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Over the past decades, multiple gyrokinetic codes have shown to be able to simulate turbulence and associated transport in the core of Tokamak devices. However, their application to the edge and scrape-off layer (SOL) region presents significant challenges. To date, only few codes and models have been adapted to SOL/edge conditions. To further study the SOL region in particular, with its steep temperature and density gradients as well as large fluctuation amplitudes, the full-f particle-in-cell code PICLS has been developed. PICLS is based on a full-f gyrokinetic model with linearised field equations, considers kinetic electrons and uses logical sheath boundary conditions. In the past, PICLS was verified by applying it to a well-studied 1D parallel transport problem during an edge-localized mode in the SOL under both collisionless and collisional conditions, for which a Lenard-Bernstein collision operator was implemented. PICLS recently was extended towards three spatial dimensions to study turbulence in open-field-line regions in slab and closed-field-line toroidal geometries. In this work, we will focus on the models and methods we used for extending the code towards three spatial dimensions, including validation efforts and comparisons with other existing codes in closed-field-line geometry

Ring resonators are crucial in silicon photonics for various applications, but conventional designs face performance trade-offs. Here a third-order polynomial interconnected circular (TOPIC) bend is proposed to revolutionize the ring designs fundamentally. The TOPIC bend has a unique feature of continuous curvature and curvature derivative, which is theoretically derived to be essential for waveguide loss optimization. With the TOPIC bend, the silicon ring resonators demonstrated here have achieved three records to the best of our knowledge: the smallest radius (0.7 $\mathrm{\mu m}$) for silicon rings resonating with single guided mode, the lowest thermal tuning power (5.85 mW/$\pi$) for silicon rings with FSR $\geq$3.2 THz, and the first silicon ring-based WDM 32$\times$100 GHz filter. The filter has doubled the channel amount compared to the state of the art, and meanwhile achieved low insertion loss (1.91 $\pm$ 0.28 dB) and low tuning power (283 GHz/mW). Moreover, the TOPIC bend is not limited to ring applications, it can also be used to create bends with an arbitrary angle, with the advantages of ultra-compact radius and heater integration, which are expected to replace all circular bends in integrated photonics, greatly reducing system size and power consumption.

We develop a new approach to the investigation of normalized solutions for nonlinear Schr\"odinger equations based on the analysis of the masses of ground states of the corresponding action functional. Our first result is a complete characterization of the masses of action ground states, obtained via a Darboux-type property for the derivative of the action ground state level. We then exploit this result to tackle normalized solutions with a twofold perspective. First, we prove existence of normalized nodal solutions for every mass in the $L^2$-subcritical regime, and for a whole interval of masses in the $L^2$-critical and supercritical cases. Then, we show when least energy normalized solutions/least energy normalized nodal solutions are action ground states/nodal action ground states., Comment: 21 pages

This paper introduces a novel hypergraph classification algorithm. The use of hypergraphs in this framework has been widely studied. In previous work, hypergraph models are typically constructed using distance or attribute based methods. That is, hyperedges are generated by connecting a set of samples which are within a certain distance or have a common attribute. These methods however, do not often focus on multi-way interactions directly. The algorithm provided in this paper looks to address this problem by constructing hypergraphs which explore multi-way interactions of any order. We also increase the performance and robustness of the algorithm by using a population of hypergraphs. The algorithm is evaluated on two datasets, demonstrating promising performance compared to a generic random forest classification algorithm.

Superconducting diode effects have recently attracted much attention for their potential applications in superconducting logic circuits. Several mechanisms such as magneto-chiral effects, finite momentum Cooper pairing, asymmetric edge currents have been proposed to give rise to a supercurrent diode effect in different materials. In this work, we establish the presence of a large intrinsic Josephson diode effect in a type-II Dirac semimetal $1T-PtTe_2$ facilitated by its helical spin-momentum locking and distinguish it from other extrinsic effects. The magnitude of the Josephson diode effect is shown to be directly correlated to the large second-harmonic component of the supercurrent that is induced by the significant contribution of the topological spin-momentum locked states that promote coherent Andreev processes in the junction. We denote such junctions, where the relative phase between the two harmonics corresponding to charge transfers of $2e$ and $4e$ can be tuned by a magnetic field, as second order ${\phi}_0$-junctions. The direct correspondence between the second harmonic supercurrent component and the diode effect in $1T-PtTe_2$ junctions makes topological semimetals with high transparency an ideal platform to study and implement the Josephson diode effect, while also enabling further research on higher order supercurrent transport in Josephson junctions.

