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Thermodynamic models for electrochemical systems
Application oriented research topic of WIAS
Model based investigations of electrochemical double layers, porous catalysts in fuel cells, and battery materials
The behavior of electrochemical systems is widely investigated with continuum physics models. Applications range from single crystal electrochemistry to lithium batteries and fuel cells, from biological nano-pores to electrolysis and corrosion science, and further. The common basis for all application is the theory of non-equilibrium thermo-electrodynamics [1,2]. At the Weierstraß-Institute general models for electrochemical systems are systematically derived. Asymptotic analysis methods are further employed to derived reduced non-equilibrium models for various electrodes and electrolytes, and the corresponding boundary conditions.
Metal/electrolyte interface
A detailed model for a general electrolytic mixture was developed, which may adsorb and react on a metal surface. It is based on coupled volume and surface thermodynamics [3] where we account for adsorption and solvation of the ionic species.
Figure 1: Computed structure and a resulting sketch of the Ag/0.1M NaF interface.
For charged interfaces in equilibrium, this model leads to a coupled Poisson-momentum equation systems [4], which can be used to compute the structure of the double layer (Fig. 1). It is further possible to derive the capacity of the electrode/electrolyte interface (Fig. 2), a property which is precisely measured for many materials. This allows for a rigorous validation of our model, which shows some remarkable agreement to experimental data [3].
Figure 2: Computed capacity of the Ag(110) 0.1M NaF interface.
Electron transfer reactions
Electron transfer reactions at the interface between an electrolyte and an electrode are the pivotal phenomenon of all electrochemical systems for storage and conversion of energy. The Butler-Volmer equation describes the dependence of the reaction rates on a potential difference across the interface and on the concentrations of the different species at the interface. At WIAS, new boundary conditions of generalized Butler-Volmer type were derived based on non-equilibrium thermodynamics [5]. The predictive capabilities of this theory are validated for various, well defined electrochemical cells. and is applied to complex systems like batteries and fuel cells.
Figure 3: Experimental setup copper deposition.
Figure 4: Current-Voltage diagram for the electro-deposition of metal with different electrolyte concentrations. At high imposed currents diffusional transport in the electrolyte causes a lack of reacting ions at the electrode, leading to a blow-up of the potential.
Thermodynamically consistent discretizations
The numerical solution of generalized Poisson-Nernst-Planck systems like the one derived in [5] in higher space dimensions and general geometries requires the development of specifically tailored discretization approaches which have the potential to preserve the thermodynamic properties of the continuous problem. For this purpose, a generalization of the Scharfetter-Gummel upwind finite volume scheme successfully employed in the field of semiconductor device simulation to the case Poisson-Nernst-Planck problems with ion volume constraints and solvent balancing has been proposed [6].
Figure 5: Simulated IV curves for an electrolytic diode. Difference between standard and improved Nernst-Planck models.
Modeling of transport and reaction processes for magnesium-air batteries
As magnesium is highly abundant, comparably cheap and sufficiently reactive, rechargeable magnesium air batteries are an interesting option for large scale energy storage. The development of strategies for the realization of this battery type is the subject of the research network MgLuft which is funded by the German Ministry of Education and Research. The WIAS subproject is concerned with the model based interpretation of flow cell experiments supporting the acquisition of transport data in organic electrolytes and information or reaction kinetics [7] and the modeling of transport and reaction processes in the electrodes of such a cell.
Figure 6: Calculated streamlines of electrolyte flow in an experimental flow cell.
[1] I. Müller, Thermodynamics, Pitman, 1985.
[2] S. de Groot, P. Mazur, Non-Equilibrium Thermodynamics, Dover Publications, 1984.
[3] W. Dreyer, C. Guhlke and M. Landstorfer, Theory and structure of the metal electrolyte/interface incorporating adsorption and solvation effects, Preprint no. 2058, WIAS, Berlin, 2014.
[4] W. Dreyer, C. Guhlke and M. Landstorfer, A mixture theory of electrolytes containing solvation effects, Electrochemistry Communications, 43 (2014), pp. 75-78.
[5] W. Dreyer, C. Guhlke and R. Müller, Modeling of electrochemical double layers in thermodynamic non- equilibrium, Phys. Chem. Chem. Phys., 17 (2015), pp. 27176-27194.
[6] J. Fuhrmann, Comparison and numerical treatment of generalised Nernst-Planck models, Computer Physics Communications, 196 (2015), pp. 166-178.
[7] J. Fuhrmann, A. Linke, C. Merdon, F. Neumann, T. Streckenbach, H. Baltruschat, and M. Khodayari, Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data, Preprint no. 2161, WIAS, Berlin, 2015.
H.-Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci, eds., PDE 2015: Theory and Applications of Partial Differential Equations, 10 of Discrete and Continuous Dynamical Systems -- Series S, American Institute of Mathematical Science, Springfield, 2017, iv+933 pages, (Collection Published).
W. Dreyer, C. Guhlke, M. Landstorfer, R. Müller, New insights on the interfacial tension of electrochemical interfaces and the Lippmann equation, European Journal of Applied Mathematics, 29 (2018), pp. 708--753, DOI 10.1017/S0956792517000341 .
The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Based on the framework of continuum thermo-electrodynamics we provide some crucial new insights to this relation. In a previous work we have derived a general thermodynamic consistent model for electrochemical interfaces, which showed a remarkable agreement to single crystal experimental data. Here we apply the model to a curved liquid metal electrode. If the electrode radius is large compared to the Debye length, we apply asymptotic analysis methods and obtain the Lippmann equation. We give precise definitions of the involved quantities and show that the interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and contributions arising from the adjacent space charge layers. This finding is confirmed by a comparison of our model to experimental data of several mercury-electrolyte interfaces. We obtain qualitative and quantitative agreement in the 2V potential range for various salt concentrations. We also discuss the validity of our asymptotic model when the electrode curvature radius is comparable to the Debye length.
M. Khodayari, P. Reinsberg, A.A. Abd-El-Latif, Ch. Merdon, J. Fuhrmann, H. Baltruschat, Determining solubility and diffusivity by using a flow cell coupled to a mass spectrometer, ChemPhysChem, 17 (2016), pp. 1647--1655.
W. Dreyer, C. Guhlke, M. Landstorfer, Theory and structure of the metal/electrolyte interface incorporating adsorption and solvation effects, Electrochimica Acta, 201 (2016), pp. 187--219.
In this work we present a continuum theory for the metal/electrolyte interface which explicitly takes into account adsorption and partial solvation on the metal surface. It is based on a general theory of coupled thermo-electrodynamics for volumes and surfaces, utilized here in equilibrium and a 1D approximation. We provide explicit free energy models for the volumetric metal and electrolyte phases and derive a surface free energy for the species present on the metal surface. This surface mixture theory explicitly takes into account the very different amount of sites an adsorbate requires, originating from solvation effects on the surface. Additionally we account for electron transfer reactions on the surface and the associated stripping of the solvation shell. Based on our overall surface free energy we thus provide explicit expressions of the surface chemical potentials of all constituents. The equilibrium representations of the coverages and the overall charge are briefly summarized.
Our model is then used to describe two examples: (i) a silver single crystal electrode with (100) face in contact to a (0.01M NaF + 0.01M KPF6) aqueous solution, and (ii) a general metal surface in contact to some electrolytic solution AC for which an electron transfer reaction occurs in the potential range of interest. We reflect the actual modeling procedure for these examples and discuss the respective model parameters. Due to the representations of the coverages in terms of the applied potential we provide an adsorption map and introduce adsorption potentials. Finally we investigate the structure of the space charge layer at the metal/surface/electrolyte interface by means of numerical solutions of the coupled Poisson-momentum equation system for various applied potentials. It turns out that various layers self-consistently form within the overall space charge region, which are compared to historic and recent pictures of the double layer. Based on this we present new interpretations of what is known as inner and outer Helmholtz-planes and finally provide a thermodynamic consistent picture of the metal/electrolyte interface structure.
W. Dreyer, C. Guhlke, R. Müller, A new perspective on the electron transfer: Recovering the Butler--Volmer equation in non-equilibrium thermodynamics, Physical Chemistry Chemical Physics, 18 (2016), pp. 24966--24983, DOI 10.1039/C6CP04142F .
Understanding and correct mathematical description of electron transfer reaction is a central question in electrochemistry. Typically the electron transfer reactions are described by the Butler-Volmer equation which has its origin in kinetic theories. The Butler-Volmer equation relates interfacial reaction rates to bulk quantities like the electrostatic potential and electrolyte concentrations. Since in the classical form, the validity of the Butler-Volmer equation is limited to some simple electrochemical systems, many attempts have been made to generalize the Butler-Volmer equation. Based on non-equilibrium thermodynamics we have recently derived a reduced model for the electrode-electrolyte interface. This reduced model includes surface reactions but does not resolve the charge layer at the interface. Instead it is locally electroneutral and consistently incorporates all features of the double layer into a set of interface conditions. In the context of this reduced model we are able to derive a general Butler-Volmer equation. We discuss the application of the new Butler-Volmer equations to different scenarios like electron transfer reactions at metal electrodes, the intercalation process in lithium-iron-phosphate electrodes and adsorption processes. We illustrate the theory by an example of electroplating.
J. Fuhrmann, A numerical strategy for Nernst--Planck systems with solvation effect, Fuel Cells, 16 (2016), pp. 704--714.
J. Fuhrmann, A. Linke, Ch. Merdon, F. Neumann, T. Streckenbach, H. Baltruschat, M. Khodayari, Inverse modeling of thin layer flow cells for detection of solubility, transport and reaction coefficients from experimental data, Electrochimica Acta, 211 (2016), pp. 1--10.
Thin layer flow cells are used in electrochemical research as experimental devices which allow to perform investigations of electrocatalytic surface reactions under controlled conditions using reasonably small electrolyte volumes. The paper introduces a general approach to simulate the complete cell using accurate numerical simulation of the coupled flow, transport and reaction processes in a flow cell. The approach is based on a mass conservative coupling of a divergence-free finite element method for fluid flow and a stable finite volume method for mass transport. It allows to perform stable and efficient forward simulations that comply with the physical bounds namely mass conservation and maximum principles for the involved species. In this context, several recent approaches to obtain divergence-free velocities from finite element simulations are discussed. In order to perform parameter identification, the forward simulation method is coupled to standard optimization tools. After an assessment of the inverse modeling approach using known realistic data, first results of the identification of solubility and transport data for O2 dissolved in organic electrolytes are presented. A plausibility study for a more complex situation with surface reactions concludes the paper and shows possible extensions of the scope of the presented numerical tools.
W. Dreyer, C. Guhlke, R. Müller, Modeling of electrochemical double layers in thermodynamic non-equilibrium, Physical Chemistry Chemical Physics, 17 (2015), pp. 27176--27194, DOI 10.1039/C5CP03836G .
We consider the contact between an electrolyte and a solid electrode. At first we formulate a thermodynamic consistent model that resolves boundary layers at interfaces. The model includes charge transport, diffusion, chemical reactions, viscosity, elasticity and polarization under isothermal conditions. There is a coupling between these phenomena that particularly involves the local pressure in the electrolyte. Therefore the momentum balance is of major importance for the correct description of the layers.
The width of the boundary layers is typically very small compared to the macroscopic dimensions of the system. In a second step we thus apply the method of asymptotic analysis to derive a simpler reduced model that does not resolve the boundary layers but instead incorporates the electrochemical properties of the layers into a set of new boundary conditions. For a metal-electrolyte interface, we derive a qualitative description of the double layer capacitance without the need to resolve space charge layers.
J. Fuhrmann, Comparison and numerical treatment of generalized Nernst--Planck models, Computer Physics Communications. An International Journal and Program Library for Computational Physics and Physical Chemistry, 196 (2015), pp. 166--178.
