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Thermal radiative transfer models physical phenomena ranging from supernovas in astrophysics to radiation from a hohlraum striking a fusion target in plasma physics. Transport and absorption of particles in radiative transfer at different rates lead to a complex interaction between the material and particles that involves highly varying time scales. Resolving these effects can require prohibitively small step sizes, which, combined with nonlinear effects and the particle density's high-dimensional phase space, render conventional numerical methods computationally expensive. This work presents an asymptotic--preserving, mass conservative, rank-adaptive, and parallel integrator for a macro--micro decomposition-based dynamical low-rank approximation of the thermal radiative transfer equations. The proposed integrator efficiently incorporates reflection-transmission type boundary conditions in the low-rank factors. It captures the nonlinear effects of thermal radiation and is energy stable with the step size restriction capturing both hyperbolic and parabolic CFL conditions. The efficacy of the proposed integrator is demonstrated with numerical experiments., Comment: 33 pages, 7 figures

Long-term time series forecasting is critical in domains such as finance, economics, and energy, where accurate and reliable predictions over extended horizons drive strategic decision-making. Despite the progress in machine learning-based models, the impact of temporal noise in extended lookback windows remains underexplored, often degrading model performance and computational efficiency. In this paper, we propose a novel framework that addresses these challenges by integrating the Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT) to perform noise reduction and extract robust long-term features. These transformations enable the separation of meaningful temporal patterns from noise in both the time and frequency domains. To complement this, we introduce a lightweight low-rank linear prediction layer that not only reduces the influence of residual noise but also improves memory efficiency. Our approach demonstrates competitive robustness to noisy input, significantly reduces computational complexity, and achieves competitive or state-of-the-art forecasting performance across diverse benchmark datasets. Extensive experiments reveal that the proposed framework is particularly effective in scenarios with high noise levels or irregular patterns, making it well suited for real-world forecasting tasks. The code is available in https://github.com/forgee-master/HADL.

Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide variety of kinetic partial differential equations is the concept of dynamical low-rank approximation (DLRA). In this paper, we consider the thermal radiative transfer equations with Su-Olson closure, leading to a linearized kinetic model. For the conducted theoretical and practical considerations we use a multiplicative splitting of the distribution function that poses additional challenges in finding an energy stable discretization and deriving a hyperbolic Courant-Friedrichs-Lewy (CFL) condition. We propose such an energy stable DLRA scheme that makes use of the augmented basis update & Galerkin integrator. This integrator allows for additional basis augmentations, enabling us to give a mathematically rigorous proof of energy stability and local mass conservation. Numerical examples confirm the derived properties and show the computational advantages of the DLRA scheme compared to a numerical solution of the full system of equations.

Layer factorization has emerged as a widely used technique for training memory-efficient neural networks. However, layer factorization methods face several challenges, particularly a lack of robustness during the training process. To overcome this limitation, dynamical low-rank training methods have been developed, utilizing robust time integration techniques for low-rank matrix differential equations. Although these approaches facilitate efficient training, they still depend on computationally intensive QR and singular value decompositions of matrices with small rank. In this work, we introduce a novel low-rank training method that reduces the number of required QR decompositions. Our approach integrates an augmentation step into a projector-splitting scheme, ensuring convergence to a locally optimal solution. We provide a rigorous theoretical analysis of the proposed method and demonstrate its effectiveness across multiple benchmarks.

