Numerical Toolkit Research Articles

An experimental and numerical framework to assess the temperature distribution in complex He II-cooled magnet geometries

In the context of the High Luminosity upgrade of the Large Hadron Collider at CERN, a framework implementing experimental techniques and numerical analysis has been developed to systematically assess the temperature distribution in complex He II-cooled composite magnet geometries. The experiments are designed to measure the heat transfer coefficients in the magnet coil layers using coil samples in a stagnant superfluid helium bath. A numerical tool-kit has been developed to facilitate intensive parametric studies, in addition to estimation of helium content via a phenomenological model. The workflow of the tool-kit is built to handle complex geometries composed of different materials each with their temperature-dependent properties, at low computational cost. This framework has been validated with experimental data obtained from laboratory-scale experiments on impregnated coil samples, reported and discussed here. Three use cases for the developed numerical tool, with increasing levels of complexity, are presented and its results discussed.

Analyzing warp drive spacetimes with Warp Factory

The field of warp research has been dominated by analytical methods to investigate potential solutions. However, these approaches often favor simple metric forms that facilitate analysis but ultimately limit the range of exploration of novel solutions. So far the proposed solutions have been unphysical, requiring energy condition violations and large energy requirements. To overcome the analytical limitations in warp research, we introduce Warp Factory: a numerical toolkit designed for modeling warp drive spacetimes. By leveraging numerical analysis, Warp Factory enables the examination of general warp drive geometries by evaluating the Einstein field equations and computing energy conditions. Furthermore, this comprehensive toolkit provides the determination of metric scalars and insightful visualizations in both 2D and 3D, offering a deeper understanding of metrics and their corresponding stress–energy tensors. The paper delves into the methodology employed by Warp Factory in evaluating the physicality of warp drive spacetimes and highlights its application in assessing commonly modeled warp drive metrics. By leveraging the capabilities of Warp Factory, we aim to further warp drive research and hopefully bring us closer to realizing physically achievable warp drives.

PyMoosh: a comprehensive numerical toolkit for computing the optical properties of multilayered structures

We present PyMoosh, a Python-based simulation library designed to provide a comprehensive set of numerical tools allowing the computation of essentially all optical characteristics of multilayered structures, ranging from reflectance and transmittance to guided modes and photovoltaic efficiency. PyMoosh is designed not just for research purposes, but also for use cases in education. To this end, we have invested significant effort in ensuring the user-friendliness and simplicity of the interface. PyMoosh has been developed in line with the principles of open science and considering the fact that multilayered structures are increasingly being used as a testing ground for optimization and deep learning approaches. We provide in this paper the theoretical basis at the core of PyMoosh, an overview of its capabilities, as well as a comparison between the different numerical methods implemented in terms of speed and stability. We are convinced such a versatile tool will be useful for the community in many ways.

A Level Set-Based Solver for Two-Phase Incompressible Flows: Extension to Magnetic Fluids

Development of a two-phase incompressible solver for magnetic flows in the magnetostatic case is presented. The proposed numerical toolkit couples the Navier–Stokes equations of hydrodynamics with Maxwell's equations of electromagnetism to model the behaviour of magnetic flows in the presence of a magnetic field. To this end, a rigorous implementation of a second-order two-phase solver for incompressible nonmagnetic flows is introduced first. This solver is implemented in the finite-difference framework, where a fifth-order conservative level set method is employed to capture the evolution of the interface, along with an incompressible solver based on the projection scheme to model the fluids. The solver demonstrates excellent performance even with high density ratios across the interface (Atwood number ≈ 1 ), while effectively preserving the mass conservation property. Subsequently, the numerical discretisation of Maxwell's equations under the magnetostatic assumption is described in detail, utilising the vector potential formulation. The primary second-order solver for two-phase flows is extended to the case of magnetic flows, by incorporating the Lorentz force into the momentum equation, accounting for high magnetic permeability ratios across the interface. The implemented solver is then utilised for examining the deformation of ferrofluid droplets in both quiescent and shear flow regimes across various susceptibility values of the droplets. The results suggest that increasing the susceptibility value of the ferrofluid droplet can affect its deformation and rotation in low capillary regimes. In higher capillary flows, increasing the magnetic permeability jump across the interface can further lead to droplet breakup as well. The effect of this property is also investigated for the Rayleigh–Taylor instability growth in magnetic fluids.

