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Energy-Variational Solutions for Viscoelastic Fluid Models
No full textIn this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be shown constructively by an adapted minimizing movement scheme. Weak-strong uniqueness follows by a suitable relative energy inequality. Our main motivation is to apply the general framework to viscoelastic fluid models. Therefore, we give a short overview on different versions of such models and their derivation. The abstract result is applied to two of these viscoelastic fluid models in full detail. In the conclusion, we comment on further applications of the general theory and its possible impact
Foundational Competencies and Responsibilities of a Research Software Engineer
Get PDFThe term Research Software Engineer, or RSE, emerged a little over 10 years ago as a way to represent individuals working in the research community but focusing on software development. The term has been widely adopted and there are a number of high-level definitions of what an RSE is. However, the roles of RSEs vary depending on the institutional context they work in. At one end of the spectrum, RSE roles may look similar to a traditional research role. At the other extreme, they resemble that of a software engineer in industry. Most RSE roles inhabit the space between these two extremes. Therefore, providing a straightforward, comprehensive definition of what an RSE does and what experience, skills and competencies are required to become one is challenging. In this community paper we define the broad notion of what an RSE is, explore the different types of work they undertake, and define a list of foundational competencies as well as values that outline the general profile of an RSE. Further research and training can build upon this foundation of skills and focus on various aspects in greater detail. We expect that graduates and practitioners will have a larger and more diverse set of skills than outlined here. On this basis, we elaborate on the progression of these skills along different dimensions. We look at specific types of RSE roles, propose recommendations for organisations, give examples of future specialisations, and detail how existing curricula fit into this framework
Theory of the Linewidth-Power Product of Photonic-Crystal Surface-Emitting Lasers
No full textA general theory for the intrinsic (Lorentzian) linewidth of photonic–crystal surface–emitting lasers (PCSELs) is presented. The effect of spontaneous emission is modeled by a classical Langevin force entering the equation for the slowly varying waves. The solution of the coupled–wave equations, describing the propagation of four basic waves within the plane of the photonic crystal, is expanded in terms of the solutions of the associated spectral problem, i.e. the laser modes. Expressions are given for photon number, rate of spontaneous emission into the laser mode, Petermann factor and effective Henry factor entering the general formula for the linewidth. The theoretical framework is applied to the calculation of the linewidth–power product of air–hole and all–semiconductor PCSELs. For output powers in the Watt range, intrinsic linewidths in the kHz range are obtained in agreement with recent experimental result
ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Ex Vivo Diffusion MRI Data - Software
No full textDiffusion MRI (dMRI) has become a crucial imaging technique in the field of neuroscience, with a growing number of clinical applications. Although most studies still focus on the brain, there is a growing interest in utilizing dMRI to investigate the healthy or injured spinal cord. The past decade has also seen the development of biophysical models that link MR-based diffusion measures to underlying microscopic tissue characteristics, which necessitates validation through ex vivo dMRI measurements. Building upon 13 years of research and development, we present an open-source, MATLAB-based academic software toolkit dubbed ACID: A Comprehensive Toolbox for Image Processing and Modeling of Brain, Spinal Cord, and Ex Vivo Diffusion MRI Data. ACID is an extension to the Statistical Parametric Mapping (SPM) software, designed to process and model dMRI data of the brain, spinal cord, and ex vivo specimens by incorporating state-of-the-art artifact correction tools, diffusion and kurtosis tensor imaging, and biophysical models that enable the estimation of microstructural properties in white matter. Additionally, the software includes an array of linear and non-linear fitting algorithms for accurate diffusion parameter estimation. By adhering to the Brain Imaging Data Structure (BIDS) data organization principles, ACID facilitates standardized analysis, ensures compatibility with other BIDS-compliant software, and aligns with the growing availability of large databases utilizing the BIDS format. Furthermore, being integrated into the popular SPM framework, ACID benefits from a wide range of segmentation, spatial processing, and statistical analysis tools as well as a large and growing number of SPM extensions. As such, this comprehensive toolbox covers the entire processing chain from raw DICOM data to group-level statistics, all within a single software package
Interaction-Force Transport Gradient Flows
No full textThis paper presents a new gradient flow dissipation geometry over non-negative and probability measures. This is motivated by a principled construction that combines the unbalanced optimal transport and interaction forces modeled by reproducing kernels. Using a precise connection between the Hellinger geometry and the maximum mean discrepancy (MMD), we propose the interaction-force transport (IFT) gradient flows and its spherical variant via an infimal convolution of the Wasserstein and spherical MMD tensors. We then develop a particle-based optimization algorithm based on the JKO-splitting scheme of the mass-preserving spherical IFT gradient flows. Finally, we provide both theoretical global exponential convergence guarantees and improved empirical simulation results for applying the IFT gradient flows to the sampling task of MMD-minimization. Furthermore, we prove that the spherical IFT gradient flow enjoys the best of both worlds by providing the global exponential convergence guarantee for both the MMD and KL energ
