436 research outputs found

    Multiphysics simulation of corona discharge induced ionic wind

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    Ionic wind devices or electrostatic fluid accelerators are becoming of increasing interest as tools for thermal management, in particular for semiconductor devices. In this work, we present a numerical model for predicting the performance of such devices, whose main benefit is the ability to accurately predict the amount of charge injected at the corona electrode. Our multiphysics numerical model consists of a highly nonlinear strongly coupled set of PDEs including the Navier-Stokes equations for fluid flow, Poisson's equation for electrostatic potential, charge continuity and heat transfer equations. To solve this system we employ a staggered solution algorithm that generalizes Gummel's algorithm for charge transport in semiconductors. Predictions of our simulations are validated by comparison with experimental measurements and are shown to closely match. Finally, our simulation tool is used to estimate the effectiveness of the design of an electrohydrodynamic cooling apparatus for power electronics applications.Comment: 24 pages, 17 figure

    Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks

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    In this paper a novel device aimed at controlling the mechanical vibrations of plates by means of a set of electrically-interconnected piezoelectric actuators is described. The actuators are embedded uniformly in the plate wherein they connect every node of an electric network to ground, thus playing the two-fold role of capacitive element in the electric network and of couple suppliers. A mathematical model is introduced to describe the propagation of electro-mechanical waves in the device; its validity is restricted to the case of wave-forms with wave-length greater than the dimension of the piezoelectric actuators used. A self-resonance criterion is established which assures the possibility of electro-mechanical energy exchange. Finally the problem of vibration control in simply supported and clamped plates is addressed; the optimal net-impedance is determined. The results indicate that the proposed device can improve the performances of piezoelectric actuationComment: 22 page

    Analytical and Numerical Study of Photocurrent Transients in Organic Polymer Solar Cells

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    This article is an attempt to provide a self consistent picture, including existence analysis and numerical solution algorithms, of the mathematical problems arising from modeling photocurrent transients in Organic-polymer Solar Cells (OSCs). The mathematical model for OSCs consists of a system of nonlinear diffusion-reaction partial differential equations (PDEs) with electrostatic convection, coupled to a kinetic ordinary differential equation (ODE). We propose a suitable reformulation of the model that allows us to prove the existence of a solution in both stationary and transient conditions and to better highlight the role of exciton dynamics in determining the device turn-on time. For the numerical treatment of the problem, we carry out a temporal semi-discretization using an implicit adaptive method, and the resulting sequence of differential subproblems is linearized using the Newton-Raphson method with inexact evaluation of the Jacobian. Then, we use exponentially fitted finite elements for the spatial discretization, and we carry out a thorough validation of the computational model by extensively investigating the impact of the model parameters on photocurrent transient times.Comment: 20 pages, 11 figure

    Holographic Plasmons

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    Since holography yields exact results, even in situations where perturbation theory is not applicable, it is an ideal framework for modeling strongly correlated systems. We extend previous holographic methods to take the dynamical charge response into account and use this to perform the first holographic computation of the dispersion relation for plasmons. As the dynamical charge response of strange metals can be measured using the new technique of momentum-resolved electron energy-loss spectroscopy (M-EELS), plasmon properties are the next milestone in verifying predictions from holographic models of new states of matter.Comment: 12 pages, 2 figures. v2: Minor changes v3: Minor adjustments v4: Published versio

    Intertwined Orders in Holography: Pair and Charge Density Waves

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    Building on [1], we examine a holographic model in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. The symmetry breaking is realized through the St\"{u}ckelberg mechanism, and leads to a scalar condensate and a charge density which are spatially modulated and exhibit unidirectional stripe order. Depending on the choice of parameters, the oscillations of the scalar condensate can average out to zero, with a frequency which is half of that of the charge density. In this case the system realizes some of the key features of pair density wave order. The model also admits a phase with co-existing superconducting and charge density wave orders, in which the scalar condensate has a uniform component. In our construction the various orders are intertwined with each other and have a common origin. The fully backreacted geometry is computed numerically, including for the case in which the theory contains axions. The latter can be added to explicitly break translational symmetry and mimic lattice-type effects.Comment: 37 pages, 17 figure