A Combined Usage of NLP Libraries Towards Analyzing Software Documents

Software documents are commonly processed by natural language processing (NLP) libraries to extract information. The libraries provide similar functional APIs to achieve NLP tasks, numerous toolkits result in a problem of selection. In this work, we propose a method to combine the strengths of different NLP libraries to avoid the subjective selection of a specific NLP library. The combined usage is conducted through two steps, i.e. document-level selection of primary NLP library and sentence-level overwriting. The primary NLP library is determined according to the overlap degree of the results. The highest overlap degree indicated the most effective NLP library on a specific NLP task. Through sentence-level overwriting, the possible fine-gained improvements from other libraries are extracted to overwrite the outputs of primary library. We evaluate the combined method with six widely used NLP libraries and 200 documents from three different sources. The results show that the combined method can generally outperform all the studied NLP libraries in terms of accuracy. The finding means that our combined method can be used instead of individual NLP library for more effective results.

Seeing Like a Toolkit: How Toolkits Envision the Work of AI Ethics

Numerous toolkits have been developed to support ethical AI development. However, toolkits, like all tools, encode assumptions in their design about what work should be done and how. In this paper, we conduct a qualitative analysis of 27 AI ethics toolkits to critically examine how the work of ethics is imagined and how it is supported by these toolkits. Specifically, we examine the discourses toolkits rely on when talking about ethical issues, who they imagine should do the work of ethics, and how they envision the work practices involved in addressing ethics. Among the toolkits, we identify a mismatch between the imagined work of ethics and the support the toolkits provide for doing that work. In particular, we identify a lack of guidance around how to navigate labor, organizational, and institutional power dynamics as they relate to performing ethical work. We use these omissions to chart future work for researchers and designers of AI ethics toolkits.

Measuring Encapsulation Efficiency in Cell-Mimicking Giant Unilamellar Vesicles.

One of the main drivers within the field of bottom-up synthetic biology is to develop artificial chemical machines, perhaps even living systems, that have programmable functionality. Numerous toolkits exist to generate giant unilamellar vesicle-based artificial cells. However, methods able to quantitatively measure their molecular constituents upon formation is an underdeveloped area. We report an artificial cell quality control (AC/QC) protocol using a microfluidic-based single-molecule approach, enabling the absolute quantification of encapsulated biomolecules. While the measured average encapsulation efficiency was 11.4 ± 6.8%, the AC/QC method allowed us to determine encapsulation efficiencies per vesicle, which varied significantly from 2.4 to 41%. We show that it is possible to achieve a desired concentration of biomolecule within each vesicle by commensurate compensation of its concentration in the seed emulsion. However, the variability in encapsulation efficiency suggests caution is necessary when using such vesicles as simplified biological models or standards.

Burnout: A Call to Action From the AUA Workforce Workgroup.

We hypothesize burnout has failed to improve and certain demographics may be disproportionately affected. The AUA Workforce Workgroup examined work from the annual AUA Census over the past several years. Particular to this study, relevant burnout-related data were examined from the past 5 years. In 2021, 36.7% of urologists reported burnout compared to 36.2% in 2016. Burnout in men decreased from 36.3% to 35.2%, but increased in women from 35.3% to 49.2%. When examined by age, the largest increases in burnout were seen in those <45 years old, increasing from 37.9% to 44.8%, followed by 45-54 years old, increasing from 43.4% to 44.6%. When asked about the effect of COVID-19 on burnout, 54% of urologists didn't feel COVID-19 impacted burnout. Beyond burnout, only 25.0% of men and 4.6% of women reported no conflict between work and personal responsibilities, while 25.7% of men and 44.7% of women resolved these conflicts in favor of work or were unable to resolve them. Of respondents, 22.5% of men and 37.1% of women were "dissatisfied" with work-life balance. Similarly, 33.6% of men reported their work schedule does not leave enough time for personal/family life, compared to 57.5% of women. Overall, urologists have higher burnout now when compared to 2016. The gender discrepancy has vastly widened with women experiencing burnout at an increased rate of 14% compared to 2016, while burnout in men decreased by 1%. Burnout has increased the most in those <45 years old. Further action is needed to substantiate the causes of burnout.