Spatial-Temporal Graph (STG) data is characterized as dynamic, heterogenous, and non-stationary, leading to the continuous challenge of spatial-temporal graph learning. In the past few years, various GNN-based methods have been proposed to solely focus on mimicking the relationships among node individuals of the STG network, ignoring the significance of modeling the intrinsic features that exist in STG system over time. In contrast, modern Selective State Space Models (SSSMs) present a new approach which treat STG Network as a system, and meticulously explore the STG system's dynamic state evolution across temporal dimension. In this work, we introduce Spatial-Temporal Graph Mamba (STG-Mamba) as the first exploration of leveraging the powerful selective state space models for STG learning by treating STG Network as a system, and employing the Spatial-Temporal Selective State Space Module (ST-S3M) to precisely focus on the selected STG latent features. Furthermore, to strengthen GNN's ability of modeling STG data under the setting of selective state space models, we propose Kalman Filtering Graph Neural Networks (KFGN) for dynamically integrate and upgrade the STG embeddings from different temporal granularities through a learnable Kalman Filtering statistical theory-based approach. Extensive empirical studies are conducted on three benchmark STG forecasting datasets, demonstrating the performance superiority and computational efficiency of STG-Mamba. It not only surpasses existing state-of-the-art methods in terms of STG forecasting performance, but also effectively alleviate the computational bottleneck of large-scale graph networks in reducing the computational cost of FLOPs and test inference time. The implementation code is available at: \url{https://github.com/LincanLi98/STG-Mamba}.

To the best of our knowledge, this paper has achieved the lowest thermal tuning power (5.85 mW/pi) for silicon rings with FSR>=3.2 THz, and the first silicon ring-based WDM-32x100 GHz filter., Comment: 3 pages submitted for conference

Isolated Sign Language Recognition (SLR) has mostly been applied on datasets containing signs executed slowly and clearly by a limited group of signers. In real-world scenarios, however, we are met with challenging visual conditions, coarticulated signing, small datasets, and the need for signer independent models. To tackle this difficult problem, we require a robust feature extractor to process the sign language videos. One could expect human pose estimators to be ideal candidates. However, due to a domain mismatch with their training sets and challenging poses in sign language, they lack robustness on sign language data and image-based models often still outperform keypoint-based models. Furthermore, whereas the common practice of transfer learning with image-based models yields even higher accuracy, keypoint-based models are typically trained from scratch on every SLR dataset. These factors limit their usefulness for SLR. From the existing literature, it is also not clear which, if any, pose estimator performs best for SLR. We compare the three most popular pose estimators for SLR: OpenPose, MMPose and MediaPipe. We show that through keypoint normalization, missing keypoint imputation, and learning a pose embedding, we can obtain significantly better results and enable transfer learning. We show that keypoint-based embeddings contain cross-lingual features: they can transfer between sign languages and achieve competitive performance even when fine-tuning only the classifier layer of an SLR model on a target sign language. We furthermore achieve better performance using fine-tuned transferred embeddings than models trained only on the target sign language. The embeddings can also be learned in a multilingual fashion. The application of these embeddings could prove particularly useful for low resource sign languages in the future.

We investigate existence and nonexistence of action ground states and nodal action ground states for the nonlinear Schr\"odinger equation on noncompact metric graphs with rather general boundary conditions. We first obtain abstract sufficient conditions for existence, typical of problems with lack of compactness, in terms of ``levels at infinity'' for the action functional associated with the problems. Then we analyze in detail two relevant classes of graphs. For noncompact graphs with finitely many edges, we detect purely topological sharp conditions preventing the existence of ground states or of nodal ground states. We also investigate analogous conditions of metrical nature. The negative results are complemented by several sufficient conditions to ensure existence, either of topological or metrical nature, or a combination of the two. For graphs with infinitely many edges, all bounded, we focus on periodic graphs and infinite trees. In these cases, our results completely describe the phenomenology. Furthermore, we study nodal domains and nodal sets of nodal ground states and we show that the situation on graphs can be totally different from that on domains of $\mathbb{R}^N$., Comment: 29 pages, 10 figures