    Solution Map Analysis of a Multiscale Drift-Diffusion Model for Organic Solar Cells

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    In this article we address the theoretical study of a multiscale drift-diffusion (DD) model for the description of photoconversion mechanisms in organic solar cells. The multiscale nature of the formulation is based on the co-presence of light absorption, conversion and diffusion phenomena that occur in the three-dimensional material bulk, of charge photoconversion phenomena that occur at the two-dimensional material interface separating acceptor and donor material phases, and of charge separation and subsequent charge transport in each three-dimensional material phase to device terminals that are driven by drift and diffusion electrical forces. The model accounts for the nonlinear interaction among four species: excitons, polarons, electrons and holes, and allows to quantitatively predict the electrical current collected at the device contacts of the cell. Existence and uniqueness of weak solutions of the DD system, as well as nonnegativity of all species concentrations, are proved in the stationary regime via a solution map that is a variant of the Gummel iteration commonly used in the treatment of the DD model for inorganic semiconductors. The results are established upon assuming suitable restrictions on the data and some regularity property on the mixed boundary value problem for the Poisson equation. The theoretical conclusions are numerically validated on the simulation of three-dimensional problems characterized by realistic values of the physical parameters

    Reconstruction Methods for Inverse Problems with Partial Data

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    Stability of two-dimensional forced Navier-Stokes flow on a bounded circular domain

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    This research is concerned with the stability of a two-dimensional, electromagnetically forced, zonal flow on a circular domain. Flows like these are found in nature (e.g. shear flow in the atmosphere, Jovian disk) and experiment (e.g. plasma flow in a Fusion reactor) and a requirement for experiments is often that these types of flows remain stable and axi-symmetric. A numerical method is developed based on a spectral expansion into an infinite system of ordinary differential equations for velocity functions resulting from a Stokes eigenvalue problem. The system is truncated to gain a finite-dimensional system which is useful for computations of both equilibrium flows and strongly disturbed flows. Numerical results are compared to both finite difference method results and analytical results for the equilibrium basic flow. Both linear and nonlinear stability are explored for the Navier-Stokes equations on the circular domain and for the system of ordinary differential equations. Differences in stability and the evolution of perturbations are explained on the basis of discrepancies between infinite-dimensional partial differential equations like the Navier-Stokes equations and a finite-dimensional system of ordinary differential equations resulting from a Galerkin truncation. On the basis of both stability analyses a control system is developed which stabilizes the system of ordinary differential equations to stay in a desired equilibrium. It is argued that this control system is also usable for the control of the Navier-Stokes equations. This research is concerned with the stability of a two-dimensional, electromagnetically forced, zonal flow on a circular domain. Flows like these are found in nature (e.g. shear flow in the atmosphere, Jovian disk) and experiment (e.g. plasma flow in a Fusion reactor) and a requirement for experiments is often that these types of flows remain stable and axi-symmetric. A numerical method is developed based on a spectral expansion into an infinite system of ordinary differential equations for velocity functions resulting from a Stokes eigenvalue problem. The system is truncated to gain a finite-dimensional system which is useful for computations of both equilibrium flows and strongly disturbed flows. Numerical results are compared to both finite difference method results and analytical results for the equilibrium basic flow. Both linear and nonlinear stability are explored for the Navier-Stokes equations on the circular domain and for the system of ordinary differential equations. Differences in stability and the evolution of perturbations are explained on the basis of discrepancies between infinite-dimensional partial differential equations like the Navier-Stokes equations and a finite-dimensional system of ordinary differential equations resulting from a Galerkin truncation. On the basis of both stability analyses a control system is developed which stabilizes the system of ordinary differential equations to stay in a desired equilibrium. It is argued that this control system is also usable for the control of the Navier-Stokes equations
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