomson law and a dynamic Young-Laplace law.
- ItemA quasi-incompressible diffuse interface model with phase transition(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Aki, Gonca; Dreyer, Wolfgang; Giesselmann, Jan; Kraus, ChristineThis work introduces a new thermodynamically consistent diffuse model for two-component flows of incompressible fluids. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. To this end, we consider two scaling regimes where in one case we recover the Euler equations and in the other case the Navier-Stokes equations in the bulk phases equipped with admissible interfacial conditions. For the Navier-Stokes regime, we further assume the densities of the fluids are close to each other in the sense of a small parameter which is related to the interfacial thickness of the diffuse model.
- ItemA compressible mixture model with phase transition(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Dreyer, Wolfgang; Giesselmann, Jan; Kraus, ChristianeWe introduce a new thermodynamically consistent diffuse interface model of AllenCahn/NavierStokes type for multi-component flows with phase transitions and chemical reactions. For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques. We consider two scaling regimes, i.e. a non-dissipative and a dissipative regime, where we recover in the sharp interface limit a generalized Allen-Cahn/Euler system for mixtures with chemical reactions in the bulk phases equipped with admissible interfacial conditions. The interfacial conditions satify, for instance, a YoungLaplace and a Stefan type law.
- ItemOptimal control for a phase field system with a possibly singular potential(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela; Rocca, ElisabettaIn this paper we study a distributed control problem for a phase-field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions.
- ItemSliding modes for a phase-field system(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Barbu, Viorel; Colli, Pierluigi; Gilardi, Gianni; Marinoschi, Gabriela; Rocca, ElisabettaIn the present contribution the sliding mode control (SMC) problem for a phasefield model of Caginalp type is considered. First we prove the well-posedness and some regularity results for the phase-field type state systems modified by the statefeedback control laws. Then, we show that the chosen SMC laws force the system to reach within finite time the sliding manifold (that we chose in order that one of the physical variables or a combination of them remains constant in time). We study three different types of feedback control laws: the first one appears in the internal energy balance and forces a linear combination of the temperature and the phase to reach a given (space dependent) value, while the second and third ones are added in the phase relation and lead the phase onto a prescribed target phi*. While the control law is non-local in space for the first two problems, it is local in the third one, i.e., its value at any point and any time just depends on the value of the state.