This work suggests several methods of uncertainty treatment in multiscale modelling and describes their application to a system of coupled turbulent transport simulations of a tokamak plasma. We propose a method to quantify the usually aleatoric uncertainty of a system in a quasi-stationary state, estimating the mean values and their errors for quantities of interest, which is average heat fluxes in the case of turbulence simulations. The method defines the stationarity of the system and suggests a way to balance the computational cost of simulation and the accuracy of estimation. This allows, contrary to many approaches, to incorporate aleatoric uncertainties in the analysis of the model and to have a quantifiable decision for simulation runtime. Furthermore, the paper describes methods for quantifying the epistemic uncertainty of a model and the results of such a procedure for turbulence simulations, identifying the model's sensitivity to particular input parameters and sensitivity to uncertainties in total. Finally, we introduce a surrogate model approach based on Gaussian Process Regression and present a preliminary result of training and analysing the performance of such a model based on turbulence simulation data. Such an approach shows a potential to significantly decrease the computational cost of the uncertainty propagation for the given model, making it feasible on current HPC systems.

Two-dimensional chromium ditelluride (CrTe2) is a promising ferromagnetic layered material that exhibits long-range ferromagnetic ordering in the monolayer limit. The formation energies of the different possible structural phases (1T, 1H, 2H) calculated from density functional theory (DFT) show that the 1T phase is the ground state, and the energetic transition barriers between the phases, calculated by the nudged elastic band method, are large, on the order of 0.5 eV. The self-consistent Hubbard $U$ correction parameters are calculated for all the phases of CrTe$_2$. The calculated magnetic moment of 1T-CrTe$_2$ with $\geq 2$ layers lies in the plane, whereas the magnetic moment of a monolayer is out-of-plane. Band filling and tensile bi-axial strain cause the magnetic moment of a monolayer to switch from out-of-plane to in-plane, and compressive bi-axial strain in a bilayer causes the magnetic moment to switch from in-plane to out-of-plane. The magnetic anisotropy is shown to originate from the large spin orbit coupling (SOC) of the Te atoms and the anisotropy of the exchange coupling constants $J_{xy}$ and $J_z$ in an XXZ type Hamiltonian. Renormalized spin wave theory using experimental values for the magnetic anisotropy energy and Curie temperatures provides a range of values for the nearest neighbor exchange coupling.

We observe enhanced three-fold symmetric helicity-dependent topological photocurrents using time-domain THz spectroscopy in epitaxially-grown Bi2Se3 with reduced crystallographic twinning. It is established how twinned crystal domains introduce competing responses that obscure inherent nonlinear optical responses of the intrinsic crystal structure. Minimizing this defect reveals strong nonlinear optical response currents whose magnitude and direction depend on the alignment of the excitation to the crystal axes and follow the three-fold rotational symmetry of the crystal structure. Notably, the azimuthal dependence of the photoresponse persists for helical excitations -- an unprecedented result we attribute to the photon drag effect, where the photon momentum acts as an applied in-plane field that is stationary in the laboratory frame. Additionally, the sign of the resultant THz signal inverts when the helicity of incident light is switched from right to left circularly polarized, indicating a reversal of the photocurrent. Our results demonstrate that even extended domain defects can obscure intrinsic physical processes, making the study of single domain thin films crucial to the observation of phenomena that couple topological order and crystal symmetries., Comment: 34 pages, 14 figures

We introduce and derive the Fourier-enhanced 3D electrostatic field solver of the gyrokinetic full-f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily parallelizable and thus save run time. The presented solver is then verified using two different approaches of manufactured solutions. The test setup used for this effort is a pinch geometry with ITG-like electric potential, containing one non-periodic and two periodic directions, one of which will be discrete Fourier transformed. The results of these tests show that in all three dimensions the L2-error decreases with a constant rate close to the ideal prediction, depending on the degree of the chosen basis functions., Comment: 30 pages, 10 figures