In its most widespread, classical formulation, the Nernst-Planck-Poisson system for ion transport in electrolytes fails to take into account finite ion sizes. As a consequence, it predicts unphysically high ion concentrations near electrode surfaces. Historical and recent approaches to an approriate modification of the model are able to fix this problem. Several appropriate formulations are compared in this paper. The resulting equations are reformulated using absolute activities as basic variables describing the species amounts. This reformulation allows to introduce a straightforward generalisation of the Scharfetter-Gummel finite volume discretization scheme for drift-diffusion equations. It is shown that it is thermodynamically consistent in the sense that the solution of the corresponding discretized generalized Poisson-Boltzmann system describing the thermodynamic equilibrium is a stationary state of the discretized time-dependent generalized Nernst-Planck system. Numerical examples demonstrate the improved physical correctness of the generalised models and the feasibility of the numerical approach.
A. Mielke, J. Haskovec, P.A. Markowich, On uniform decay of the entropy for reaction-diffusion systems, Journal of Dynamics and Differential Equations, 27 (2015), pp. 897--928.
In this work we derive entropy decay estimates for a class of nonlinear reaction-diffusion systems modeling reversible chemical reactions under the assumption of detailed balance. In particular, we provide explicit bounds for the exponential decay of the relative logarithmic entropy, being based essentially on the application of the log-Sobolev inequality and a convexification argument only, making it quite robust to model variations. An important feature of our analysis is the interaction of the two different dissipative mechanisms: pure diffusion, forcing the system asymptotically to the homogeneous state, and pure reaction, forcing the solution to the (possibly inhomogeneous) chemical equilibrium. Only the interaction of both mechanisms provides the convergence to the homogeneous equilibrium. Moreover, we introduce two generalizations of the main result: we allow for vanishing diffusion constants in some chemical components, and we consider different entropy functionals. We provide a few examples to highlight the usability of our approach and shortly discuss possible further applications and open questions.
M. Liero, A. Mielke, Gradient structures and geodesic convexity for reaction-diffusion systems, Philosophical Transactions of the Royal Society A : Mathematical, Physical & Engineering Sciences, 371 (2013), pp. 20120346/1--20120346/28.
We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory. We consider systems of reaction-diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sum of a diffusion part of Wasserstein type and a reaction part. We provide methods for establishing geodesic lambda-convexity of the entropy functional by purely differential methods, thus circumventing arguments from mass transportation. Finally, several examples, including a drift-diffusion system, provide a survey on the applicability of the theory.
M. Liero, Passing from bulk to bulk/surface evolution in the Allen--Cahn equation, NoDEA. Nonlinear Differential Equations and Applications, 20 (2013), pp. 919--942.
In this paper we formulate a boundary layer approximation for an Allen-Cahn-type equation involving a small parameter $eps$. Here, $eps$ is related to the thickness of the boundary layer and we are interested in the limit when $eps$ tends to 0 in order to derive nontrivial boundary conditions. The evolution of the system is written as an energy balance formulation of the L^2-gradient flow with the corresponding Allen-Cahn energy functional. By transforming the boundary layer to a fixed domain we show the convergence of the solutions to a solution of a limit system. This is done by using concepts related to Gamma- and Mosco convergence. By considering different scalings in the boundary layer we obtain different boundary conditions.
A. Glitzky, A. Mielke, A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces, ZAMP Zeitschrift fur Angewandte Mathematik und Physik. ZAMP. Journal of Applied Mathematics and Physics. Journal de Mathematiques et de Physique Appliquees, 64 (2013), pp. 29--52.
We derive gradient-flow formulations for systems describing drift-diffusion processes of a finite number of species which undergo mass-action type reversible reactions. Our investigations cover heterostructures, where material parameter may depend in a nonsmooth way on the space variable. The main results concern a gradient flow formulation for electro-reaction-diffusion systems with active interfaces permitting drift-diffusion processes and reactions of species living on the interface and transfer mechanisms allowing bulk species to jump into an interface or to pass through interfaces. The gradient flows are formulated in terms of two functionals: the free energy and the dissipation potential. Both functionals consist of a bulk and an interface integral. The interface integrals determine the interface dynamics as well as the self-consistent coupling to the model in the bulk. The advantage of the gradient structure is that it automatically generates thermodynamically consistent models.
W. Dreyer, C. Guhlke, R. Müller, Overcoming the shortcomings of the Nernst--Planck model, Physical Chemistry Chemical Physics, 15 (2013), pp. 7075--7086, DOI 10.1039/C3CP44390F .
This is a study on electrolytes that takes a thermodynamically consistent coupling between mechanics and diffusion into account. It removes some inherent deficiencies of the popular Nernst-Planck model. A boundary problem for equilibrium processes is used to illustrate the new features of our model.
A. Mielke, Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions, Discrete and Continuous Dynamical Systems -- Series S, 6 (2013), pp. 479--499.
We show that many couplings between parabolic systems for processes in solids can be formulated as a gradient system with respect to the total free energy or the total entropy. This includes Allen-Cahn, Cahn-Hilliard, and reaction-diffusion systems and the heat equation. For this, we write the coupled system as an Onsager system (X,Φ,K) defining the evolution $dot U$= - K(U) DΦ(U). Here Φ is the driving functional, while the Onsager operator K(U) is symmetric and positive semidefinite. If the inverse G=K-1 exists, the triple (X,Φ,G) defines a gradient system. Onsager systems are well suited to model bulk-interface interactions by using the dual dissipation potential Ψ*(U, Ξ)= ½ 〈Ξ K(U) Ξ〉. Then, the two functionals Φ and Ψ* can be written as a sum of a volume integral and a surface integral, respectively. The latter may contain interactions of the driving forces in the interface as well as the traces of the driving forces from the bulk. Thus, capture and escape mechanisms like thermionic emission appear naturally in Onsager systems, namely simply through integration by parts.
M. Liero, Th. Roche, Rigorous derivation of a plate theory in linear elastoplasticity via $Gamma$-convergence, NoDEA. Nonlinear Differential Equations and Applications, 19 (2012), pp. 437--457.
This paper deals with dimension reduction in linearized elastoplasticity in the rate-independent case. The reference configuration of the elastoplastic body is given by a two-dimensional middle surface and a small but positive thickness. We derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations which are coupled via plastic strains. The convergence analysis is based on an abstract Gamma convergence theory for rate-independent evolution formulated in the framework of energetic solutions. This concept is based on an energy-storage functional and a dissipation functional, such that the notion of solution is phrased in terms of a stability condition and an energy balance.
CH. Batallion, F. Bouchon, C. Chainais-Hillairet, J. Fuhrmann, E. Hoarau, R. Touzani, Numerical methods for the simulation of a corrosion model in a nuclear waste deep repository, Journal of Computational Physics, 231 (2012), pp. 6213--6231.
In this paper, we design numerical methods for a PDE system arising in corrosion modelling. This system describes the evolution of a dense oxide layer. It is based on a drift-diffusion system and includes moving boundary equations. The choice of the numerical methods is justified by a stability analysis and by the study of their numerical performance. Finally, numerical experiments with real-life data shows the efficiency of the developed methods.
A. Glitzky, An electronic model for solar cells including active interfaces and energy resolved defect densities, SIAM Journal on Mathematical Analysis, 44 (2012), pp. 3874--3900.
We introduce an electronic model for solar cells taking into account heterostructures with active interfaces and energy resolved volume and interface trap densities. The model consists of continuity equations for electrons and holes with thermionic emission transfer conditions at the interface and of ODEs for the trap densities with energy level and spatial position as parameters, where the right hand sides contain generation-recombination as well as ionization reactions. This system is coupled with a Poisson equation for the electrostatic potential. We show the thermodynamic correctness of the model and prove a priori estimates for the solutions to the evolution system. Moreover, existence and uniqueness of weak solutions of the problem are proven. For this purpose we solve a regularized problem and verify bounds of the corresponding solution not depending on the regularization level.
J. Fuhrmann, H. Zhao, H. Langmach, Y.E. Seidel, Z. Jusys, R.J. Behm, The role of reactive reaction intermediates in two-step heterogeneous electro-catalytic reactions: A model study, Fuel Cells, 11 (2011), pp. 501--510.
Experimental investigations of heterogeneous electrocatalytic reactions have been performed in flow cells which provide an environment with controlled parameters. Measurements of the oxygen reduction reaction in a flow cell with an electrode consisting of an array of Pt nanodisks on a glassy carbon substrate exhibited a decreasing fraction of the intermediate $H_2O_2$ in the overall reaction products with increasing density of the nanodiscs. A similar result is true for the dependence on the catalyst loading in the case of a supported Pt/C catalyst thin-film electrode, where the fraction of the intermediate decreases with increasing catalyst loading. Similar effects have been detected for the methanol oxidation. We present a model of multistep heterogeneous electrocatalytic oxidation and reduction reactions based on an adsorption-reaction-desorption scheme using the Langmuir assumption and macroscopic transport equations. A continuum based model problem in a vertical cross section of a rectangular flow cell is proposed in order to explain basic principles of the experimental situation. It includes three model species A, B, C, which undergo adsorption and desorption at a catalyst surface, as well as adsorbate reactions from A to B to C. These surface reactions are coupled with diffusion and advection in the Hagen Poiseuille flow in the flow chamber of the cell. Both high velocity asymptotic theory and a finite volume numerical are used to obtain approximate solutions to the model. Both approaches show a behaviour similar to the experimentally observed. Working in more general situations, the finite volume scheme was applied to a catalyst layer consisting of a number of small catalytically active areas corresponding to nanodisks. Good qualitative agreement with the experimental findings was established for this case as well.
A. Mielke, A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems, Nonlinearity, 24 (2011), pp. 1329--1346.
In recent years the theory of Wasserstein distances has opened up a new treatment of the diffusion equations as gradient systems, where the entropy takes the role of the driving functional and where the space is equipped with the Wasserstein metric. We show that this structure can be generalized to closed reaction-diffusion systems, where the free energy (or the entropy) is the driving functional and further conserved quantities may exists, like the total number of chemical species. The metric is constructed by using the dual dissipation potential, which is a convex function of the chemical potentials. In particular, it is possible to treat diffusion and reaction terms simultaneously. The same ideas extend to semiconductor equations involving the electron and hole densities, the electrostatic potential, and the temperature.
A. Glitzky, Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems, Mathematische Nachrichten, 284 (2011), pp. 2159--2174.
Our focus are energy estimates for discretized reaction-diffusion systems for a finite number of species. We introduce a discretization scheme (Voronoi finite volume in space and fully implicit in time) which has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For a class of Voronoi finite volume meshes we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the discrete free energy to its equilibrium value with a unified rate of decay for this class of discretizations. The essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly by taking into account sequences of Voronoi finite volume meshes. Essential ingredient in that proof is a discrete Sobolev-Poincaré inequality.
A. Glitzky, J.A. Griepentrog, Discrete Sobolev--Poincaré inequalities for Voronoi finite volume approximations, SIAM Journal on Numerical Analysis, 48 (2010), pp. 372--391.
We prove a discrete Sobolev-Poincare inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev's integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove a discrete Poincare inequality for space dimensions greater or equal to two.
R. Haller-Dintelmann, Ch. Meyer, J. Rehberg, A. Schiela, Hölder continuity and optimal control for nonsmooth elliptic problems, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 60 (2009), pp. 397--428.
