TY - GEN A1 - Schmidt, Heiko A1 - Oevermann, Michael A1 - Bastiaans, Rob J.M. A1 - Kerstein, Alan R. T1 - A priori Tabulation of Turbulent Flame Speeds via a Combination of a Stochastic Mixing Model and Flamelet Generated Manifolds N2 - In this paper we propose a technique for a priori turbulent flame speed tabulation (TFST) for a given parameter space in standard combustion-regime diagrams. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. Results are compared to an algebraic model and to direct numerical simulations (DNS). T3 - ZIB-Report - 08-02 KW - Verbrennung KW - Flammenstrukturen KW - stochastisches Turbulenzmodell KW - FGM KW - turbulente Brenngeschwindigkeiten KW - turbulent premixed combustion KW - flame structures KW - linear eddy model KW - flamelet generated manifolds KW - turbulent flame speeds Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10532 SN - 1438-0064 ER - TY - GEN A1 - Carqué, Gunter A1 - Owinoh, Antony Z. A1 - Klein, Rupert A1 - Majda, Andrew J. T1 - Asymptotic Scale Analysis of Precipitating Clouds N2 - Asymptotic analyses of the three dimensional compressible flow equations coupled with transport equations for the mixing ratios of water vapour, cloud water and rain water are described. We obtain reduced systems of equations for two particular regimes of length and time scales: Models for the long time evolution of deep convective columns and for the short time evolution of shallow convective layers. The asymptotic deep convective column model is anelastic, yet the vertical motion is pressure free, i.e., it evolves freely in interaction with buoyancy while the horizontal divergence adjusts to fullfil the anelastic constraint. The perturbation pressure guaranteeing compliance with the horizontal divergence constraint obeys a Poisson-type equation. Surprisingly, the vertical velocity plays an important role in the horizontal dynamics through the Coriolis term. The vertical acceleration in a saturated column is directly determined by the buoyancy induced by potential temperature differences relative to the background stratification. This potential temperature deviation is a conserved quantity. Evaporation is the only important microphysical process in the undersaturated regime. The evaporation rate depends on the saturation deficit and the amount of rain water present and determines the (downward) vertical velocity and the distribution of water vapour. To connect the deep convective column solutions to top and bottom boundary conditions, a different flow regime needs to be accounted for. Within shallow layers whose depth is comparable to the column diameters, adjustment to physical boundary conditions can take place. This is the second regime considered in this report. The shallow convective layer regime is shown to be asymptotically described by Boussinesq-type equations. These equations are closed by evolution equations which show that, in the saturated regime, the distributions of potential temperature and cloud water are determined by a condensation rate that is directly proportional to the vertical velocity. In the undersaturated regime, the potential temperature distribution is determined by the amount of rain present, since the water vapour in this case is shown to be a conserved quantity. In both regimes the distribution of rain water depends on the rain water flux. T3 - ZIB-Report - 08-03 KW - atmospheric moist convection KW - deep convection KW - shallow convection KW - precipitating clouds KW - asymptotic analysis Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10548 SN - 1438-0064 ER - TY - GEN A1 - Oevermann, Michael A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Linear-Eddy Modeling of Autoignition under Thermal Stratification N2 - The influence of thermal stratification on autoignition at constant volume and high pressure is investigated under turbulent conditions using the one-dimensional Linear-Eddy Model (LEM) and detailed hydrogen/air chemistry. Results are presented for the influence of initial temperature inhomogeneities on the heat release rate and the relative importance of diffusion and chemical reactions. The predicted heat release rates are compared with heat release rates of Chen et al. and Hawkes et al. obtained by two-dimensional Direct Numerical Simulations (DNS). Using the definition of Chen et al. for the displacement speed of the H2 mass fraction tracked at the location of maximum heat release, and a comparison of budget terms, different combustion modes including ignition front propagation and deflagration waves are identified and the results are compared to the DNS data. The LEM approach shows qualitatively and quantitatively reasonable agreement with the DNS data over the whole range of investigated temperature fluctuations. The results presented in this work suggest that LEM is a potential candidate as a sub-model for CFD calculations of HCCI engines. T3 - ZIB-Report - 08-05 KW - HCCI KW - Selbstzündung KW - Turbulenz KW - Linear-Eddy Modell KW - HCCI KW - autoignition KW - thermal explosion KW - turbulence KW - Linear-Eddy Model Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10562 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton T1 - An Extended Mathematical Framework for Barrier Methods in Function Space N2 - An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control. T3 - ZIB-Report - 08-07 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10593 SN - 1438-0064 ER - TY - GEN A1 - Ruprecht, Daniel A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Transparent boundary conditons for time-dependent problems N2 - A new approach to derive transparent boundary conditions (TBCs) for wave, Schrödinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior, and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients. T3 - ZIB-Report - 07-12 KW - transparent boundary condition KW - non-reflecting boundary condition KW - pole condition KW - wave equation KW - Schrödinger equation KW - drift diffusion equation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9558 ER - TY - GEN A1 - Kube, Susanna A1 - Lasser, Caroline A1 - Weber, Marcus T1 - Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics N2 - Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy. T3 - ZIB-Report - 07-17 KW - Metropolis Monte Carlo KW - approximation KW - quadrature KW - oscillating functions Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9604 ER - TY - JOUR A1 - Garcia Santiago, Xavier A1 - Hammerschmidt, Martin A1 - Sachs, Johannes A1 - Burger, Sven A1 - Kwon, Hyunah A1 - Knöller, Marvin A1 - Arens, Tilo A1 - Fischer, Peer A1 - Fernandez-Corbaton, Ivan A1 - Rockstuhl, Carsten T1 - Toward maximally electromagnetically chiral scatterers at optical frequencies JF - ACS Photonics Y1 - 2022 U6 - https://doi.org/10.1021/acsphotonics.1c01887 VL - 9 SP - 1954 ER - TY - GEN A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics N2 - Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal. T3 - ZIB-Report - 21-15 KW - linear reaction networks KW - cross-correlation KW - neurotransmission Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82674 SN - 1438-0064 ER - TY - JOUR A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Ray, Sourav A1 - Wulkow, Hanna A1 - Celik, M. Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design JF - Scientific Reports N2 - We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-27699-w VL - 13 IS - 607 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - THES A1 - Pakhomov, Anton T1 - Efficient modeling and optimization of surface second-harmonic generation from nanophotonic components Y1 - 2021 U6 - https://doi.org/10.22032/dbt.49369 ER -