We compare ground states for the nonlinear Schr\"odinger equation on metric graphs, defined as global minimizers of the action functional constrained on the Nehari manifold, and least action solutions, namely minimizers of the action among all solutions to the equation. In principle, four alternative cases may take place: ground states do exist (thus coinciding with least action solutions); ground states do not exist while least action solutions do; both ground states and least action solutions do not exist and the levels of the two minimizing problems coincide; both ground states and least action solutions do not exist and the levels of the two minimizing problems are different. We show that in the context of metric graphs all four alternatives do occur. This is accomplished by a careful analysis of doubly constrained variational problems. As a by-product, we obtain new multiplicity results for positive solutions on a wide class of noncompact metric graphs., Comment: 27 pages, 4 figures

Nonreciprocal superconducting devices have attracted growing interest in recent years as they potentially enable directional charge transport for applications in superconducting quantum circuits. Specifically, the superconducting diode effect has been explored in two-terminal devices that exhibit superconducting transport in one current direction while showing dissipative transport in the opposite direction. Here, we exploit multi-terminal Josephson junctions (MTJJs) to engineer magnetic-field-free nonreciprocity in multi-port networks. We show that when treated as a two-port electrical network, a three-terminal Josephson junction (JJ) with an asymmetric graphene region exhibits reconfigurable two-port nonreciprocity. We observe nonreciprocal (reciprocal) transport between superconducting terminals with broken (preserved) spatial mirror symmetry. We explain our observations by considering a circuit-network of JJs with different critical currents.

There is growing interest in using multi-terminal Josephson junctions (MTJJs) as a platform to artificially emulate topological phases and to investigate complex superconducting mechanisms such as quartet and multiplet Cooper pairings. Current experimental signatures in MTJJs have led to conflicting interpretations of the salient features. In this work, we report a collaborative experimental and theoretical investigation of graphene-based four-terminal Josephson junctions. We observe resonant features in the differential resistance maps that resemble those ascribed to multiplet Cooper pairings. To understand these features, we model our junctions using a circuit network of coupled two-terminal resistively and capacitively shunted junctions (RCSJs). Under appropriate bias current, the model predicts that a current flowing between two diagonal terminals in a four-terminal geometry may be represented as a sinusoidal function of a weighted sum of the superconducting phases. We show that starting from a semi-classical model with diffusive current-phase relations, the MTJJ effectively emulates a general form of the expected current-phase relation for multiplet Cooper pairings. Our study therefore suggests that differential resistance measurements alone are insufficient to conclusively distinguish resonant Andreev reflection processes from semi-classical circuit-network effects., Comment: 9 pages, 8 figures

Magnetic transition metal chalcogenides form an emerging platform for exploring spin-orbit driven Berry phase phenomena owing to the nontrivial interplay between topology and magnetism. Here we show that the anomalous Hall effect in pristine Cr2Te3 thin films manifests a unique temperature-dependent sign reversal at nonzero magnetization, resulting from the momentum-space Berry curvature as established by first-principles simulations. The sign change is strain tunable, enabled by the sharp and well-defined substrate/film interface in the quasi-two-dimensional Cr2Te3 epitaxial films, revealed by scanning transmission electron microscopy and depth-sensitive polarized neutron reflectometry. This Berry phase effect further introduces hump-shaped Hall peaks in pristine Cr2Te3 near the coercive field during the magnetization switching process, owing to the presence of strain-modulated magnetic domains. The versatile interface tunability of Berry curvature in Cr2Te3 thin films offers new opportunities for topological electronics., Comment: Main: 9 pages, 5 figures; SI: 5 pages, 9 figures

The surface state of a 3D topological insulator (3DTI) is a spin-momentum locked conductive state, whose large spin hall angle can be used for the energy-efficient spin orbit torque based switching of an overlying ferromagnet (FM). Conversely, the gated switching of the magnetization of a separate FM in or out of the TI surface plane, can turn on and off the TI surface current. The gate tunability of the TI Dirac cone gap helps reduce its sub-threshold swing. By exploiting this reciprocal behaviour, we can use two FM/3DTI heterostructures to design a 1-Transistor 1-magnetic tunnel junction random access memory unit (1T1MTJ RAM) for an ultra low power Processing-in-Memory (PiM) architecture. Our calculation involves combining the Fokker-Planck equation with the Non-equilibrium Green Function (NEGF) based flow of conduction electrons and Landau-Lifshitz-Gilbert (LLG) based dynamics of magnetization. Our combined approach allows us to connect device performance metrics with underlying material parameters, which can guide proposed experimental and fabrication efforts., Comment: 5 pages, 4 figures