The well known De Giorgi result on Hölder continuity for solutions of the Dirichlet problem is re-established for mixed boundary value problems, provided that the underlying domain is a Lipschitz domain and the border between the Dirichlet and the Neumann boundary part satisfies a very general geometric condition. Implications of this result for optimal control theory are presented.
R. Haller-Dintelmann, J. Rehberg, Maximal parabolic regularity for divergence operators including mixed boundary conditions, Journal of Differential Equations, 247 (2009), pp. 1354--1396.
We show that elliptic second order operators $A$ of divergence type fulfill maximal parabolic regularity on distribution spaces, even if the underlying domain is highly non-smooth and $A$ is complemented with mixed boundary conditions. Applications to quasilinear parabolic equations with non-smooth data are presented.
J. Fuhrmann, A. Linke, H. Langmach, H. Baltruschat, Numerical calculation of the limiting current for a cylindrical thin layer flow cell, Electrochimica Acta, 55 (2009), pp. 430--438.
A. Glitzky, K. Gärtner, Energy estimates for continuous and discretized electro-reaction-diffusion systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 70 (2009), pp. 788--805.
We consider electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistic relations.
We investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. Here the essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly.
The same properties are shown for an implicit time discretized version of the problem. Moreover, we provide a space discretized scheme for the electro-reaction-diffusion system which is dissipative (the free energy decays monotonously). On a fixed grid we use for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species.
A. Glitzky, Energy estimates for electro-reaction-diffusion systems with partly fast kinetics, Discrete and Continuous Dynamical Systems, 25 (2009), pp. 159--174.
We start from a basic model for the transport of charged species in heterostructures containing the mechanisms diffusion, drift and reactions in the domain and at its boundary. Considering limit cases of partly fast kinetics we derive reduced models. This reduction can be interpreted as some kind of projection scheme for the weak formulation of the basic electro--reaction--diffusion system. We verify assertions concerning invariants and steady states and prove the monotone and exponential decay of the free energy along solutions to the reduced problem and to its fully implicit discrete-time version by means of the results of the basic problem. Moreover we make a comparison of prolongated quantities with the solutions to the basic model.
R. Haller-Dintelmann, H.-Chr. Kaiser, J. Rehberg, Elliptic model problems including mixed boundary conditions and material heterogeneities, Journal de Mathématiques Pures et Appliquées, 89 (2008), pp. 25--48.
M. Hieber, J. Rehberg, Quasilinear parabolic systems with mixed boundary conditions on nonsmooth domains, SIAM Journal on Mathematical Analysis, 40 (2008), pp. 292--305.
In this paper we investigate quasilinear systems of reaction-diffusion equations with mixed Dirichlet-Neumann bondary conditions on non smooth domains. Using techniques from maximal regularity and heat-kernel estimates we prove existence of a unique solution to systems of this type.
J. Fuhrmann, H. Zhao, E. Holzbecher, H. Langmach, Flow, transport, and reactions in a thin layer flow cell, Journal of Fuel Cell Science and Technology, 5 (2008), pp. 021008/1--021008/10.
A. Glitzky, Exponential decay of the free energy for discretized electro-reaction-diffusion systems, Nonlinearity, 21 (2008), pp. 1989--2009.
Our focus are electro-reaction-diffusion systems consisting of continuity equations for a finite number of species coupled with a Poisson equation. We take into account heterostructures, anisotropic materials and rather general statistical relations. We introduce a discretization scheme (in space and fully implicit in time) using a fixed grid but for each species different Voronoi boxes which are defined with respect to the anisotropy matrix occurring in the flux term of this species. This scheme has the special property that it preserves the main features of the continuous systems, namely positivity, dissipativity and flux conservation. For the discretized electro-reaction-diffusion system we investigate thermodynamic equilibria and prove for solutions to the evolution system the monotone and exponential decay of the free energy to its equilibrium value. The essential idea is an estimate of the free energy by the dissipation rate which is proved indirectly.
J.A. Griepentrog, Maximal regularity for nonsmooth parabolic problems in Sobolev--Morrey spaces, Advances in Differential Equations, 12 (2007), pp. 1031--1078.
This text is devoted to maximal regularity results for second order parabolic systems on LIPSCHITZ domains of space dimension greater or equal than three with diagonal principal part, nonsmooth coefficients, and nonhomogeneous mixed boundary conditions. We show that the corresponding class of initial boundary value problems generates isomorphisms between two scales of SOBOLEV-MORREY spaces for solutions and right hand sides introduced in the first part of our presentation. The solutions depend smoothly on the data of the problem. Moreover, they are HOELDER continuous in time and space up to the boundary for a certain range of MORREY exponents. Due to the complete continuity of embedding and trace maps these results remain true for a broad class of unbounded lower order coefficients.
J.A. Griepentrog, Sobolev--Morrey spaces associated with evolution equations, Advances in Differential Equations, 12 (2007), pp. 781--840.
In this text we introduce new classes of SOBOLEV-MORREY spaces being adequate for the regularity theory of second order parabolic boundary value problems on LIPSCHITZ domains of space dimension greater or equal than three with nonsmooth coefficients and mixed boundary conditions. We prove embedding and trace theorems as well as invariance properties of these spaces with respect to localization, LIPSCHITZ transformation, and reflection. In the second part of our presentation we show that the class of second order parabolic systems with diagonal principal part generates isomorphisms between the above mentioned SOBOLEV-MORREY spaces of solutions and right hand sides.
O. Minet, H. Gajewski, J.A. Griepentrog, J. Beuthan, The analysis of laser light scattering during rheumatoid arthritis by image segmentation, Laser Physics Letters, 4 (2007), pp. 604--610.
J. Elschner, H.-Chr. Kaiser, J. Rehberg, G. Schmidt, $W^1,q$ regularity results for elliptic transmission problems on heterogeneous polyhedra, Mathematical Models & Methods in Applied Sciences, 17 (2007), pp. 593--615.
J. Elschner, J. Rehberg, G. Schmidt, Optimal regularity for elliptic transmission problems including $C^1$ interfaces, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 9 (2007), pp. 233--252.
We prove an optimal regularity result for elliptic operators $-nabla cdot mu nabla:W^1,q_0 rightarrow W^-1,q$ for a $q>3$ in the case when the coefficient function $mu$ has a jump across a $C^1$ interface and is continuous elsewhere. A counterexample shows that the $C^1$ condition cannot be relaxed in general. Finally, we draw some conclusions for corresponding parabolic operators.
A. Glitzky, R. Hünlich, Resolvent estimates in $W^-1,p$ related to strongly coupled linear parabolic systems with coupled nonsmooth capacities, Mathematical Methods in the Applied Sciences, 30 (2007), pp. 2215--2232.
We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in $W^-1,p$ spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain $L^p$ estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result.
H. Gajewski, J.A. Griepentrog, A descent method for the free energy of multicomponent systems, Discrete and Continuous Dynamical Systems, 15 (2006), pp. 505--528.
H.-Chr. Kaiser, H. Neidhardt, J. Rehberg, Classical solutions of quasilinear parabolic systems on two dimensional domains, NoDEA. Nonlinear Differential Equations and Applications, 13 (2006), pp. 287-310.
M. Baro, H. Neidhardt, J. Rehberg, Current coupling of drift-diffusion models and dissipative Schrödinger--Poisson systems: Dissipative hybrid models, SIAM Journal on Mathematical Analysis, 37 (2005), pp. 941--981.
A. Glitzky, R. Hünlich, Global existence result for pair diffusion models, SIAM Journal on Mathematical Analysis, 36 (2005), pp. 1200--1225.
A. Glitzky, R. Hünlich, Stationary energy models for semiconductor devices with incompletely ionized impurities, ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik, 85 (2005), pp. 778--792.
J. Rehberg, Quasilinear parabolic equations in $L^p$, Progress in Nonlinear Differential Equations and their Applications, 64 (2005), pp. 413-419.
V. Maz'ya, J. Elschner, J. Rehberg, G. Schmidt, Solutions for quasilinear nonsmooth evolution systems in $L^p$, Archive for Rational Mechanics and Analysis, 171 (2004), pp. 219--262.
H. Gajewski, I.V. Skrypnik, On unique solvability of nonlocal drift-diffusion-type problems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 56 (2004), pp. 803--830.
H. Gajewski, I.V. Skrypnik, To the uniqueness problem for nonlinear parabolic equations, Discrete and Continuous Dynamical Systems, 10 (2004), pp. 315--336.
A. Glitzky, W. Merz, Single dopant diffusion in semiconductor technology, Mathematical Methods in the Applied Sciences, 27 (2004), pp. 133--154.
A. Glitzky, R. Hünlich, Stationary solutions of two-dimensional heterogeneous energy models with multiple species, Banach Center Publications, 66 (2004), pp. 135-151.
A. Glitzky, Electro-reaction-diffusion systems with nonlocal constraints, Mathematische Nachrichten, 277 (2004), pp. 14--46.
H. Gajewski, K. Zacharias, On a nonlocal phase separation model, Journal of Mathematical Analysis and Applications, 286 (2003), pp. 11--31.
G. Albinus, H. Gajewski, R. Hünlich, Thermodynamic design of energy models of semiconductor devices, Nonlinearity, 15 (2002), pp. 367--383.
H. Gajewski, On a nonlocal model of non-isothermal phase separation, Advances in Mathematical Sciences and Applications, 12 (2002), pp. 569--586.
J.A. Griepentrog, K. Gröger, H.-Chr. Kaiser, J. Rehberg, Interpolation for function spaces related to mixed boundary value problems, Mathematische Nachrichten, 241 (2002), pp. 110--120.
J.A. Griepentrog, Linear elliptic boundary value problems with non-smooth data: Campanato spaces of functionals, Mathematische Nachrichten, 243 (2002), pp. 19--42.
A. Glitzky, R. Hünlich, Global properties of pair diffusion models, Advances in Mathematical Sciences and Applications, 11 (2001), pp. 293--321.
J.A. Griepentrog, H.-Chr. Kaiser, J. Rehberg, Heat kernel and resolvent properties for second order elliptic differential operators with general boundary conditions on $Lsp p$, Advances in Mathematical Sciences and Applications, 11 (2001), pp. 87--112.
W. Merz, A. Glitzky, R. Hünlich, K. Pulverer, Strong solutions for pair diffusion models in homogeneous semiconductors, Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, 2 (2001), pp. 541-567.
J.A. Griepentrog, L. Recke, Linear elliptic boundary value problems with non-smooth data: Normal solvability on Sobolev-Campanato spaces, Mathematische Nachrichten, 225 (2001), pp. 39--74.
A. Glitzky, R. Hünlich, Electro-reaction-diffusion systems including cluster reactions of higher order, Mathematische Nachrichten, 216 (2000), pp. 95--118.
A. Fiebach, A. Glitzky, Uniform estimate of the relative free energy by the dissipation rate for finite volume discretized reaction-diffusion systems, in: Finite Volumes for Complex Applications VII -- Methods and Theoretical Aspects -- FVCA 7, Berlin, June 2014, J. Fuhrmann, M. Ohlberger, Ch. Rohde, eds., 77 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2014, pp. 275--283.
We prove a uniform Poincare-like estimate of the relative free energy by the dissipation rate for implicit Euler, finite volume discretized reaction-diffusion systems. This result is proven indirectly and ensures the exponential decay of the relative free energy with a unified decay rate for admissible finite volume meshes.
A. Glitzky, A. Mielke, L. Recke, M. Wolfrum, S. Yanchuk, D2 -- Mathematics for optoelectronic devices, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 243--256.
J. Fuhrmann, A. Linke, Ch. Merdon, Coupling of fluid flow and solute transport using a divergence-free reconstruction of the Crouzeix--Raviart element, in: Finite Volumes for Complex Applications VII -- Elliptic, Parabolic and Hyperbolic Problems -- FVCA 7, Berlin, June 2014, J. Fuhrmann, M. Ohlberger, Ch. Rohde, eds., 78 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2014, pp. 587--595.
J. Fuhrmann, K. Gärtner, Modeling of two-phase flow and catalytic reaction kinetics for DMFCs, in: Device and Materials Modeling in PEM Fuel Cells, S. Paddison, K. Promislow, eds., 113 of Topics in Applied Physics, Springer, Berlin/Heidelberg, 2009, pp. 297--316.
H. Gajewski, J.A. Griepentrog, A. Mielke, J. Beuthan, U. Zabarylo, O. Minet, Image segmentation for the investigation of scattered-light images when laser-optically diagnosing rheumatoid arthritis, in: Mathematics -- Key Technology for the Future, W. Jäger, H.-J. Krebs, eds., Springer, Heidelberg, 2008, pp. 149--161.
M. Ehrhardt, J. Fuhrmann, A. Linke, E. Holzbecher, Mathematical modeling of channel-porous layer interfaces in PEM fuel cells, in: Proceedings of FDFC2008 --- Fundamentals and Developments of Fuel Cell Conference 2008, Nancy, France, December 10--12 (CD), 2008, pp. 8 pages.
In proton exchange membrane (PEM) fuel cells, the transport of the fuel to the active zones, and the removal of the reaction products are realized using a combination of channels and porous diffusion layers. In order to improve existing mathematical and numerical models of PEM fuel cells, a deeper understanding of the coupling of the flow processes in the channels and diffusion layers is necessary.
After discussing different mathematical models for PEM fuel cells, the work will focus on the description of the coupling of the free flow in the channel region with the filtration velocity in the porous diffusion layer as well as interface conditions between them.