Addressing Maternal Mental Health: Progress, Challenges, and Potential Solutions

Addressing Maternal Mental Health: Progress, Challenges, and Potential Solutions

A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure

Characterizing stellar convection in multiple dimensions is a topic at the forefront of stellar astrophysics. Numerical simulations are an essential tool for this task. We present an extension of the existing numerical tool-kit A-MaZe that enables such simulations of stratified flows in a gravitational field. The finite-volume based, cell-centered, and time-explicit hydrodynamics solver of A-MaZe was extended such that the scheme is now well-balanced in both momentum and energy. The algorithm maintains an initially static balance between gravity and pressure to machine precision. Quasi-stationary convection in slab-geometry preserves gas energy (internal plus kinetic) on average, despite strong local up- and down-drafts. By contrast, a more standard numerical scheme is demonstrated to result in substantial gains of energy within a short time on purely numerical grounds. The test is further used to point out the role of dimensionality, viscosity, and Rayleigh number for compressible convection. Applications to a young sun in 2D and 3D, covering a part of the inner radiative zone, as well as the outer convective zone, demonstrate that the scheme meets its initial design goal. Comparison with results obtained for a physically identical setup with a time-implicit code show qualitative agreement.

Refinement and Application of a Generic CFD Toolkit Covering the Heat Flows in Combined Solid-Liquid Systems to Investigate Thermal Quench Limits of Superconducting Magnets

The recently developed robust multiregion numerical toolkit for the modeling of heat flows in combined solid-liquid systems is extended to cover larger temperature domains, crossing the superfluid (HeII) to normal helium (HeI) phase transition, and to include NbTi cables that feature open electrical insulation, porous to superfluid helium. The aim is to probe the influence of thermal design details on the temperature margin of superconducting magnets. The model enhancements are discussed and the model is applied to analyze the results of a particle beam loss test in an LHC main dipole. We show and quantify the degree to which the build characteristics of the superconducting magnet, such as electrical insulation and interlayer fishbones, influence the local temperature margin and, hence, the quench level seen by the magnet.

Development and application of a generic CFD toolkit covering the heat flows in combined solid–liquid systems with emphasis on the thermal design of HiLumi superconducting magnets

The main objective of this work is to develop a robust multi-region numerical toolkit for the modeling of heat flows in combined solid–liquid systems. Specifically heat transfer in complex cryogenic system geometries involving super-fluid helium. The incentive originates from the need to support the design of superconductive magnets in the framework of the HiLumi-LHC project (Brüning and Rossi, 2015) [1]. The intent is, instead of solving heat flows in restricted domains, to be able to model a full magnet section in one go including all relevant construction details as accurately as possible. The toolkit was applied to the so-called MQXF quadrupole magnet design. Parametrisation studies were used to find a compromise in thermal design and electro-mechanical construction constraints. The cooling performance is evaluated in terms of temperature margin of the magnets under full steady state heat load conditions and in terms of maximal sustainable load. We also present transient response to pulse heat loads of varying duration and power and the system response to time-varying cold source temperatures.

A numerical toolkit to understand the mechanics of partially saturated granular materials

The mechanisms by which a wetting, non-saturating liquid bestows macroscopic cohesion and strength to a granular material are usually not accessible to micromechanical investigations for saturations exceeding the pendular regime of isolated menisci, easily studied by discrete element models (DEM). The paper by Delenne et al. (J. Fluid Mech., 2015, vol. 762, R5) exploiting a multiphase lattice Boltzmann approach, pioneers the simulation of the micromorphology and of the mechanical effects on grains of an interstitial liquid, in equilibrium with its vapour, for the whole saturation range. Interestingly, in accordance with some experiments and phenomenological models, the results suggest that the mechanical effect of capillary forces is maximized for some intermediate saturation level (near 40 % in the model), well beyond the pendular range. In general, the proposed simulation technique opens the way to many studies of partially saturated granular assemblies, for different saturation or imbibition processes and histories.

