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- ItemA coarse‐grained electrothermal model for organic semiconductor devices(Chichester, West Sussex : Wiley, 2022) Glitzky, Annegret; Liero, Matthias; Nika, GrigorWe derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion- based electrothermal models with thermistor-type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss–Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.
- ItemDerivation of effective models from heterogenous Cosserat media via periodic unfolding(Milano : Springer, 2021) Nika, GrigorWe derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Struct. 38 (26-27): 4585-4608 ’01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case.
- ItemAn existence result for a class of nonlinear magnetorheological composites(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Nika, GrigorWe prove existence of a weak solution for a nonlinear, multi-physics, multi-scale problem of magnetorheological suspensions introduced in Nika & Vernescu (Z. Angew. Math. Phys., 71(1):1--19, '20). The hybrid model couples the Stokes' equation with the quasi-static Maxwell's equations through the Lorentz force and the Maxwell stress tensor. The proof of existence is based on: i) the augmented variational formulation of Maxwell's equations, ii) the definition of a new function space for the magnetic induction and the proof of a Poincaré type inequality, iii) the Altman--Shinbrot fixed point theorem when the magnetic Reynold's number, Rm, is small.
- ItemMicro-geometry effects on the nonlinear effective yield strength response of magnetorheological fluids(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Nika, Grigor; Vernescu, BogdanWe use the novel constitutive model in [15], derived using the homogenization method, to investigate the effect particle chain microstructures have on the properties of the magnetorheological fluid. The model allows to compute the constitutive coefficients for different geometries. Different geometrical realizations of chains can significantly change the magnetorheological effect of the suspension. Numerical simulations suggest that particle size is also important as the increase of the overall particle surface area can lead to a decrease of the overall magnetorheological effect while keeping the volume fraction constant.
- ItemMultiscale modeling of magnetorheological suspensions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Nika, Grigor; Vernescu, BogdanWe develop a multiscale approach to describe the behavior of a suspension of solid magnetizable particles in a viscous non-conducting fluid in the presence of an externally applied magnetic field. By upscaling the quasi-static Maxwell equations coupled with the Stokes' equations we are able to capture the magnetorheological effect. The model we obtain generalizes the one introduced by Neuringer & Rosensweig for quasistatic phenomena. We derive the macroscopic constitutive properties explicitly in terms of the solutions of local problems. The effective coefficients have a nonlinear dependence on the volume fraction when chain structures are present. The velocity profiles computed for some simple flows, exhibit an apparent yield stress and the flowprofile resembles a Bingham fluid flow.
- ItemDerivation of effective models from heterogenous Cosserat media via periodic unfolding(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Nika, GrigorWe derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Structures 38 (26-27): 4585-4608 '01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case.
- ItemAn existence result for a class of electrothermal drift-diffusion models with Gauss--Fermi statistics for organic semiconductors(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Glitzky, Annegret; Liero, Matthias; Nika, GrigorThis work is concerned with the analysis of a drift-diffusion model for the electrothermal behavior of organic semiconductor devices. A "generalized Van Roosbroeck'' system coupled to the heat equation is employed, where the former consists of continuity equations for electrons and holes and a Poisson equation for the electrostatic potential, and the latter features source terms containing Joule heat contributions and recombination heat. Special features of organic semiconductors like Gauss--Fermi statistics and mobilities functions depending on the electric field strength are taken into account. We prove the existence of solutions for the stationary problem by an iteration scheme and Schauder's fixed point theorem. The underlying solution concept is related to weak solutions of the Van Roosbroeck system and entropy solutions of the heat equation. Additionally, for data compatible with thermodynamic equilibrium, the uniqueness of the solution is verified. It was recently shown that self-heating significantly influences the electronic properties of organic semiconductor devices. Therefore, modeling the coupled electric and thermal responses of organic semiconductors is essential for predicting the effects of temperature on the overall behavior of the device. This work puts the electrothermal drift-diffusion model for organic semiconductors on a sound analytical basis.
- ItemDesign and testing of 3D-printed micro-architectured polymer materials exhibiting a negative Poisson's ratio(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Agnelli, Filippo; Constantinescu, Andrei; Nika, GrigorThis work proposes the complete design cycle for several auxetic materials where the cycle consists of three steps (i) the design of the micro-architecture, (ii) the manufacturing of the material and (iii) the testing of the material. In more precise terms, we aim to obtain domain micro-architectured materials with a prescribed elasticity tensor and Poisson's ratio. In order to reach this goal we use topology optimization via the level set method for the material design process. Specimens are manufactured using a commercial stereo-lithography Ember printer and mechanically tested. The observed displacement and strain fields during tensile testing obtained by digital image correlation match the predictions from the FE simulation.
- ItemA coarse-grained electrothermal model for organic semiconductor devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Glitzky, Annegret; Liero, Matthias; Nika, GrigorWe derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion based electrothermal models with thermistor type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss--Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.
- ItemAn effective bulk-surface thermistor model for large-area organic light-emitting diodes(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Glitzky, Annegret; Liero, Matthias; Nika, GrigorThe existence of a weak solution for an effective system of partial differential equations describing the electrothermal behavior of large-area organic light-emitting diodes (OLEDs) is proved. The effective system consists of the heat equation in the three-dimensional bulk glass substrate and two semi-linear equations for the current flow through the electrodes coupled to algebraic equations for the continuity of the electrical fluxes through the organic layers. The electrical problem is formulated on the (curvilinear) surface of the glass substrate where the OLED is mounted. The source terms in the heat equation are due to Joule heating and are hence concentrated on the part of the boundary where the current-flow equation is posed. The existence of weak solutions to the effective system is proved via Schauder's fixed-point theorem. Moreover, since the heat sources are a priori only in $L^1$, the concept of entropy solutions is used.