The difficulty in finding effective coupling conditions at the interface between the channel flow and the membrane lies in the fact that often the orders of the corresponding differential operators are different, e.g., when using stationary (Navier-)Stokes and Darcy's equation. Alternatively, using the Brinkman model for the porous media this difficulty does not occur.
We will review different interface conditions, including the well-known Beavers-Joseph-Saffman boundary condition and its recent improvement by Le Bars and Worster.
U. Bandelow, H. Gajewski, R. Hünlich, Thermodynamic designed energy model, in: Proceedings of the IEEE/LEOS 3rd International Conference on Numerical Simulation of Semiconductor Optoelectronic Devices (NUSOD'03), J. Piprek, ed., 2003, pp. 35--37.
H. Gajewski, H.-Chr. Kaiser, H. Langmach, R. Nürnberg, R.H. Richter, Mathematical modelling and numerical simulation of semiconductor detectors, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 355--364.
I.V. Skrypnik, H. Gajewski, On the uniqueness of solutions to nonlinear elliptic and parabolic problems (in Russian), in: Differ. Uravn. i Din. Sist., dedicated to the 80th anniversary of the Academician Evgenii Frolovich Mishchenko, Suzdal, 2000, 236 of Tr. Mat. Inst. Steklova, Moscow, Russia, 2002, pp. 318--327.
U. Bandelow, H. Gajewski, H.-Chr. Kaiser, Modeling combined effects of carrier injection, photon dynamics and heating in Strained Multi-Quantum-Well Laser, in: Physics and Simulation of Optoelectronic Devices VIII, R.H. Binder, P. Blood, M. Osinski, eds., 3944 of Proceedings of SPIE, SPIE, Bellingham, WA, 2000, pp. 301--310.
G. Schwarz, E. Schöll, R. Nürnberg, H. Gajewski, Simulation of current filamentation in an extended drift-diffusion model, in: EQUADIFF 99: International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels, eds., 2, World Scientific, Singapore [u. a.], 2000, pp. 1334--1336.
H. Gajewski, K. Zacharias, On a reaction-diffusion system modelling chemotaxis, in: EQUADIFF 99: International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels, eds., 2, World Scientific, Singapore [u. a.], 2000, pp. 1098--1103.
H.-Chr. Kaiser, J. Rehberg, About some mathematical questions concerning the embedding of Schrödinger-Poisson systems into the drift-diffusion model of semiconductor devices, in: EQUADIFF 99: International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels, eds., 2, World Scientific, Singapore [u. a.], 2000, pp. 1328--1333.
L. Donati, M. Heida, M. Weber, B. Keller, Estimation of the infinitesimal generator by square-root approximation, Preprint no. 2416, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2416 .
For the analysis of molecular processes, the estimation of time-scales, i.e., transition rates, is very important. Estimating the transition rates between molecular conformations is -- from a mathematical point of view -- an invariant subspace projection problem. A certain infinitesimal generator acting on function space is projected to a low-dimensional rate matrix. This projection can be performed in two steps. First, the infinitesimal generator is discretized, then the invariant subspace is approximated and used for the subspace projection. In our approach, the discretization will be based on a Voronoi tessellation of the conformational space. We will show that the discretized infinitesimal generator can simply be approximated by the geometric average of the Boltzmann weights of the Voronoi cells. Thus, there is a direct correlation between the potential energy surface of molecular structures and the transition rates of conformational changes. We present results for a 2d-diffusion process and Alanine dipeptide.
W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part III: Compactness and convergence, Preprint no. 2397, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2397 .
We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper, which continues the investigations of [DDGG17a, DDGG17b], we prove the compactness of the solution vector, and existence and convergence for the approximation schemes. We point at simple structural PDE arguments as an adequate substitute to the Aubin--Lions compactness Lemma and its generalisations: These familiar techniques attain their limit in the context of our model in which the relationship between time derivatives (transport) and diffusion gradients is highly non linear.
W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part II: Approximation and a priori estimates, Preprint no. 2396, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2396 .
We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper, which continues the investigation of [DDGG17a], we derive for thermodynamically consistent approximation schemes the natural uniform estimates associated with the dissipations. Our results essentially improve our former study [DDGG16], in particular the a priori estimates concerning the relative chemical potentials.
W. Dreyer, P.-É. Druet, P. Gajewski, C. Guhlke, Analysis of improved Nernst--Planck--Poisson models of compressible isothermal electrolytes. Part I: Derivation of the model and survey of the results, Preprint no. 2395, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2395 .
We consider an improved Nernst--Planck--Poisson model first proposed by Dreyer et al. in 2013 for compressible isothermal electrolytes in non equilibrium. The model takes into account the elastic deformation of the medium that induces an inherent coupling of mass and momentum transport. The model consists of convection--diffusion--reaction equations for the constituents of the mixture, of the Navier-Stokes equation for the barycentric velocity, and of the Poisson equation for the electrical potential. Due to the principle of mass conservation, cross--diffusion phenomena must occur and the mobility matrix (Onsager matrix) has a kernel. In this paper we establish the existence of a global--in--time weak solution for the full model, allowing for a general structure of the mobility tensor and for chemical reactions with highly non linear rates in the bulk and on the active boundary. We characterise the singular states of the system, showing that the chemical species can vanish only globally in space, and that this phenomenon must be concentrated in a compact set of measure zero in time. With respect to our former study [DDGG16], we also essentially improve the a priori estimates, in particular concerning the relative chemical potentials.
W. Dreyer, J. Fuhrmann, P. Gajewski, C. Guhlke, M. Landstorfer, M. Maurelli, R. Müller, Stochastic model for LiFePO4-electrodes, ModVal14 -- 14th Symposium on Fuel Cell and Battery Modeling and Experimental Validation, Karlsruhe, March 2 - 3, 2017.
CH. Merdon, A novel concept for the discretisation of the coupled Nernst--Planck--Poisson--Navier--Stokes system, 14th Symposium on Fuel Cell Modelling and Experimental Validation (MODVAL 14), March 2 - 3, 2017, Karlsruher Institut für Technologie, Institut für Angewandte Materialien, Karlsruhe, Germany, March 3, 2017.
P.-É. Druet, Analysis of recent Nernst--Planck--Poisson--Navier--Stokes systems of electrolytes, 88th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2017), Section S14 ``Applied Analysis'', March 6 - 10, 2017, Bauhaus Universität Weimar/Technische Universität Ilmenau, Weimar, March 7, 2017.
P.-É. Druet, Existence of weak solutions for improved Nernst--Planck--Poisson models of compressible electrolytes, Seminar EDE, Czech Academy of Sciences, Institute of Mathematics, Department of Evolution Differential Equations (EDE), Prague, Czech Republic, January 10, 2017.
CH. Merdon, J. Fuhrmann, A. Linke, A.A. Abd-El-Latif, M. Khodayari, P. Reinsberg, H. Baltruschat, Inverse modelling of thin layer flow cells and RRDEs, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.
R. Müller, W. Dreyer, J. Fuhrmann, C. Guhlke, New insights into Butler--Volmer kinetics from thermodynamic modeling, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.
P.-É. Druet, Existence of global weak solutions for generalized Poisson--Nernst--Planck systems, 7th European Congress of Mathematics (ECM), minisymposium ``Analysis of Thermodynamically Consistent Models of Electrolytes in the Context of Battery Research'', July 18 - 22, 2016, Technische Universität Berlin, Berlin, July 20, 2016.
J. Fuhrmann, Ch. Merdon, A thermodynamically consistent numerical approach to Nernst--Planck--Poisson systems with volume constraints, The 67th Annual Meeting of the International Society of Electrochemistry, Den Haag, Netherlands, August 21 - 26, 2016.
J. Fuhrmann, W. Dreyer, C. Guhlke, M. Landstorfer, R. Müller, A. Linke, Ch. Merdon, Modeling and numerics for electrochemical systems, Micro Battery and Capacitive Energy Harvesting Materials -- Results of the MatFlexEnd Project, Universität Wien, Austria, September 19, 2016.
J. Fuhrmann, A. Linke, Ch. Merdon, M. Khodayari , H. Baltruschat, Detection of solubility, transport and reaction coefficients from experimental data by inverse modelling of thin layer flow cells, 1st Leibniz MMS Mini Workshop on CFD & GFD, WIAS Berlin, September 8 - 9, 2016.
J. Fuhrmann, A. Linke, Ch. Merdon, W. Dreyer, C. Guhle, M. Landstorfer, R. Müller, Numerical methods for electrochemical systems, 2nd Graz Battery Days, Graz, Austria, September 27 - 28, 2016.
C. Guhlke, J. Fuhrmann, W. Dreyer, R. Müller, M. Landstorfer, Modeling of batteries, Batterieforum Deutschland 2016, Berlin, April 6 - 8, 2016.
CH. Merdon, Inverse modeling of thin layer flow cells for detection of solubility transport and reaction coefficients from experimental data, 17th Topical Meeting of the International Society of Electrochemistry Multiscale Analysis of Electrochemical Systems, May 31 - June 3, 2015, Saint Malo Congress Center, France, June 1, 2015.
A. Mielke, Chemical Master Equation: Coarse graining via gradient structures, Kolloquium des SFB 1114 ``Scaling Cascades in Complex Systems'', Freie Universität Berlin, Fachbereich Mathematik, Berlin, June 4, 2015.
A. Mielke, Evolutionary $Gamma$-convergence for generalized gradient systems, Workshop ``Gradient Flows'', June 22 - 23, 2015, Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, Paris, France, June 22, 2015.
M. Liero, On dissipation distances for reaction-diffusion equations --- The Hellinger--Kantorovich distance, Workshop ``Entropy Methods, PDEs, Functional Inequalities, and Applications'', June 30 - July 4, 2014, Banff International Research Station for Mathematical Innovation and Discovery (BIRS), Canada, July 1, 2014.
M. Liero, On dissipation distances for reaction-diffusion equations --- The Hellinger--Kantorovich distance, RIPE60 -- Rate Independent Processes and Evolution Workshop, June 24 - 26, 2014, Prague, Czech Republic, June 24, 2014.
A. Linke, Ch. Merdon, Optimal and pressure-independent $L^2$ velocity error estimates for a modified Crouzeix--Raviart element with BDM reconstructions, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin-Brandenburgische Akademie der Wissenschaften, June 15 - 20, 2014.
A. Fiebach, A. Glitzky, Uniform estimate of the relative free energy by the dissipation rate for finite volume discretized reaction-diffusion systems, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin, June 15 - 20, 2014.
A. Glitzky, Drift-diffusion models for heterostructures in photovoltaics, 8th European Conference on Elliptic and Parabolic Problems, Minisymposium ``Qualitative Properties of Nonlinear Elliptic and Parabolic Equations'', May 26 - 30, 2014, Universität Zürich, Institut für Mathematik, organized in Gaeta, Italy, May 27, 2014.
M. Thomas, Thermomechanical modeling of dissipative processes in elastic media via energy and entropy, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 8: Emergence and Dynamics of Patterns in Nonlinear Partial Differential Equations from Mathematical Science, July 7 - 11, 2014, Madrid, Spain, July 8, 2014.
J. Fuhrmann, A. Linke, Ch. Merdon, M. Khodayari, H. Baltruschat, Detection of solubility, transport and reaction coefficients from experimental data by inverse modeling of thin layer flow cells, 65th Annual Meeting of the International Society of Electrochemistry, Lausanne, Switzerland, August 31 - September 5, 2014.
J. Fuhrmann, A. Linke, Ch. Merdon, Coupling of fluid flow and solute transport using a divergence-free reconstruction of the Crouzeix--Raviart element, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin-Brandenburgische Akademie der Wissenschaften, June 15 - 20, 2014.
J. Fuhrmann, Activity based finite volume methods for generalised Nernst--Planck--Poisson systems, The International Symposium of Finite Volumes for Complex Applications VII (FVCA 7), Berlin-Brandenburgische Akademie der Wissenschaften, June 15 - 20, 2014.
A. Mielke, On a metric and geometric approach to reaction-diffusion systems as gradient systems, Mathematics Colloquium, Jacobs University Bremen, School of Engineering and Science, December 1, 2014.
A. Mielke, A reaction-diffusion equation as a Hellinger--Kantorovich gradient flow, ERC Workshop on Optimal Transportation and Applications, October 27 - 31, 2014, Centro di Ricerca Matematica ``Ennio De Giorgi'', Pisa, Italy, October 29, 2014.
J. Rehberg, On non-smooth parabolic equations, Workshop ``Maxwell--Stefan meets Navier--Stokes/Modeling and Analysis of Reactive Multi-Component Flows'', March 31 - April 2, 2014, Universität Halle, April 1, 2014.
J. Rehberg, Optimal Sobolev regularity for second order divergence operators, 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2014), Session on Applied Operator Theory, March 10 - 14, 2014, Friedrich-Alexander Universität Erlangen-Nürnberg, March 13, 2014.
S. Reichelt, Homogenization of degenerated reaction-diffusion equations, Doktorandenforum der Leibniz-Gemeinschaft, Sektion D, Berlin, June 6 - 7, 2013.
M. Liero, On gradient structures for drift-reaction-diffusion systems and Markov chains, Analysis Seminar, University of Bath, Mathematical Sciences, UK, November 21, 2013.
M. Liero, Gradient structures and geodesic convexity for reaction-diffusion system, SIAM Conference on Mathematical Aspects of Materials Science (MS13), Minisymposium ``Material Modelling and Gradient Flows'' (MS100), June 9 - 12, 2013, Philadelphia, USA, June 12, 2013.