CrSBr, a van der Waals material, stands out as an air-stable magnetic semiconductor with appealing intrinsic properties such as crystalline anisotropy, quasi-1D electronic characteristics, layer-dependent antiferromagnetism, and non-linear optical effects. In this study, we investigate the differences between the absorption and emission spectra, focusing on the origin of the emission peak near 1.7 eV observed in the photoluminescence spectrum of CrSBr. Our findings are corroborated by excitation-dependent Raman experiments. Additionally, we explore the anti-Stokes Raman spectra and observe an anomalously high anti-Stokes to Stokes intensity ratio of up to 0.8, which varies significantly with excitation laser power and crystallographic orientation relative to the polarization of the scattered light. This ratio is notably higher than that observed in graphene ($\approx$ 0.1) and MoS$_2$ ($\approx$ 0.4), highlighting the unique vibrational and electronic interactions in CrSBr. Lastly, we examine stimulated Raman scattering and calculate the Raman gain in CrSBr, which attains a value of 1 $\times$ 10$^{8}$ cm/GW, nearly four orders of magnitude higher than that of previously studied three-dimensional systems., Comment: 22 pages, 4 figures

The radiative transfer equation models various physical processes ranging from plasma simulations to radiation therapy. In practice, these phenomena are often subject to uncertainties. Modeling and propagating these uncertainties requires accurate and efficient solvers for the radiative transfer equations. Due to the equation's high-dimensional phase space, fine-grid solutions of the radiative transfer equation are computationally expensive and memory-intensive. In recent years, dynamical low-rank approximation has become a popular method for solving kinetic equations due to the development of computationally inexpensive, memory-efficient and robust algorithms like the augmented basis update \& Galerkin integrator. In this work, we propose a low-rank Monte Carlo estimator and combine it with a control variate strategy based on multi-fidelity low-rank approximations for variance reduction. We investigate the error analytically and numerically and find that a joint approach to balance rank and grid size is necessary. Numerical experiments further show that the efficiency of estimators can be improved using dynamical low-rank approximation, especially in the context of control variates., Comment: 16 pages, 2 figures, 1 table, Submitted to Proceedings of MCQMC 2024

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction approach which evolves the solution on a low-rank manifold in time, making computations feasible at much higher resolutions and reducing the overall run-time and memory footprint. For this, we use a hybrid dynamical low-rank approach based on a collided-uncollided split, i.e., the transport equation is split through a collision source method. Uncollided particles are described using a ray tracer, facilitating the inclusion of boundary conditions and straggling, whereas collided particles are represented using a moment method combined with the dynamical low-rank approximation. Here the energy is treated as a pseudo-time and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. We can reproduce the results of a full-rank reference code at a much lower rank and thus computational cost and memory usage. The solution further achieves comparable accuracy with respect to TOPAS MC as previous deterministic approaches., Comment: to be published in proceedings of M&C 2025

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six--dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

Computing the numerical solution to high-dimensional tensor differential equations can lead to prohibitive computational costs and memory requirements. To reduce the memory and computational footprint, dynamical low-rank approximation (DLRA) has proven to be a promising approach. DLRA represents the solution as a low-rank tensor factorization and evolves the resulting low-rank factors in time. A central challenge in DLRA is to find time integration schemes that are robust to the arising small singular values. A robust parallel basis update & Galerkin integrator, which simultaneously evolves all low-rank factors, has recently been derived for matrix differential equations. This work extends the parallel low-rank matrix integrator to Tucker tensors and general tree tensor networks, yielding an algorithm in which all bases and connecting tensors are evolved in parallel over a time step. We formulate the algorithm, provide a robust error bound, and demonstrate the efficiency of the new integrators for problems in quantum many-body physics, uncertainty quantification, and radiative transfer.

The numerical method of dynamical low-rank approximation (DLRA) has recently been applied to various kinetic equations showing a significant reduction of the computational effort. In this paper, we apply this concept to the linear Boltzmann-Bhatnagar-Gross-Krook (Boltzmann-BGK) equation which due its high dimensionality is challenging to solve. Inspired by the special structure of the non-linear Boltzmann-BGK problem, we consider a multiplicative splitting of the distribution function. We propose a rank-adaptive DLRA scheme making use of the basis update & Galerkin integrator and combine it with an additional basis augmentation to ensure numerical stability, for which an analytical proof is given and a classical hyperbolic Courant-Friedrichs-Lewy (CFL) condition is derived. This allows for a further acceleration of computational times and a better understanding of the underlying problem in finding a suitable discretization of the system. Numerical results of a series of different test examples confirm the accuracy and efficiency of the proposed method compared to the numerical solution of the full system.