In support of urban adaptation: a participatory assessment process for secondary cities in Vietnam and Bangladesh

Vietnam and Bangladesh are countries already impacted by weather-related extreme events. Scientific modelling projections indicate that climate change, and changes to climate variability, will increase risks for both countries in the future. Targeting this challenging contemporary agenda, this paper reflects on the lessons learned from a collaborative research project, funded by the Asia Pacific Network for Global Change Research, which was carried out jointly in the Vietnamese city of Huế and the Bangladeshi city of Satkhira. The focus on secondary cities was intentional as they face unique challenges – a combination of rapid growth and development, adverse climate-related impacts, and in many cases less institutional adaptive capacity than their primary city counterparts. Whilst numerous assessment tool kits already exist, these have typically been developed for rural or natural resource contexts. Therefore, the objective of this action research activity was to develop a flexible suite of participatory assessment tools and methodologies that were refined specifically for the urban context; as well as being easy to use by local practitioners at the city and neighbourhood scales. This paper summarizes the research and stakeholder engagement activity that was carried out before presenting the main findings from each of the case study cities (detailing both climate-related risks and potential adaptation options). This analysis is further extended to include a reflective critique of the assessment process, a comparative analysis of the activity carried out in the two case studies, and the ‘South–South’ learning process that occurred between project partners. Key findings are then distilled to put forward recommendations in support of climate change assessment activity in secondary cities across the Asia-Pacific region.

Numerical toolkit for electronic quantum transport at finite frequency

Building on the many existing algorithms for calculating the DC transport properties of quantum tight-binding models, we develop a systematic approach that expresses finite frequency observables in terms of the stationary Green's function of the system, i.e. the natural output of most DC numerical codes. Our framework allows to extend the simulations capabilities of existing codes to a large class of observables including, for instance, AC conductance, quantum capacitance, quantum pumping, spin pumping or photo-assisted shot noise. The theory is developed within the framework of Keldysh formalism and we provide explicit links with the alternative (and equivalent) scattering approach. We illustrate the formalism with a study of the AC conductance in a quantum point contact and an electronic Mach-Zehnder interferometer in the quantum Hall regime.

Quench sensitivity to defects and shear banding in nematic polymer film flows

A flow-orientation algorithm [S. Heidenreich, S. Hess, M.G. Forest, X. Yang, R. Zhou, Robustness of pulsating jet-like layers in sheared nano-rod dispersions, J. Non-Newtonian Fluid Mech., in press, doi:10.1016/j.physletb.2003.10.071; X. Yang, Z. Cui, M.G. Forest, J. Shen, Q. Wang, Dimensional robustness and instability of sheared, semi-dilute, nano-rod dispersions, SIAM Multiscale Model. Simul. 7 (2008) 622–654] for nematic (liquid crystalline) polymer films is coupled with the homogenized effective conductivity tensor of the rod-matrix composite [H. Zhou, X. Zheng, M.G. Forest, Q. Wang, R. Lipton, Extension-enhanced conductivity of liquid crystalline polymer nano-composites, Macromol. Symp. 28 (2005) 81–85; X. Zheng, M.G. Forest, R. Lipton, R. Zhou, Q. Wang, Exact scaling laws for electrical conductivity properties of nematic polymer nano-composite monodomains, Adv. Funct. Mater. 15 (4) (2005) 627–638; X. Zheng, M.G. Forest, R. Zhou, Q. Wang, R. Lipton, Anisotropy and dynamic ranges in effective properties of sheared nematic polymer nano-composites, Adv. Funct. Mater. 15 (2005) 2029–2035; X. Zheng, M.G. Forest, R. Lipton, R. Zhou, Nematic polymer mechanics: flow-induced anisotropy, Continuum Mech. Thermodyn. 18 (2007) 377–394; X. Zheng, M.G. Forest, R. Vaia, M. Arlen, A strategy for dimensional percolation in sheared nano-rod dispersions, Adv. Mater. 19 (22) (2007) 4038–4043] to simulate a simultaneous thermal quench and arrest of the film flow. The final orientational morphology yields nematic polymer film features that determine film performance: anisotropy and heterogeneity in the thermal conductivity tensor, and residual shear and normal stresses. With this numerical toolkit, we amplify an inherent source of nematic polymer film non-uniformity for identical processing conditions. It is well-known that steady parallel plate driving conditions yield unsteady nematic polymer behavior such as director tumbling and wagging, defects, and shear bands. We show that the timing of initial cooling and arrest of plate motion produces different solid films, even with identical isothermal and quench protocols! Simulations show flow reversal and gradient elasticity bands are created when the quench and plate arrest are applied in phase with isothermal shear bands and defect layers, reminiscent of effects reported for small molar mass liquid crystals [R.S. Akopyan, R.B. Alaverdian, E.A. Santrosian, Y.S. Chilingarian, Thermomechanical effects in the nematic liquid crystals, J. Appl. Phys. 90 (2001) 3371–3376; R.S. Hakobyan, G.L. Yesayan, B.Y. Zeldovich, Thermomechanical oscillations in hybrid nematic liquid crystals, Phys. Rev. E 73 (2006) 061707].

Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing

This paper describes a novel numerical algorithm for simulating interfacial dynamics of non-Newtonian fluids. The interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. The property and evolution of the interfacial layer is governed by a phase-field variable ϕ that obeys a Cahn–Hilliard type of convection-diffusion equation. This circumvents the task of directly tracking the interface, and produces the correct interfacial tension from the free energy stored in the mixing layer. Viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase-field framework. The greatest challenge of this approach is in resolving the sharp gradients at the interface. This is achieved by using an efficient adaptive meshing scheme governed by the phase-field variable. The finite-element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large-scale two-phase systems of complex fluids. In two-dimensional and axisymmetric three-dimensional implementations, the numerical toolkit is applied here to drop deformation in shear and elongational flows, rise of drops and retraction of drops and torii. Some of these solutions serve as validation of the method and illustrate its key features, while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces.

Stellar collisions during binary-binary and binary-single star interactions

Physical collisions between stars occur frequently in dense star clusters, either via close encounters between two single stars, or during strong dynamical interactions involving binary stars. Here we study stellar collisions that occur during binary-single and binary-binary interactions, by performing numerical scattering experiments. Our results include cross sections, branching ratios, and sample distributions of parameters for various outcomes. For interactions of hard binaries containing main-sequence stars, we find that the normalized cross section for at least one collision to occur (between any two of the four stars involved) is essentially unity, and that the probability of collisions involving more than two stars is significant. Hydrodynamic calculations have shown that the effective radius of a collision product can be 2-30 times larger than the normal main-sequence radius for a star of the same total mass. We study the effect of this expansion, and find that it increases the probability of further collisions considerably. We discuss these results in the context of recent observations of blue stragglers in globular clusters with masses exceeding twice the main-sequence turnoff mass. We also present Fewbody, a new, freely available numerical toolkit for simulating small-N gravitational dynamics that is particularly suited to performing scattering experiments.

A toolkit for numerical simulation of PDEs. II. Solving generic multiphysics problems

Numerical simulations of partial different equations are used in a variety of domains, allowing complete testing and simulation of a product or process even before it is created. However, numerical solvers are not used in all the domains where such equations arise due to the lack of available software or knowledge of numerical methods by scientists. The difficulty of writing a numerical solver is even greater for multiphysics problems, which combine distinct but coupled physical phenomena into a single simulation. In this article, we demonstrate how an existing high-order accurate generic numerical toolkit based on the finite-volume method was modified to allow complex multiphysics problems to be solved easily. We describe how data exchange between the different physical phenomena, the most critical process of a generic multiphysics solver, was made possible using variable association. The modifications to the generic numerical toolkit are detailed and numerical results to both field and interface coupling problems are presented.

Developing numerical libraries in Java

The rapid and widespread adoption of Java has created a demand for reliable and reusable mathematical software components to support the growing number of compute-intensive applications now under development, particularly in science and engineering. In this paper we address practical issues of the Java language and environment which have an effect on numerical library design and development. Benchmarks which illustrate the current levels of performance of key numerical kernels on a variety of Java platforms are presented. Finally, a strategy for the development of a fundamental numerical toolkit for Java is proposed and its current status is described.