M. Liero, On gradient structures and geodesic convexity for reaction-diffusion systems, Research Seminar, Westfälische Wilhelms-Universität Münster, Institut für Numerische und Angewandte Mathematik, April 17, 2013.
A. Glitzky, Continuous and finite volume discretized reaction-diffusion systems in heterostructures, Asymptotic Behaviour of Systems of PDE Arising in Physics and Biology: Theoretical and Numerical Points of View, November 6 - 8, 2013, Lille 1 University -- Science and Technology, France, November 6, 2013.
A. Mielke, Gradient structures and uniform global decay for reaction-diffusion systems, Mathematisches Kolloquium, Universität Bielefeld, Fakultät für Mathematik, April 25, 2013.
A. Mielke, On the geometry of reaction-diffusion systems: Optimal transport versus reaction, Recent Trends in Differential Equations: Analysis and Discretisation Methods, November 7 - 9, 2013, Technische Universität Berlin, Institut für Mathematik, November 9, 2013.
A. Mielke, Using gradient structures for modeling semiconductors, Eindhoven University of Technology, Institute for Complex Molecular Systems, Netherlands, February 21, 2013.
M. Liero, Interfaces in reaction-diffusion systems, Seminar ``Dünne Schichten'', Technische Universität Berlin, Institut für Mathematik, February 9, 2012.
A. Glitzky, An electronic model for solar cells taking into account active interfaces, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24 - 28, 2012, WIAS Berlin, September 27, 2012.
M. Thomas, Thermomechanical modeling via energy and entropy, Seminar on Applied Mathematics, University of Pavia, Department of Mathematics, Italy, February 14, 2012.
M. Thomas, Thermomechanical modeling via energy and entropy using GENERIC, Workshop ``Mechanics of Materials'', March 19 - 23, 2012, Mathematisches Forschungsinstitut Oberwolfach, March 22, 2012.
A. Mielke, Entropy gradient flows for Markow chains and reaction-diffusion systems, Berlin-Leipzig-Seminar ``Analysis/Probability Theory'', WIAS Berlin, April 13, 2012.
A. Mielke, Gradienten-Strukturen und geodätische Konvexität für Markov-Ketten und Reaktions-Diffusions-Systeme, Augsburger Kolloquium, Universität Augsburg, Institut für Mathematik, May 8, 2012.
A. Mielke, Multidimensional modeling and simulation of optoelectronic devices, Challenge Workshop ``Modeling, Simulation and Optimisation Tools'', September 24 - 26, 2012, Technische Universität Berlin, September 24, 2012.
A. Mielke, On geodesic convexity for reaction-diffusion systems, Seminar on Applied Mathematics, Università di Pavia, Dipartimento di Matematica, Italy, March 6, 2012.
A. Mielke, On gradient flows and reaction-diffusion systems, Institutskolloquium, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, December 3, 2012.
A. Mielke, On gradient structures and geodesic convexity for energy-reaction-diffusion systems and Markov chains, ERC Workshop on Optimal Transportation and Applications, November 5 - 9, 2012, Centro di Ricerca Matematica ``Ennio De Giorgi'', Pisa, Italy, November 8, 2012.
A. Mielke, On gradient structures for Markov chains and reaction-diffusion systems, Applied & Computational Analysis (ACA) Seminar, University of Cambridge, Department of Applied Mathematics and Theoretical Physics (DAMTP), UK, June 14, 2012.
A. Mielke, Using gradient structures for modeling semiconductors, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24 - 28, 2012, WIAS Berlin, September 24, 2012.
A. Mielke, Thermodynamical modeling of bulk-interface interaction in reaction-diffusion systems, Interfaces and Discontinuities in Solids, Liquids and Crystals (INDI2011), June 20 - 23, 2011, Gargnano (Brescia), Italy, June 20, 2011.
A. Mielke, Mathematical approaches to thermodynamic modeling, Autumn School on Mathematical Principles for and Advances in Continuum Mechanics, November 7 - 12, 2011, Centro di Ricerca Matematica ``Ennio De Giorgi'', Pisa, Italy.
A. Glitzky, Uniform exponential decay of the free energy for Voronoi finite volume discretized reaction-diffusion systems, 8th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Special Session on Reaction Diffusion Systems, May 25 - 28, 2010, Technische Universität Dresden, May 26, 2010.
A. Mielke, Gradient structures for reaction-diffusion systems and semiconductor equations, 81th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2010), Session on Applied Analysis, March 22 - 26, 2010, Universität Karlsruhe, March 24, 2010.
A. Linke, Divergence-free mixed finite elements for the incompressible Navier--Stokes equations, Universität Stuttgart, Institut für Wasserbau, December 8, 2009.
M. Ehrhardt, J. Fuhrmann, A. Linke, Finite volume methods for the simulation of flow cell experiments, Workshop ``New Trends in Model Coupling --- Theory, Numerics & Applications'' (NTMC'09), Paris, France, September 2 - 4, 2009.
M. Ehrhardt, The fluid-porous interface problem: Analytic and numerical solutions to flow cell problems, 6th Symposium on Fuel Cell Modelling and Experimental Validation (MODVAL 6), March 25 - 26, 2009, Evangelische Akademie Baden, Bad Herrenalb, March 26, 2009.
M. Ehrhardt, The fluid-porous interface problem: Analytic and numerical solutions to flow cell problems, Mathematical Models in Medicine, Business, Engineering (XI JORNADAS IMM), September 8 - 11, 2009, Technical University of Valencia, Institute of Multidisciplinary Mathematics, Spain, September 10, 2009.
J. Fuhrmann, Mathematical and numerical models of electrochemical processes related to porous media, International Conference on Non-linearities and Upscaling in Porous Media (NUPUS), October 5 - 7, 2009, Universität Stuttgart, October 6, 2009.
J. Fuhrmann, Model based numerical impedance calculation in electrochemical systems, 6th Symposium on Fuel Cell Modelling and Experimental Validation (MODVAL 6), March 25 - 26, 2009, Evangelische Akademie Baden, Bad Herrenalb, March 25, 2009.
J. Fuhrmann, Numerical modeling in electrochemistry, Conference on Scientific Computing (ALGORITMY 2009), March 15 - 20, 2009, Slovak University of Technology, Department of Mathematics and Descriptive Geometry, Podbanské, March 17, 2005.
A. Linke, Mass conservative coupling of fluid flow and species transport in electrochemical flow cells, 13th Conference on Mathematics of Finite Elements and Applications (MAFELAP 2009), June 9 - 12, 2009, Brunel University, London, UK, June 10, 2009.
A. Linke, The discretization of coupled flows and the problem of mass conservation, Workshop on Discretization Methods for Viscous Flows, Part II: Compressible and Incompressible Flows, June 24 - 26, 2009, Porquerolles, Toulon, France, June 25, 2009.
A. Linke, The discretization of coupled flows and the problem of mass conservation, Seventh Negev Applied Mathematical Workshop, July 6 - 8, 2009, Ben Gurion University of the Negev, Jacob Blaustein Institute for Desert Research, Sede Boqer Campus, Israel, July 7, 2009.
J. Rehberg, Quasilinear parabolic equations in distribution spaces, International Conference on Nonlinear Parabolic Problems in Honor of Herbert Amann, May 10 - 16, 2009, Stefan Banach International Mathematical Center, Bedlewo, Poland, May 12, 2009.
E. Holzbecher, H. Zhao, J. Fuhrmann, A. Linke, H. Langmach, Numerical investigation of thin layer flow cells, 4th Gerischer Symposium, Berlin, June 25 - 27, 2008.
E. Bänsch, H. Berninger, U. Böhm, A. Bronstert, M. Ehrhardt, R. Forster, J. Fuhrmann, R. Klein, R. Kornhuber, A. Linke, A. Owinoh, J. Volkholz, Pakt für Forschung und Innovation: Das Forschungsnetzwerk ``Gekoppelte Strömungsprozesse in Energie- und Umweltforschung'', Show of the Leibniz Association ``Exzellenz durch Vernetzung. Kooperationsprojekte der deutschen Wissenschaftsorganisationen mit Hochschulen im Pakt für Forschung und Innovation'', Berlin, November 12, 2008.
M. Ehrhardt, O. Gloger, Th. Dietrich, O. Hellwich, K. Graf, E. Nagel, Level Set Methoden zur Segmentierung von kardiologischen MR-Bildern, 22. Treffpunkt Medizintechnik: Fortschritte in der medizinischen Bildgebung, Charité, Campus Virchow Klinikum Berlin, May 22, 2008.
A. Glitzky, Energy estimates for continuous and discretized reaction-diffusion systems in heterostructures, Annual Meeting of the Deutsche Mathematiker-Vereinigung 2008, minisymposium ``Analysis of Reaction-Diffusion Systems with Internal Interfaces'', September 15 - 19, 2008, Friedrich-Alexander-Universität Erlangen-Nürnberg, September 15, 2008.
A. Glitzky, Energy estimates for space and time discretized electro-reaction-diffusion systems, Conference on Differential Equations and Applications to Mathematical Biology, June 23 - 27, 2008, Université Le Havre, France, June 26, 2008.
A. Linke, Mass conservative coupling of fluid flow and species transport in electrochemical flow cells, Annual Meeting of the Deutsche Mathematiker-Vereinigung 2008, September 15 - 19, 2008, Friedrich-Alexander-Universität Erlangen-Nürnberg, September 16, 2008.
A. Linke, Mass conservative coupling of fluid flow and species transport in electrochemical flow cells, Georg-August-Universität Göttingen, November 11, 2008.
J. Rehberg, Hölder continuity for elliptic and parabolic problems, Analysis-Tag, Technische Universität Darmstadt, Fachbereich Mathematik, November 27, 2008.
A. Glitzky, Energy estimates for reaction-diffusion processes of charged species, 6th International Congress on Industrial and Applied Mathematics (ICIAM), July 16 - 20, 2007, ETH Zürich, Switzerland, July 16, 2007.
J. Rehberg, An elliptic model problem including mixed boundary conditions and material heterogeneities, Fifth Singular Days, April 23 - 27, 2007, International Center for Mathematical Meetings, Luminy, France, April 26, 2007.
J. Rehberg, Maximal parabolic regularity on Sobolev spaces, The Eighteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2007), September 17 - 29, 2007, Laspi-Batiliman, Ukraine, September 18, 2007.
F. Schmid, An evolution model in contact mechanics with dry friction, 6th International Congress on Industrial and Applied Mathematics (ICIAM), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.
A. Glitzky, Energy estimates for electro-reaction-diffusion systems with partly fast kinetics, 6th AIMS International Conference on Dynamical Systems, Differential Equations & Applications, June 25 - 28, 2006, Université de Poitiers, France, June 27, 2006.
J. Rehberg, Existence and uniqueness for van Roosbroeck's system in Lebesque spaces, Conference ``Recent Advances in Nonlinear Partial Differential Equations and Applications'', Toledo, Spain, June 7 - 10, 2006.
J. Rehberg, Regularity for nonsmooth elliptic problems, Crimean Autumn Mathematical School, September 20 - 25, 2006, Vernadskiy Tavricheskiy National University, Laspi, Ukraine, September 21, 2006.
J. Rehberg, Elliptische und parabolische Probleme aus Anwendungen, Kolloquium im Fachbereich Mathematik, Universität Darmstadt, May 18, 2005.
J. Rehberg, Existence, uniqeness and regularity for quasilinear parabolic systems, International Conference ``Nonlinear Partial Differential Equations'', September 17 - 24, 2005, Institute of Applied Mathematics and Mechanics Donetsk, Alushta, Ukraine, September 18, 2005.
J. Rehberg, H$^1,q$-regularity for linear, elliptic boundary value problems, Regularity for nonlinear and linear PDEs in nonsmooth domains - Analysis, simulation and application, September 5 - 7, 2005, Universität Stuttgart, Deutsche Forschungsgemeinschaft (SFB 404), Hirschegg, Austria, September 6, 2005.
J. Rehberg, Regularität für elliptische Probleme mit unglatten Daten, Oberseminar Prof. Escher/Prof. Schrohe, Technische Universität Hannover, December 13, 2005.
J. Rehberg, Analysis of macroscopic and quantum mechanical semiconductor models, International Visitor Program ``Nonlinear Parabolic Problems'', August 8 - November 18, 2005, Finnish Mathematical Society (FMS), University of Helsinki, and Helsinki University of Technology, Finland, November 1, 2005.
J. Rehberg, Existence, uniqueness and regularity for quasilinear parabolic systems, Conference ``Nonlinear Parabolic Problems'', October 17 - 21, 2005, Finnish Mathematical Society (FMS), University of Helsinki, and Helsinki University of Technology, Finland, October 20, 2005.
J. Rehberg, Elliptische und parabolische Probleme mit unglatten Daten, Technische Universität Darmstadt, Fachbereich Mathematik, December 14, 2004.
J. Rehberg, Quasilinear parabolic equations in $L^p$, Nonlinear Elliptic and Parabolic Problems: A Special Tribute to the Work of Herbert Amann, June 28 - 30, 2004, Universität Zürich, Institut für Mathematik, Switzerland, June 29, 2004.
J. Rehberg, The two-dimensional van Roosbroeck system has solutions in $L^p$, Workshop ``Advances in Mathematical Semiconductor Modelling: Devices and Circuits'', March 2 - 6, 2004, Chinese-German Centre for Science Promotion, Beijing, China, March 5, 2004.
A. Glitzky, R. Hünlich, Stationary solutions of two-dimensional heterogeneous energy models with multiple species, Nonlocal Elliptic and Parabolic Problems, September 9 - 11, 2003, Bedlewo, Poland, September 10, 2003.
H.-Chr. Kaiser, On space discretization of reaction-diffusion systems with discontinuous coefficients and mixed boundary conditions, 2nd GAMM Seminar on Microstructures, January 10 - 11, 2003, Ruhr-Universität Bochum, Institut für Mechanik, January 10, 2003.
J. Rehberg, Solvability and regularity for parabolic equations with nonsmooth data, International Conference ``Nonlinear Partial Differential Equations'', September 15 - 21, 2003, National Academy of Sciences of Ukraine, Institute of Applied Mathematics and Mechanics, Alushta, September 17, 2003.
Dr. Jürgen Fuhrmann
Contributing Groups of WIAS
Mathematical Context
Algorithms for the generation of 3D boundary conforming Delaunay meshes
Numerical Methods for PDEs with Stochastic Data
Numerical methods for coupled systems in computational fluid dynamics
Systems of partial differential equations: modeling, numerical analysis and simulation
Investigation of Electrochemical Double Layers in Solid Oxide Cells (EDLSOC)
Modellbasierte Abschätzung der Lebensdauer von gealterten Li-Batterien für die 2nd-Life Anwendung als stationärer Stromspeicher (MALLi2)
Multi-Material Electrocatalysis (MULTECAT)
Sensing with Nanopores
Verbundprojekt "Wege zu sekundären Mg/Ca -- Luft-Batterien"
Related main application areas