We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton's characteristic functions and conservation of luminous flux, and briefly explain the connection with the mathematical theory of optimal transport. We outline several iterative least-squares solvers for our models and demonstrate their performance for a few challenging problems., Comment: 23 pages

This paper introduces a novel neural network-based approach to solving the Monge-Amp\`ere equation with the transport boundary condition, specifically targeted towards optical design applications. We leverage multilayer perceptron networks to learn approximate solutions by minimizing a loss function that encompasses the equation's residual, boundary conditions, and convexity constraints. Our main results demonstrate the efficacy of this method, optimized using L-BFGS, through a series of test cases encompassing symmetric and asymmetric circle-to-circle, square-to-circle, and circle-to-flower reflector mapping problems. Comparative analysis with a conventional least-squares finite-difference solver reveals the competitive, and often superior, performance of our neural network approach on the test cases examined here. A comprehensive hyperparameter study further illuminates the impact of factors such as sampling density, network architecture, and optimization algorithm. While promising, further investigation is needed to verify the method's robustness for more complicated problems and to ensure consistent convergence. Nonetheless, the simplicity and adaptability of this neural network-based approach position it as a compelling alternative to specialized partial differential equation solvers.

Low-Rank Adaptation (LoRA) has become a widely used method for parameter-efficient fine-tuning of large-scale, pre-trained neural networks. However, LoRA and its extensions face several challenges, including the need for rank adaptivity, robustness, and computational efficiency during the fine-tuning process. We introduce GeoLoRA, a novel approach that addresses these limitations by leveraging dynamical low-rank approximation theory. GeoLoRA requires only a single backpropagation pass over the small-rank adapters, significantly reducing computational cost as compared to similar dynamical low-rank training methods and making it faster than popular baselines such as AdaLoRA. This allows GeoLoRA to efficiently adapt the allocated parameter budget across the model, achieving smaller low-rank adapters compared to heuristic methods like AdaLoRA and LoRA, while maintaining critical convergence, descent, and error-bound theoretical guarantees. The resulting method is not only more efficient but also more robust to varying hyperparameter settings. We demonstrate the effectiveness of GeoLoRA on several state-of-the-art benchmarks, showing that it outperforms existing methods in both accuracy and computational efficiency.

Computing the dominant eigenvalue is important in nuclear systems as it determines the stability of the system (i.e. whether the system is sub or supercritical). Recently, the work of Kusch, Whewell, McClarren and Frank \cite{KWMF} showed that performing a low-rank approximation can be very effective in reducing the high memory requirement and computational cost of such problems. In this work, we propose a rank adaptive approach that changes the rank during the inverse power iteration. This allows us to progressively increase the rank (i.e. changing the fidelity of the model) as we get closer to convergence, thereby further reducing computational cost. We then exploit this multi-fidelity approach to optimize a simplified nuclear reactor. In this case the system is parameterized and the values of the parameters that give criticality are sought.

Nanotubes align molecules into one dimensional chains creating collective states through the coupling of the molecular transition dipole moments. These collective excitations have strong fluorescence, narrow bandwidth, and shifted emission/absorption energies. We study the optical properties of {\alpha}-sexithiophene chains in boron nitride nanotubes by combining fluorescence with far- and near-field absorption spectroscopy. The inner nanotube diameter determines the number of encapsulated molecular chains. A single chain of {\alpha}-sexithiophene molecules has an optical absorption and emission spectrum that is red-shifted by almost 300 meV compared to the monomer emission, which is much larger than expected from dipole-dipole coupling. The collective state splits into excitation and emission channels with a Stokes shift of 200 meV for chains with two or more files. Our study emphasises the formation of a delocalized collective state through Coulomb coupling of the transition moments that shows a remarkable tuneability in transition energy.