Automatic translation from signed to spoken languages is an interdisciplinary research domain, lying on the intersection of computer vision, machine translation and linguistics. Nevertheless, research in this domain is performed mostly by computer scientists in isolation. As the domain is becoming increasingly popular - the majority of scientific papers on the topic of sign language translation have been published in the past three years - we provide an overview of the state of the art as well as some required background in the different related disciplines. We give a high-level introduction to sign language linguistics and machine translation to illustrate the requirements of automatic sign language translation. We present a systematic literature review to illustrate the state of the art in the domain and then, harking back to the requirements, lay out several challenges for future research. We find that significant advances have been made on the shoulders of spoken language machine translation research. However, current approaches are often not linguistically motivated or are not adapted to the different input modality of sign languages. We explore challenges related to the representation of sign language data, the collection of datasets, the need for interdisciplinary research and requirements for moving beyond research, towards applications. Based on our findings, we advocate for interdisciplinary research and to base future research on linguistic analysis of sign languages. Furthermore, the inclusion of deaf and hearing end users of sign language translation applications in use case identification, data collection and evaluation is of the utmost importance in the creation of useful sign language translation models. We recommend iterative, human-in-the-loop, design and development of sign language translation models., Comment: This is the version of the article submitted to peer review to Universal Access in the Information Society. Please refer to "De Coster, M., Shterionov, D., Van Herreweghe, M. et al. Machine translation from signed to spoken languages: state of the art and challenges. Univ Access Inf Soc (2023)." for the published and updated version

New Grad's-Zhdanov module is implemented in the SOLPS-ITER code and applied to ITER impurity transport simulations. Significant difference appears in the helium transport due to improved parallel kinetic coefficients. As a result 30\% decrease of the separatrix-averaged helium relative concentration is observed for the constant helium source and pumping speed. Change of the impurity behaviour is discussed. For the neon changes are less pronounced. For the first time the ion distribution functions are studied in the ITER Scrape-off layer conditions to reveal the origin of the kinetic coefficient improvements and theory limitations., Comment: This is the pre-submission version. The published version can be found using DOI

Self-consistent full-size turbulent-transport simulations of the divertor and SOL of existing tokamaks have recently become feasible. This enables the direct comparison of turbulence simulations against experimental measurements. In this work, we perform a series of diverted Ohmic L-mode discharges on the TCV tokamak, building a first-of-a-kind dataset for the validation of edge turbulence models. This dataset, referred to as TCV-X21, contains measurements from 5 diagnostic systems -- giving a total of 45 1- and 2-D comparison observables in two toroidal magnetic field directions. The dataset is used to validate three flux-driven 3D fluid-turbulence models: GBS, GRILLIX and TOKAM3X. With each model, we perform simulations of the TCV-X21 scenario, tuning the particle and power source rates to achieve a reasonable match of the upstream separatrix value of density and electron temperature. We find that the simulations match the experimental profiles for most observables at the OMP -- both in terms of profile shape and absolute magnitude -- while a poorer agreement is found towards the divertor targets. The match between simulation and experiment is seen to be sensitive to the value of the resistivity, the heat conductivities, the power injection rate and the choice of sheath boundary conditions. Additionally, despite targeting a sheath-limited regime, the discrepancy between simulations and experiment also suggests that the neutral dynamics should be included. The results of this validation show that turbulence models are able to perform simulations of existing devices and achieve reasonable agreement with experimental measurements. Where disagreement is found, the validation helps to identify how the models can be improved. By publicly releasing the experimental dataset, this work should help to guide and accelerate the development of predictive turbulence simulations of the edge and SOL.

New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improved versions of the expressions written in [V. M. Zhdanov. Transport Processes in Multicomponent Plasma, vol. 44. 10 2002.], based on Grad's 21N-moment method. Both explicit and approximate approaches for transport coefficients calculation are considered. Accurate application of this closure for the Braginskii transport equations is discussed. Viscosity dependence on the heat flux is taken into account. Improved expressions are implemented into the SOLPS-ITER code and tested for deuterium and neon ITER cases. Some typos found in [V. M. Zhdanov. Transport Processes in Multicomponent Plasma, vol. 44. 10 2002.] are corrected., Comment: This is the pre-submission version. The published version can be found using DOI