A man in his 20s was seriously injured after been hit by a car in Bray early this morning.
The pedestrian, was rushed to Beaumont Hospital after the accident on Killarney Road.
It is understood that the male was walking on the road shortly after 1 am when he was hit by a car.
He was taken to hospital where he was described as being in a 'critical condition'.
The road remains closed and local diversions are in place.


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Citizens' Square
HRIC Daily Brief
HRIC Publications
Program Foci
June Fourth
China and the United Nations
709 Crackdown
"12.26 Citizen Case"
The Changsha 3 Case
Statement by Liu Ping's Family
Liu Ping's family
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Asset Transparency
New Citizens Movement
More topics >>
Li Sihua
Liu Ping
Wei Zhongping
All defenders >>
On June 19, 2014, the Yushui District People's Court in Xinyu, Jiangxi Province, sentenced three asset transparency advocates to prison terms ranging from six and a half years to three years. Liu Ping (刘萍) and Wei Zhongping (魏忠平) were sentenced to six and a half years in prison for "picking quarrels and provoking troubles" (寻衅滋事), "gathering a crowd to disrupt order in a public place" (聚众扰乱公共场所秩序), and "using an evil cult to undermine law enforcement" (利用邪教组织破坏法律实施). Li Sihua (李思华) was sentenced to three years in prison for "picking quarrels and provoking troubles" (寻衅滋事). Liu Ping's family issued the below statement following the verdict.
[Translation by Human Rights in China]
In fact, I have so far not shed a single tear because of this verdict. One can even say that my reaction has been more that of contempt. Such severe reprisals—against the call for disclosure of officials' assets and the demand for [the right to] stand as candidates in people's congress elections, both of which have exposed the authorities' naked hypocrisy—exceeded everyone's expectations.
For more than a year, I have frequently reflected on my own actions—why did I desperately try to stop my mother and ignore the ruthlessness and evil that exist in today's society? Right now I feel profound remorse. The price my mother and others are paying is the result of our indifference and cowardice. We only cared about our own "home" and our own interests. We treated things like democracy, constitutionalism, and free society as jokes. We did not let them concern us, and we were apathetic. But the consequence is that the courageous paid a painful price for our cowardice.
The verdict came: Liu Ping and Wei Zhongping received six years and six months each; Li Sihua, three years. In the next six years or so, the parents of the three will grow old, and Wei Zhongping's and Li Sihua's daughters will face the most important exams in their lives: university and high school entrance exams. Therefore, this verdict is a tragedy not only for the three defendants but also for the three families, and for the legal system in China. During their imprisonment, their parents may die of old age, and, without their parent's encouragement, their children may head in a wrong path. Of course, those in power could foresee this. But they went ahead, to assume the role of the executioner, and are feeling immensely self-satisfied and proud.
Before the verdict was announced, almost everyone thought the sentences would be two to three years. Some even thought they would be released soon because they had done nothing and had already been in detention for more than a year. Even lawyers thought they would be convicted of one count for sure, but thought that two would be evil. In my heart I had also hoped it would turn out this way. But then they prohibited Liu Ping's daughter from attending the sentencing hearing, revoked Liu Ping's mother's qualification to attend, deliberately timed [the sentencing hearing] so that the lawyers could not come, and made my school restrain me [by withholding] my graduation certificate. In this series of actions, I sensed danger. I tossed and turned and could not sleep the night before the verdict. I told reporters that the sentence could be heavy. I didn't expect that to be so prophetic.
Up until now, the outcome has been determined. It has also made me realize that the road ahead will certainly be rocky. The verdict in Liu Ping's case is in fact the authorities' warning to others, telling everyone: "Don't do these things. I am afraid, and must teach you a lesson! Don't talk to me about democracy and constitutionalism!" See, how foolish and laughable.
I remember a conversation I had with a friend. We were discussing why the authorities do these things when they know very well that tight control is not sustainable—they know that the harsher the crackdown, the stronger the resistance. Did they not learn from the experience of the Nazis?
Our conclusion: it is because of the interests here and now.
(See original Chinese)
HRIC Resources
Harsh Prison Terms for Advocates Undermine Official Anti-Corruption Efforts, June 19, 2014
Statement by Wei Zhongping's Brother, June 19, 2014
Verdict in the Case of Three Asset Transparency Advocates, June 19, 2014
Liu Ping's Final Statement at Trial, December 6, 2013
Supporter of Asset Transparency Advocates Kept in Iron Cage for 25 Hours, December 4, 2013
Netizen Info on Resumed Trial of Three Asset Transparency Advocates, December 4, 2013
Trial Adjourns for Asset Transparency Advocates over Right to Proper Defense, October 28, 2013
Lawyers Call for Release of Three Asset Transparency Advocates, Challenge Legality of Trial Delay, October 15, 2013
Two New Charges for Asset Transparency Advocate Liu Ping, August 29, 2013
Activist Detained on Suspicion of "Inciting Subversion of State Power" after Calling for Disclosure of Officials' Assets, May 9, 2013
Guo Feixiong: Open letter protests police brutality against two independent candidates in Xinyu, Jiangxi Province; account of incident, September 22, 2012
Activist Accused of Inciting Subversion of State Power for Distributing Leaflets, May 9, 2012
Error | Human Rights in China 中国人权 | HRIC