Near-field optical microscopy and spectroscopy provide high-resolution imaging below the diffraction limit, crucial in physics, chemistry, and biology for studying molecules, nanoparticles, and viruses. These techniques use a sharp metallic tip of an atomic force microscope (AFM) to enhance incoming and scattered light by excited near-fields at the tip apex leading to high sensitivity and a spatial resolution of a few nanometers. However, this restricts the near-field orientation to out-of-plane polarization, limiting optical polarization choices. We introduce double tips that offer in-plane polarization for enhanced imaging and spectroscopy. These double tips provide superior enhancement over single tips, although with a slightly lower spatial resolution (~30nm). They enable advanced studies of nanotubes, graphene defects, and transition metal dichalcogenides, benefiting from polarization control. The double tips allow varied polarization in tip-enhanced Raman scattering and selective excitation of transverse-electric and -magnetic polaritons, expanding the range of nanoscale samples that can be studied.

Alloying small quantities of silver into Cu(In,Ga)Se2 was shown to improve the efficiency for wide and low band gap solar cells. We study low band gap industrial Cu(In,Ga)(S,Se)2 absorbers, substituting less than 10% of the copper with silver, using absolute photoluminescence and cathodoluminescence spectroscopy. Silver improves the grain size and promotes the interdiffusion of Ga and In across the depth of the absorber, resulting in a smoother band gap gradient. However, a certain lateral inhomogeneity is observed near the front and back sides. The non-radiative losses in the bare absorbers are reduced by up to 30 meV.

Due to its reduced memory and computational demands, dynamical low-rank approximation (DLRA) has sparked significant interest in multiple research communities. A central challenge in DLRA is the development of time integrators that are robust to the curvature of the manifold of low-rank matrices. Recently, a parallel robust time integrator that permits dynamic rank adaptation and enables a fully parallel update of all low-rank factors was introduced. Despite its favorable computational efficiency, the construction as a first-order approximation to the augmented basis-update & Galerkin integrator restricts the parallel integrator's accuracy to order one. In this work, an extension to higher order is proposed by a careful basis augmentation before solving the matrix differential equations of the factorized solution. A robust error bound with an improved dependence on normal components of the vector field together with a norm preservation property up to small terms is derived. These analytic results are complemented and demonstrated through a series of numerical experiments.

The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type equation called the Rosseland approximation. The main challenges for constructing numerical schemes that exhibit the correct limiting behavior are posed by the solution's high-dimensional phase space and multi-scale effects. In this work, we propose an asymptotic-preserving and rank-adaptive dynamical low-rank approximation scheme based on the macro-micro decomposition of the particle density and a modified augmented basis-update \& Galerkin integrator. We show that this scheme, for linear particle emission by the material, dissipates energy over time under a step size restriction that captures the hyperbolic and parabolic CFL conditions. We demonstrate the efficacy of the proposed method in a series of numerical experiments., Comment: 32 pages, 5 figures

Dynamical low-rank approximation has become a valuable tool to perform an on-the-fly model order reduction for prohibitively large matrix differential equations. A core ingredient is the construction of integrators that are robust to the presence of small singular values and the resulting large time derivatives of the orthogonal factors in the low-rank matrix representation. Recently, the robust basis-update & Galerkin (BUG) class of integrators has been introduced. These methods require no steps that evolve the solution backward in time, often have favourable structure-preserving properties, and allow for parallel time-updates of the low-rank factors. The BUG framework is flexible enough to allow for adaptations to these and further requirements. However, the BUG methods presented so far have only first-order robust error bounds. This work proposes a second-order BUG integrator for dynamical low-rank approximation based on the midpoint rule. The integrator first performs a half-step with a first-order BUG integrator, followed by a Galerkin update with a suitably augmented basis. We prove a robust second-order error bound which in addition shows an improved dependence on the normal component of the vector field. These rigorous results are illustrated and complemented by a number of numerical experiments.