We present the VECMA toolkit (VECMAtk), a flexible software environment for single and multiscale simulations that introduces directly applicable and reusable procedures for verification, validation (V&V), sensitivity analysis (SA) and uncertainty quantification (UQ). It enables users to verify key aspects of their applications, systematically compare and validate the simulation outputs against observational or benchmark data, and run simulations conveniently on any platform from the desktop to current multi-petascale computers. In this sequel to our paper on VECMAtk which we presented last year, we focus on a range of functional and performance improvements that we have introduced, cover newly introduced components, and applications examples from seven different domains such as conflict modelling and environmental sciences. We also present several implemented patterns for UQ/SA and V&V, and guide the reader through one example concerning COVID-19 modelling in detail., Comment: 23 pages, 10 figures

We prove the existence of multiple positive BV-solutions of the Neumann problem $$ \begin{cases} \displaystyle -\left(\frac{u'}{\sqrt{1+u'^2}}\right)'=a(x)f(u)\quad&\mbox{in }(0,1), u'(0)=u'(1)=0,& {cases} $$ where $a(x) > 0$ and $f$ belongs to a class of nonlinear functions whose prototype example is given by $f(u) = -\lambda u + u^p$, for $\lambda > 0$ and $p > 1$. In particular, $f(0)=0$ and $f$ has a unique positive zero, denoted by $u_0$. Solutions are distinguished by the number of intersections (in a generalized sense) with the constant solution $u = u_0$. We further prove that the solutions found have continuous energy and we also give sufficient conditions on the nonlinearity to get classical solutions. The analysis is performed using an approximation of the mean curvature operator and the shooting method., Comment: 28 pages, 1 figure

Relativistic runaway electrons are a major concern in tokamaks. The European framework for Integrated Modelling (EU-IM), facilitates the integration of different plasma simulation tools by providing a standard data structure for communication that enables relatively easy integration of different physics codes. A three-level modelling approach was adopted for runaway electron simulations within the EU-IM. Recently, a number of runaway electron modelling modules have been integrated into this framework. The first level of modelling (Runaway Indicator) is limited to the indication if runaway electron generation is possible or likely. The second level (Runaway Fluid) adopts an approach similar to e.g. the GO code, using analytical formulas to estimate changes in the runaway electron current density. The third level is based on the solution of the electron kinetics. One such code is LUKE that can handle the toroidicity-induced effects by solving the bounce-averaged Fokker-Planck equation. Another approach is used in NORSE, which features a fully nonlinear collision operator that makes it capable of simulating major changes in the electron distribution, for example slide-away. Both codes handle the effect of radiation on the runaway distribution. These runaway-electron modelling codes are in different stages of integration into the EU-IM infrastructure, and into the European Transport Simulator (ETS), which is a fully capable modular 1.5D core transport simulator. ETS with Runaway Fluid was benchmarked to the GO code implementing similar physics. Coherent integration of kinetic solvers requires more effort on the coupling, especially regarding the definition of the boundary between runaway and thermal populations, and on consistent calculation of resistivity. Some of these issues are discussed.

Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. While PEG modification appeared to improve plasma retention and initial infectivity it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy is explored., Comment: 15 pages, 6 figures

Let $\Omega \subset \mathbb{R}^N$, $N \geq 2$, be a smooth bounded domain. We consider the boundary value problem \begin{equation} \label{Plambda-Abstract-ch3} \tag{$P_{\lambda}$} -\Delta u = c_{\lambda}(x) u + \mu |\nabla u|^2 + h(x)\,, \quad u \in H_0^1(\Omega) \cap L^{\infty}(\Omega)\,, \end{equation} where $c_{\lambda}$ and $h$ belong to $L^q(\Omega)$ for some $q > N/2$, $\mu$ belongs to $\mathbb{R} \setminus \{0\}$ and we write $c_{\lambda}$ under the form $c_{\lambda}:= \lambda c_{+} - c_{-}$ with $c_{+} \gneqq 0$, $c_{-} \geq 0$, $c_{+} c_{-} \equiv 0$ and $\lambda \in \mathbb{R}$. Here $c_{\lambda}$ and $h$ are both allowed to change sign. As a first main result we give a necessary and sufficient condition which guarantees the existence of a unique solution to \eqref{Plambda-Abstract-ch3} when $\lambda \leq 0$. Then, assuming that $(P_0)$ has a solution, we prove existence and multiplicity results for $\lambda > 0$. Our proofs rely on a suitable change of variable of type $v = F(u)$ and the combination of variational methods with lower and upper solution techniques.