redpajama_set_name: RedPajamaCommonCrawl


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Africa Grace Mugabe President Mugabe Zimbabwe
Mugabe expels Mugabe rival Joyce Mujuru
Joice Mujuru was once a staunch ally of Robert Mugabe and seen as a likely successor
A former vice president of Zimbabwe, Joyce Mujuru, has been expelled from the ruling party, Zanu-PF.
The party said she had plotted to remove President Robert Mugabe from office and brought the party into disrepute.
She had been been seen as a likely successor to President Mugabe but was sacked at the end of last year.
She was accused of corruption and plotting to kill the president – allegations she denied.
Mr Mugabe, 91, will have been in power for 35 years when Zimbabwe marks its independence from the UK later this month.
The first lady, Grace Mugabe – who is now a senior figure in the Zanu-PF Party – has been very vocal against Mrs Mujuru in public.
Mrs Mujuru fought alongside Mr Mugabe in the 1970s guerrilla war against white minority rule and was known as "Spill Blood".
Zanu-PF spokesman Simon Khaya Moyo said in a statement that the ruling party's top decision-makers had agreed to her dismissal citing 10 reasons.
These included plotting to remove Mr Mugabe from office, alleged corruption and bringing the party into disrepute – charges she has previously denied.
"The politburo felt that she lacked the quality of strong moral principles, honesty and decency and therefore ceases to be a member of Zanu-PF," Mr Moyo said.
'People disappearing'
Mr Mugabe has not publicly indicated a preferred candidate to take over his presidency.But in December he purged the government of several ministers, including Mrs Mujuru, and appointed Emmerson Mnangagwa as his deputy, making the former justice minister the favourite to succeed him.
Didymus Mutasa, one of the sacked ministers and a former confidante of President Mugabe, was expelled from Zanu-PF earlier this year.
He has told the BBC's Focus on Africa programme that he now fears for his life."You see people disappearing… so will they spare my life or send a sniper to shoot at me?" he said.
He said the fighting in Zanu-PF was worse than the situation under former white minority leader Ian Smith."The Smith regime was not as bad as the current regime – it's really terrible," Mr Mutasa said.
Zimbabwe's ruling party expels Mugabe rival
Mugabe's party expels rival Mujuru
Zimbabwe's ruling party expels former vice president Mujuru
Zimbabwe's Mugabe ruling party fires former deputy Mujuru
Factionalism no longer a secret in Zanu PF.
Zimbabwe's new political kid-People First
Zimbabwe Starvation Fund
Lone voices join abducted Dzamara to speak out as Mugabe clings on #ThisFlag
Mbada Diamonds Chief splashes R185m on SA property
US$1 billion Chinese loan for Mnangagwa's Zim revival
Posted on 5th April 2015 by newsafrica.	This entry was posted in Africa, Grace Mugabe, President Mugabe, Zimbabwe and tagged Didymus Mutasa, Emmerson Mnangagwa, Guerrilla warfare, Joice Mujuru, Robert Mugabe, Ruling party, Solomon Mujuru, Vice President of the United States, Zimbabwe, Zimbabwe African National Union – Patriotic Front. Bookmark the permalink.
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Bomb kills policeman in Cairo, militant leader dies in firefights »


Report: 2nd letter said she was 36 but is 25, said she had lost mother and father in car crash not true seen pic of mother.said her name is elena tyurina not true she is maria sokolova, said she was from vernary in russia but is from ukraine lugansk or cherkasy. said she was a cook but a teacher. I sent her$600 for flight to heathrow london she did not turn up. 1 hour later phoned and said so sorry but she had set fire to the hotel room where she was staying. The manager of the hotel said he will keep her passport until she paid $800 for the damage. Then asked me can i help. No way baby. Don't fall for this women she will break your heart just like she has done to me. stay away from this pro scammer.


