Filters

2010 - 201972020 - 20214

More filters

2019 - 201952020 - 20226
Reset filters

Settings

search.filters.applied.f.access: openAccess × Subject: GENERIC ×

Search Results

Now showing 1 - 10 of 11
  • Thumbnail Image
    Item
    Free energy, free entropy, and a gradient structure for thermoplasticity
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Mielke, Alexander
    In the modeling of solids the free energy, the energy, and the entropy play a central role. We show that the free entropy, which is defined as the negative of the free energy divided by the temperature, is similarly important. The derivatives of the free energy are suitable thermodynamical driving forces for reversible (i.e. Hamiltonian) parts of the dynamics, while for the dissipative parts the derivatives of the free entropy are the correct driving forces. This difference does not matter for isothermal cases nor for local materials, but it is relevant in the non-isothermal case if the densities also depend on gradients, as is the case in gradient thermoplasticity. Using the total entropy as a driving functional, we develop gradient structures for quasistatic thermoplasticity, which again features the role of the free entropy. The big advantage of the gradient structure is the possibility of deriving time-incremental minimization procedures, where the entropy-production potential minus the total entropy is minimized with respect to the internal variables and the temperature. We also highlight that the usage of an auxiliary temperature as an integrating factor in Yang/Stainier/Ortiz "A variational formulation of the coupled thermomechanical boundary-value problem for general dissipative solids" (J. Mech. Physics Solids, 54, 401-424, 2006) serves exactly the purpose to transform the reversible driving forces, obtained from the free energy, into the needed irreversible driving forces, which should have been derived from the free entropy. This reconfirms the fact that only the usage of the free entropy as driving functional for dissipative processes allows us to derive a proper variational formulation.
  • Thumbnail Image
    Item
    Multiscale thermodynamics of charged mixtures
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Vágner, Petr; Pavelka, Michal; Esen, Oğul
    A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.
  • Thumbnail Image
    Item
    GENERIC for dissipative solids with bulk-interface interaction
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Heida, Martin; Thomas, Marita
    The modeling framework of GENERIC was originally introduced by Grmela and Öttinger for thermodynamically closed systems. It is phrased with the aid of the energy and entropy as driving functionals for reversible and dissipative processes and suitable geometric structures. Based on the definition functional derivatives we propose a GENERIC framework for systems with bulk-interface interaction and apply it to discuss the GENERIC structure of models for delamination processes.
  • Thumbnail Image
    Item
    GENERIC framework for reactive fluid flows
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Zafferi, Andrea; Peschka, Dirk; Thomas, Marita
    We describe reactive fluid flows in terms of the formalism General Equation for Non-Equilibrium Reversible-Irreversible Coupling also known as GENERIC. Together with the formalism, we present the thermodynamical and mechanical foundations for the treatment of fluid flows using continuous fields and present a clear relation and transformation between a Lagrangian and an Eulerian formulation of the corresponding systems of partial differential equations. We bring the abstract framework to life by providing many physically relevant examples for reactive compressive fluid flows.
  • Thumbnail Image
    Item
    An entropic gradient structure for Lindblad equations and GENERIC for quantum systems coupled to macroscopic models
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Mittnenzweig, Markus; Mielke, Alexander
    We show that all Lindblad operators (i.e. generators of quantum semigroups) on a finite-dimensional Hilbert space satisfying the detailed balance condition with respect to the thermal equilibrium state can be written as a gradient system with respect to the relative entropy. We discuss also thermodynamically consistent couplings to macroscopic systems, either as damped Hamiltonian systems with constant temperature or as GENERIC systems.
  • Thumbnail Image
    Item
    Dissipative quantum mechanics using GENERIC
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Mielke, Alexander
    Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for Non-Equilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradient-flow contribution, which satisfy a particular non-interaction condition:
  • Thumbnail Image
    Item
    Formulation of thermo-elastic dissipative material behavior using GENERIC
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Mielke, Alexander
    The theory of GENERIC (general equations for non-equilibrium reversible irreversibel coupling) is presented in a mathematical form. It is applied first to simple mechanical systems and then generalized to standard generalized materials. It is shown that nonisothermal viscoplasticity can be cast into the form of GENERIC, if the dissipative structure is generalized from linear functionals to the more general subdifferential of convex potentials
  • Thumbnail Image
    Item
    On thermodynamical couplings of quantum mechanics and macroscopic systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Mielke, Alexander
    Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the Liouville equation for the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradient-flow contribution, which satisfy a particular non-interaction condition: q̇ = J(q)DE(q) + K(q)DS(q). We give three applications of the theory. First, we consider a finite-dimensional quantum system that is coupled to a finite number of simple heat baths, each of which is described by a scalar temperature variable. Second, we model quantum system given by a one-dimensional Schrödinger operator connected to a onedimensional heat equation on the left and on the right. Finally, we consider thermoopto-electronics, where the Maxwell-Bloch system of optics is coupled to the energydrift-diffusion system for semiconductor electronics.
  • Thumbnail Image
    Item
    Multi-dimensional modeling and simulation of semiconductor nanophotonic devices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Kantner, Markus; Höhne, Theresa; Koprucki, Thomas; Burger, Sven; Wünsche, Hans-Jürgen; Schmidt, Frank; Mielke, Alexander; Bandelow, Uwe
    Self-consistent modeling and multi-dimensional simulation of semiconductor nanophotonic devices is an important tool in the development of future integrated light sources and quantum devices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically explore their optimization potential. The efficient implementation of multi-dimensional numerical simulations for computer-aided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in device-scale modeling of quantum dot based single-photon sources and laser diodes by self-consistently coupling the optical Maxwell equations with semiclassical carrier transport models using semi-classical and fully quantum mechanical descriptions of the optically active region, respectively. For the simulation of realistic devices with complex, multi-dimensional geometries, we have developed a novel hp-adaptive finite element approach for the optical Maxwell equations, using mixed meshes adapted to the multi-scale properties of the photonic structures. For electrically driven devices, we introduced novel discretization and parameter-embedding techniques to solve the drift-diffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on various applications, including vertical-cavity surface-emitting lasers, grating couplers and single-photon sources.
  • Thumbnail Image
    Item
    Multiscale thermodynamics of charged mixtures
    (Berlin ; Heidelberg : Springer, 2021) Vágner, Petr; Pavelka, Michal; Esen, Oğul
    A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization, and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature. © 2020, The Author(s).