Global neural dynamics emerge from multi-scale brain structures, with neurons communicating through synapses to form transiently communicating networks. Network activity arises from intercellular communication that depends on the structure of connectome tracts and local connection, intracellular signalling cascades, and the extracellular molecular milieu that regulate cellular properties. Multi-scale models of brain function have begun to directly link the emergence of global brain dynamics in conscious and unconscious brain states to microscopic changes at the level of cells. In particular, AdEx mean-field models representing statistical properties of local populations of neurons have been connected following human tractography data to represent multi-scale neural phenomena in simulations using The Virtual Brain (TVB). While mean-field models can be run on personal computers for short simulations, or in parallel on high-performance computing (HPC) architectures for longer simulations and parameter scans, the computational burden remains high and vast areas of the parameter space remain unexplored. In this work, we report that our TVB-HPC framework, a modular set of methods used here to implement the TVB-AdEx model for GPU and analyze emergent dynamics, notably accelerates simulations and substantially reduces computational resource requirements. The framework preserves the stability and robustness of the TVB-AdEx model, thus facilitating finer resolution exploration of vast parameter spaces as well as longer simulations previously near impossible to perform. Given that simulation and analysis toolkits are made public as open-source packages, our framework serves as a template onto which other models can be easily scripted and personalized datasets can be used for studies of inter-individual variability of parameters related to functional brain dynamics., Comment: 21 pages, 9 figures

We present the performance of a full-length prototype of the ALICE Forward Calorimeter (FoCal). The detector is composed of a silicon-tungsten electromagnetic sampling calorimeter with longitudinal and transverse segmentation (FoCal-E) of about 20$X_0$ and a hadronic copper-scintillating-fiber calorimeter (FoCal-H) of about 5$\lambda_{\rm int}$. The data were taken between 2021 and 2023 at the CERN PS and SPS beam lines with hadron (electron) beams up to energies of 350 (300) GeV. Regarding FoCal-E, we report a comprehensive analysis of its response to minimum ionizing particles across all pad layers. The longitudinal shower profile of electromagnetic showers is measured with a layer-wise segmentation of 1$X_0$. As a projection to the performance of the final detector in electromagnetic showers, we demonstrate linearity in the full energy range, and show that the energy resolution fulfills the requirements for the physics needs. Additionally, the performance to separate two-showers events was studied by quantifying the transverse shower width. Regarding FoCal-H, we report a detailed analysis of the response to hadron beams between 60 and 350 GeV. The results are compared to simulations obtained with a Geant4 model of the test beam setup, which in particular for FoCal-E are in good agreement with the data. The energy resolution of FoCal-E was found to be lower than 3% at energies larger than 100 GeV. The response of FoCal-H to hadron beams was found to be linear, albeit with a significant intercept that is about factor 2 larger than in simulations. Its resolution, which is non-Gaussian and generally larger than in simulations, was quantified using the FWHM, and decreases from about 16% at 100 GeV to about 11% at 350 GeV. The discrepancy to simulations, which is particularly evident at low hadron energies, needs to be further investigated., Comment: 57 pages (without acronyms), 45 captioned figures

Numerical simulations of kinetic problems can become prohibitively expensive due to their large memory footprint and computational costs. A method that has proven to successfully reduce these costs is the dynamical low-rank approximation (DLRA). One key question when using DLRA methods is the construction of robust time integrators that preserve the invariances and associated conservation laws of the original problem. In this work, we demonstrate that the augmented basis update & Galerkin integrator (BUG) preserves solution invariances and the associated conservation laws when using a conservative truncation step and an appropriate time and space discretization. We present numerical comparisons to existing conservative integrators and discuss advantages and disadvantages

We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. Building on the findings of the work \cite{gotoh2018robust}, we study the connections between a class of DRO and the Taguchi method in the context of robust design optimization. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