Just as an andiron, or firedog (normally found in pairs), is a support on which logs are laid for burning, allowing air to circulate under the wood, facilitating better burn and less smoke, so the Dalmation Stone (often, and incorrectly, called Dalmation Jasper) acts as an "elevator" for the emotions.
Dalmatian Jasper is just the stone you need when you want a pick-me-up. It helps us release our tendencies to over think or over analyze, and when you wear it your mood lifts immediately, enlivening the the spirit as well as dull situations.
Not surprisingly, Dalamation Stone is also wonderful for those who work in the veterinary or animal fields.
The specimen captured here measures 3/4 X 1 X 5/8″ thick, approximately, making the pendant a rough 1 X 1 1/2 X 5/8″. Wrapped in silver plate and copper, reversible, and can be suspended from almost any chain or cord, by anybody.


A study in Singapore is fast gaining interest amongst international students. Singapore is a sovereign city-state and island country in Southeast Asia. Interestingly, Singapore's higher education system has developed into a leading force that assists in promoting its reputation as one of the world's leading centers for financial growth and technological advancements.
Students applying to any of the institutions of higher institutions in Singapore need not worry about language barrier. English is a language of instruction – Postgraduate courses in Singapore are taught in English which, as the mother tongue of many Singaporeans, is widely used.
Six national universities in Singapore are ranked among the top 50 in the world: the Nanyang Technological University, the Singapore University of Technology and Design, the National University of Singapore, the Singapore Institute of Technology, the Singapore Management University and the SIM University. These universities offer undergraduate and postgraduate degree programs in Accountancy, Information Systems Management, Business Management, Economics, the Social Sciences, Law and Computer Science.
Singapore offers five polytechnics for students who wish to earn a non-academic degree that allows them to enter the workforce immediately upon completing the program. A degree earned at a polytechnic is similar to an associate's degree or vocational certificate and takes less than two years to complete.
*Please note: These requirements differ from every institute. Some polytechnics may not have these requirements while universities might have them. Please check with the institute of your choice before applying.
How safe is the country? This is one of the reasons international students consider a study trip to Singapore. Singapore is a safe place to study at. Singapore has a well-deserved reputation for being safe and relatively crime-free.
Weather condition: Singapore's weather is warm and humid, ranging from an average of 31°C during the day and 24°C at night. It rains throughout the year with heavier rain during the monsoon season, which lasts from November to January.
These vary between study programmes and levels.
Students applying for a study visa need to prove they are fluent in English by providing the results of a Test of English as a Foreign Language (TOEFL); a General Certificate of Secondary Education (GCSE); or an International English Language Testing System (IELTS). They must also have received an acceptance letter from a university or polytechnic as well as passport photos and documentation proving their eligibility to enter a university degree program (high school diploma, for example).
Visa processing may take one to two months, depending on the validity of a student's paperwork and amount of documentation.


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You are here: Home › RV Rentals Offer Best Value for Holiday Travelers says Allstar Coaches
RV Rentals Offer Best Value for Holiday Travelers says Allstar Coaches
By Send2Press Newswire on December 7, 2011 in Automotive, Florida, FORT LAUDERDALE, Fla., Press Releases, Transportation, Travel and Tourism
FORT LAUDERDALE, Fla., Dec. 7, 2011 (SEND2PRESS NEWSWIRE) — Airfares have been steadily on the rise and weary travelers are searching for alternative means of travel as holiday season approaches. Rob Tischler, CEO of Allstar Coaches said "When considering the cost of airfare, hotels, and meals out, it's no wonder that people are turning to RV rentals. The savings are substantial, even when you incorporate fuel costs. A family of four can literally save thousands over traditional air-hotel itineraries." With such a dramatic rise, the search for alternatives is at a fever pitch. People are better looking at trains, buses and recreational vehicles.
Lynn Thompson, an RN out of Fort Lauderdale found that "renting a motorhome is a cost effective, more comfortable and less stressful alternative to traveling by plane." Travelers also appear to be getting very frustrated with the invasive searches, missed connections and outrageous fees when flying. "The last time I flew," said Thompson, "I had to pay $20 extra per seat so my family could sit together, then they lost my luggage for which I had to pay extra as well, and my 86 year old grandmother was singled out and publicly humiliated when an overzealous security agent became suspicious of her colostomy bag. Another time, our flight was delayed and we just sat on the tarmac for hours." Thompson also noted that she was able to save almost $2,000 by preparing their own meals in her RV, eliminating the expensive hotels and restaurants.
Industry insiders believe that the increased demand in RV travel can be attributed to an educated consumer base that is tiring of the rampant nickel and diming and stress associated with air travel. According to farecompare.com CEO Rick Seaney, "The average fare for holiday flights is up as much as 20 percent over last year." People are beginning to realize that there are other choices and they want to maximize their travel experience.
Allstar Coaches operates their fleet of luxury motorhome rentals from strategically located depots in nine states. With full kitchens, luxurious cabins and modern technology, these vehicles are equipped to exceed the expectations of even the most discerning traveler.
"Folks are starting to figure out what many motorhome enthusiasts have known for years; that the benefits of motorhome travel far outweigh the costs," says Von Isanogle, Fleet Operations manager at Allstar, "and that is contributing to increased sales. Record breaking airfares and those crazy fees are only helping to take them off the skyways and put them onto the highways."
For further information about RV and motorhome rentals in Florida contact Allstar Coaches at (866) 838-4465. More information online: www.allstarcoaches.com .
News Source: Allstar Coaches :: This press release was issued on behalf of the news source by Send2Press® Newswire, a service of Neotrope®. View all current news at: http://Send2PressNewswire.com .
Allstar Coaches, florida motorhome rentals, Fort Lauderdale, luxury rv rental
Third Round for Rock the Vote with Whiteflash's Say Yes Facebook Contest
Sacramento New Year's Eve 2011 at Hilton Offers Two Live Bands, a DJ, Two Free Drinks, and Champagne Toasts


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You are here: Home » Education » Postseason Honors Roll In for Parker Girls' Volleyball Team
Postseason Honors Roll In for Parker Girls' Volleyball Team
Staff | January 2, 2013	| 0 Comments
The Francis Parker School girls' volleyball team captured its 7th CIF State Championship back on December 1, its first since winning back-to-back state titles in '04 and '05. Since then, the Lancers have picked up several postseason accolades, including a Coach of the Year award and three all-section honors.
John Landicho, a Santee resident, in his first year as head coach of the program, not only led the Lancers to a 37-2 record and a State Championship, but he was honored by the UT San Diego as the 2012 San Diego Section Coach of the Year. He guided Parker to a #1 ranking in the state for Division IV teams and #2 in the nation for similar size schools. Overall, the team finished with the #6 ranking in California and #22 in the country for all schools.
The Lancers had two players, setter Erika Conners '13 (Serra Mesa resident) and outside hitter Michaela Dews '14 (Clairemont Mesa resident) earn 1st Team All-San Diego Section honors while middle blocker Alexis Salmons '13 (Old Town resident) garnered 2nd Team All-San Diego Section accolades.
Middle blocker Alexis Salmons '13 (Old Town resident) garnered 2nd Team All-San Diego Section accolades.
In the championship match, Parker defeated Sacred Heart Prep out of Atherton by scores of 25-22, 28-26, 22-25, 22-25 and 15-13. Dews recorded a match-high 20 kills to go along with 14 digs while Conners posted 55 assists and 16 digs.
The Lancers' previous State Championships came in 1986, 1987, 1988, 1998, 2004 and 2005. Landicho was an assistant coach on the '98, '04 and '05 squads.
Tags: 7th CIF State Championship, Francis Parker School
Category: Education, Local News
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OUR FIRST VENTURE INTO MORE TECHNICAL GARMENTS, THE TRAVEL PANT IS A RESULT OF THE ISSUES OUR TEAM FACES WHEN TRAVELING. THIS STYLE IS CRAFTED FROM A LIGHT AND COMFORTABLE COTTON BLEND TO ENSURE YOU'RE ALWAYS COMFORTABLE WHEN ON THE GO. IN ADDITION, THIS STYLE FEATURES A MULTITUDE OF POCKETS TO STORE EVERYTHING YOU NEED WHEN TRAVELING; THERE IS A CARGO POCKET ON THE RIGHT LEG, TWO ZIPPERED SIDE POCKETS, TWO VISIBLE ZIPPERED BACK POCKETS, AND TWO HIDDEN ZIPPERED REAR POCKETS. LASTLY, THIS STYLE FEATURES A VELCRO ANKLE CLOSURE SO YOU CAN ADJUST THE TAPER ACCORDINGLY TO THE FOOTWEAR YOU ARE WEARING.


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Q: Can an Angular ng-mousover event trigger ng-style on multiple elements? I'm currently learning Angular and I have a question.
I have two divs that change their background color on triggering the ng-mouseover directive. here is a little snippet of the two divs.

I assumed that the background variable I declared in the directives would be added to the existing $scope.
With the two divs being bound to the 'same variable' (in my mind) I assumed they would both change on when either ng-mouseover event was triggered.
Any and all help is highly appreciated.

A: Instead of background = setColor(variance), you should be defining a background variable in your local scope, and creating a function on the scope called setColor that alters the local scope background value.  You'd then want to build a function to clear that value, as opposed to setting it to an empty object within your view.

A: ng-style takes..

Expression which evals to an object whose keys are CSS style names and
  values are corresponding values for those CSS keys

I think it's impossible to say why it doesn't work without seeing what's returned from setColor(variance)

redpajama_set_name: RedPajamaStackExchange


I felt like there was lots of good info in this book. And that the reading was well-paced.
very informative. everything is not for everyone so hopefully I can implement some of what I've learned.
sublime, - such a depth and wealth of knowledge.
Have listened to this five times now and many a note has been taken.very excited to put this into action.