Gibbs measures for hardcore-SOS models on Cayley trees
Get PDFWe investigate the finite-state p-solid-on-solid model, for p = ∞, on Cayley trees of order k ≥ 2 and establish a system of functional equations where each solution corresponds to a (splitting) Gibbs measure of the model. Our main result is that, for three states, k = 2, 3 and increasing coupling strength, the number of translation-invariant Gibbs measures behaves as 1 → 3 → 5 → 6 → 7. This phase diagram is qualitatively similar to the one observed for three-state p-SOS models with p > 0 and, in the case of k = 2, we demonstrate that, on the level of the functional equations, the transition p → ∞ is continuous
A Cournot-Nash model for a coupled hydrogen and electricity market
Get PDFWe present a novel model of a coupled hydrogen and electricity market on the intraday time scale, where hydrogen gas is used as a storage device for the electric grid. Electricity is produced by renewable energy sources or by extracting hydrogen from a pipeline that is shared by non-cooperative agents. The resulting model is a generalized Nash equilibrium problem. Under certain mild assumptions, we prove that an equilibrium exists. Perspectives for future work are presented
Generative Models for the Deformation of Industrial Shapes with Linear Geometric Constraints: model order and parameter space reductions
No full textReal-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization studies require the realization of response surfaces from the parameters that determine the geometrical deformations to relevant outputs to be optimized. In this context, a crucial aspect to be addressed are the limited resources at disposal to computationally generate different geometries or to physically obtain them from direct measurements. This is the case for patient-specific biomedical applications for example. When additional linear geometrical constraints need to be imposed, the computational costs increase substantially. Such constraints include total volume conservation, barycenter location and fixed moments of inertia. We develop a new paradigm that employs generative models from machine learning to efficiently sample new geometries with linear constraints. A consequence of our approach is the reduction of the parameter space from the original geometrical parametrization to a low-dimensional latent space of the generative models. Crucial is the assessment of the quality of the distribution of the constrained geometries obtained with respect to physical and geometrical quantities of interest. Non-intrusive model order reduction is enhanced since smaller parametric spaces are considered. We test our methodology on two academic test cases: a mixed Poisson problem on the 3d Stanford bunny with fixed barycenter deformations and the multiphase turbulent incompressible Navier-Stokes equations for the Duisburg test case with fixed volume deformations of the naval hull
Representative Volume Element Approximations in Elastoplastic Spring Networks
No full textWe study the large-scale behavior of a small-strain lattice model for a network composed of elastoplastic springs with random material properties. We formulate the model as an evolutionary rate independent system. In an earlier work we derived a homogenized continuum model, which has the form of linearized elastoplasticity, as an evolutionary Γ-limit as the lattice parameter tends to zero. In the present paper we introduce a periodic representative volume element (RVE) approximation for the homogenized system. As a main result we prove convergence of the RVE approximation as the size of the RVE tends to infinity. We also show that the hysteretic stress-strain relation of the effective system can be described with the help of a generalized Prandtl–Ishlinskii operator, and we prove convergence of a periodic RVE approximation for that operator. We combine the RVE approximation with a numerical scheme for rate-independent systems and obtain a computational scheme that we use to numerically investigate the homogenized system in the specific case when the original network is given by a two-dimensional lattice model. We simulate the response of the system to cyclic and uniaxial, monotonic loading, and numerically investigate the convergence rate of the periodic RVE approximation. In particular, our simulations show that the RVE error decays with the same rate as the RVE error in the static case of linear elasticity
A Monte Carlo Approach for Simulating Electrical Conductivity in Highly Porous Ceramic Composites: Impact of Internal Structure
No full textPorous ceramic composites play an important role in several applications. This is due to their unique properties resulting from a combination of various materials. Determination of the composite properties and structure is crucial for their further development and optimization. However, composite analysis often requires complex, expensive, and time-demanding experimental work. Mathematical modeling represents an effective tool to substitute experimental approach. The present study employs a Monte Carlo 3D equivalent electronic circuit network model developed to analyze a highly porous composite on the basis of minimum easily obtainable input parameters. Solid oxide cell electrodes were used as a model example, and this study focuses primarily on materials with a porosity of 55% and higher, characterized by deviation of behavior from those of lower void fraction share. This task is approached by adding to the original Monte Carlo model an additional parameter defining the void phase coalescence phenomenon. The enhanced model accurately simulates electrical conductivity for experimental samples of up to 75% porosity. Using sample composition, single-phase properties, and experimentally determined conductivity, this model allows us to estimate data of the internal structure of the material. This approach offers a rapid and cost-effective method to study material microstructure, providing insights into properties, such as electrical conductivity and heat conductivity. The present research thus contributes to advancing predictive capabilities in understanding and optimizing the performance of composite materials with potential in various technological applications