Nonlinear optical effects are used to generate coherent light at wavelengths difficult to reach with lasers. Materials periodically poled or nanostructured in the nonlinear susceptibility in three spatial directions are called 3D nonlinear photonic crystals (NPhCs). They enable enhanced nonlinear optical conversion efficiencies, emission control, and simultaneous generation of nonlinear wavelengths. The chemical inertness of efficient second-order nonlinear materials ($\chi^{(2)}$) prohibited their nanofabrication until 2018. The current method is restricted to top-down laser-based techniques limiting the periodicity along z-axis to 10 um. We demonstrate the first bottom-up fabricated 3D NPhC in sol-gel derived barium titanate by soft-nanoimprint lithography: a woodpile with eight layers and periodicities of 1 um (xy-plane) and 300 nm (z-plane). The surface areas exceed $5.3\cdot 10^4$ um^2, which is two orders of magnitude larger than the state-of-the-art. This study is expected to initiate bottom-up fabrication of 3D NPhCs with a supremely strong and versatile nonlinear response., Comment: 11 pages, 4 figures

In this article we examine recent developments in the research area concerning the creation of end-to-end models for the complete optimization of measuring instruments. The models we consider rely on differentiable programming methods and on the specification of a software pipeline including all factors impacting performance -- from the data-generating processes to their reconstruction and the extraction of inference on the parameters of interest of a measuring instrument -- along with the careful specification of a utility function well aligned with the end goals of the experiment. Building on previous studies originated within the MODE Collaboration, we focus specifically on applications involving instruments for particle physics experimentation, as well as industrial and medical applications that share the detection of radiation as their data-generating mechanism., Comment: 70 pages, 17 figures. To be submitted to journal

Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is dynamical low-rank approximation (DLRA), which represents and evolves the solution on a low-rank manifold, thereby significantly decreasing computational and memory requirements. Efficient discretizations for the DLRA evolution equations need to be carefully constructed to guarantee stability while enabling mass conservation. In this work, we focus on the Su-Olson closure leading to a linearized internal energy model and derive a stable discretization through an implicit coupling of internal energy and particle density. Moreover, we propose a rank-adaptive strategy to preserve local mass conservation. Numerical results are presented which showcase the accuracy and efficiency of the proposed low-rank method compared to the solution of the full system.

Record efficiency in chalcopyrite-based solar cells Cu(In,Ga)(S,Se)2 is achieved using a gallium gradient to increase the band gap of the absorber towards the back side. Although this structure has successfully reduced recombination at the back contact, we demonstrate that in industrial absorbers grown in the pilot line of Avancis, the back part is a source of non-radiative recombination. Depth-resolved photoluminescence (PL) measurements reveal two main radiative recombination paths at 1.04 eV and 1.5-1.6 eV, attributed to two phases of low and high band gap material, respectively. Instead of a continuous change in the band gap throughout the thickness of the absorber, we propose a model where discrete band gap phases interlace, creating an apparent gradient. Cathodoluminescence and Raman scattering spectroscopy confirm this result. Additionally, deep defects associated to the high gap phase reduce the absorber performance. Etching away the back part of the absorber leads to an increase of one order of magnitude in the PL intensity, i.e., 60 meV in quasi Fermi level splitting. Non-radiative voltage losses correlate linearly with the relative contribution of the high energy PL peak, suggesting that reducing the high gap phase could increase the open circuit voltage by up to 180 mV.

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes them as the product of two small rank matrices. However, this approach typically requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization. In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics independently of the initialization. Furthermore, the rank of each mode is dynamically updated during training. We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

This work introduces a parallel and rank-adaptive matrix integrator for dynamical low-rank approximation. The method is related to the previously proposed rank-adaptive basis update & Galerkin (BUG) integrator but differs significantly in that all arising differential equations, both for the basis and the Galerkin coefficients, are solved in parallel. Moreover, this approach eliminates the need for a potentially costly coefficient update with augmented basis matrices. The integrator also incorporates a new step rejection strategy that enhances the robustness of both the parallel integrator and the BUG integrator. By construction, the parallel integrator inherits the robust error bound of the BUG and projector-splitting integrators. Comparisons of the parallel and BUG integrators are presented by a series of numerical experiments which demonstrate the efficiency of the proposed method, for problems from radiative transfer and radiation therapy.