Applying gyrokinetic simulations for theoretical turbulence and transport studies to the plasma edge and scrape-off layer (SOL) presents significant challenges. To in particular account for steep density and temperature gradients in the SOL, the "full-f" code PICLS was developed. PICLS is a gyrokinetic particle-in-cell (PIC) code and is based on an electrostatic model with a linearized field equation and uses kinetic electrons. In previously published results we were applying PICLS to the well-studied 1D parallel transport problem during an edge-localized mode (ELM) in the SOL without collisions. As an extension to this collision-less case and in preparation for 3D simulations, in this work a collisional model will be introduced. The implemented Lenard-Bernstein collision operator and its Langevin discretization will be shown. Conservation properties of the collision operator as well as a comparison of the collisional and non-collisional case will be discussed., Comment: 6 pages, 3 figures, PET-17 conference

Advanced divertor configurations modify the magnetic geometry of the diverter to achieve a combination of strong magnetic flux expansion, increased connection length and higher divertor volume - to improve detachment stability, neutral/impurity confinement and heat-channel broadening. In this paper, we discuss the modification of the Flux-Coordinate Independent (FCI) turbulence code GRILLIX to treat generalised magnetic geometry, to allow for the investigation of the effect of magnetic geometry on turbulent structures in the edge and SOL. The development of grids and parallel operators from numerically-defined magnetic equilibria is discussed, as is the application of boundary conditions via penalisation, with the finite-width method generalised to treat complex non-conformal boundaries. Initial testing of hyperbolic (advection) and parabolic (diffusion) test cases is presented for the Snowflake scenario., Comment: Submitted for 17th International Workshop on Plasma Edge Theory in Fusion Devices

While in recent years, gyrokinetic simulations have become the workhorse for theoretical turbulence and transport studies in the plasma core, their application to the edge and scrape-off layer (SOL) region presents significant challenges. In particular, steep density and temperature gradients as well as large fluctuation amplitudes call for a "full-f" treatment. To specifically study problems in the SOL region, the gyrokinetic particle-in-cell (PIC) code PICLS has been developed. The code is based on an electrostatic full-f model with linearised field equations and uses kinetic electrons. Here, the well-studied parallel transport problem during an edge-localized mode (ELM) in the SOL shall be investigated for one spatial dimension. The results are compared to previous gyrokinetic continuum and fully kinetic PIC simulations and show good agreement., Comment: 31 pages (including references), 6 figures, 1 table

Turbulent dynamics in the scrape-off layer (SOL) of magnetic fusion devices is intermittent with large fluctuations in density and pressure. Therefore, a model is required that allows perturbations of similar or even larger magnitude to the time-averaged background value. The fluid-turbulence code GRILLIX is extended to such a global model, which consistently accounts for large variation in plasma parameters. Derived from the drift reduced Braginskii equations, the new GRILLIX model includes electromagnetic and electron-thermal dynamics, retains global parametric dependencies and the Boussinesq approximation is not applied. The penalisation technique is combined with the flux-coordinate independent (FCI) approach [F. Hariri and M. Ottaviani, Comput.Phys.Commun. 184:2419, (2013); A. Stegmeir et al., Comput.Phys.Commun. 198:139, (2016)], which allows to study realistic diverted geometries with X-point(s) and general boundary contours. We characterise results from turbulence simulations and investigate the effect of geometry by comparing simulations in circular geometry with toroidal limiter against realistic diverted geometry at otherwise comparable parameters. Turbulence is found to be intermittent with relative fluctuation levels of up to 40% showing that a global description is indeed important. At the same time via direct comparison, we find that the Boussinesq approximation has only a small quantitative impact in a turbulent environment. In comparison to circular geometry the fluctuations are reduced in diverted geometry, which is related to a different zonal flow structure. Moreover, the fluctuation level has a more complex spatial distribution in diverted geometry. Due to local magnetic shear, which differs fundamentally in circular and diverted geometry, turbulent structures become strongly distorted in the perpendicular direction and are eventually damped away towards the X-point.