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques that allow for efficient and accurate simulations while guaranteeing physical properties like mass conservation. In this paper, we develop the first model reduction for the hyperbolic shallow water moment equations and achieve mass conservation. This is accomplished using a macro-micro decomposition of the model into a macroscopic (conservative) part and a microscopic (non-conservative) part with subsequent model reduction using either POD-Galerkin or dynamical low-rank approximation only on the microscopic (non-conservative) part. Numerical experiments showcase the performance of the new model reduction methods including high accuracy and fast computation times together with guaranteed conservation and consistency properties., Comment: Code available under https://github.com/JonasKu/Publication-Split-conservative-model-order-reduction-for-hyperbolic-shallow-water-moment-equations

We probe the extent to which dislocations reduce carrier lifetimes and alter luminescence and growth morphology in InAs quantum dots (QD) grown on silicon. These heterostructures are key ingredients to achieving a highly reliable monolithically integrated light source on silicon necessary for photonic integrated circuits. We find up to 20-30% shorter carrier lifetimes at spatially resolved individual dislocations from both the QD ground and excited states at room temperature using time-resolved cathodoluminescence spectroscopy. These lifetimes are consistent with differences in the intensity measured under steady-state excitation suggesting that trap-assisted recombination limits the minority carrier lifetime, even away from dislocations. Our techniques also reveal the dramatic growth of misfit dislocations in these structures under carrier injection fueled by recombination-enhanced dislocation glide and III-V/Si residual strain. Beyond these direct effects of increased nonradiative recombination, we find the long-range strain field of misfit dislocations deeper in the defect filter layers employed during III-V/Si growth alter the QD growth environment and introduce a crosshatch-like variation in the QD emission color and intensity when the filter layer is positioned close to the QD emitter layer. Sessile threading dislocations generate even more egregious hillock defects that also reduce emission intensities by altering layer thicknesses, as measured by transmission electron microscopy and atom probe tomography. Our work presents a more complete picture of the impacts of dislocations relevant for the development of light sources for scalable silicon photonic integrated circuits., Comment: 15 pages, 6 figures

Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computational costs and memory footprint in such settings is dynamical low-rank approximation (DLRA). Despite its efficiency, numerical methods for DLRA need to be carefully constructed to guarantee stability while preserving crucial properties of the original problem. Important physical effects that one likes to preserve with DLRA include capturing the diffusion limit in the high-scattering regimes as well as dissipating energy. In this work we propose and analyze a dynamical low-rank method based on the "unconventional" basis-update & Galerkin step integrator. We show that this method is asymptotic-preserving, i.e., it captures the diffusion limit, and energy stable under a CFL condition. The derived CFL condition captures the transition from the hyperbolic to the parabolic regime when approaching the diffusion limit.

The optimization criterion for dividends from a risky business is most often formalized in terms of the expected present value of future dividends. That criterion disregards a potential, explicit demand for stability of dividends. In particular, within actuarial risk theory, maximization of future dividends have been intensively studied as the so-called de Finetti problem. However, there the optimal strategies typically become so-called barrier strategies. These are far from stable and suboptimal affine dividend strategies have therefore received attention recently. In contrast, in the class of linear-quadratic problems a demand for stability if explicitly stressed. These have most often been studied in diffusion models different from the actuarial risk models. We bridge the gap between these patterns of thinking by deriving optimal affine dividend strategies under a linear-quadratic criterion for a general L\'evy process. We characterize the value function by the Hamilton-Jacobi-Bellman equation, solve it, and compare the objective and the optimal controls to the classical objective of maximizing expected present value of future dividends. Thereby we provide a framework within which stability of dividends from a risky business, as e.g. in classical risk theory, is explicitly demanded and explicitly obtained.