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At least 667 records · Page 37

Super-time-stepping schemes for parabolic equations with boundary conditions

In this work, we present a super-time-stepping scheme for numerically solving parabolic partial differential equations with Dirichlet boundary conditions (BC). Using the general Forward Euler scheme, one can show that by taking varying step sizes there is the potential of propagating the solution forward in time by a greater amount than with uniform step sizes, while maintaining the same order of accuracy. As shown in previous works, if one further requires that the scheme have the Convex Monotone Property (CMP), then there exists a scheme which results in linear, monotone stability of the solution. This monotone stability is highly desirable in many physical situations, such as thermal diffusion, where the physical system will not oscillate, but will behave monotonically. However, the schemes devised in previous works do not include situations that have a boundary condition, and the inclusion of boundary conditions will henceforth be our focus. It is shown that a particular Runge-Kutta-Gegenbauer class of schemes [5] will maintain the CMP even in the presence of Dirichlet BC.

97 MATHEMATICS AND COMPUTING↗

Advection versus diffusion in Richtmyer-Meshkov mixing

The Richtmyer-Meshkov (RM) instability is one of the most severe degradation mechanisms for inertial confinement fusion (ICF), and mitigating it has been a priority for the global ICF effort. In this Letter, the instability's ability to atomically mix is linked to its background decay of residual turbulent energy. Here, we show how recently derived inequalities from the mathematical theory of PDEs constrain the evolution. A model RM process at leading order may diffusively mix or retain imprints of its initial structures indefinitely, depending on initial conditions, and there exists a theoretical range of zero-mixing for certain values of parameters. The results may apply to other systems resembling scalar transport in decaying turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Late-time post-merger modeling of a compact binary: effects of relativity, r-process heating, and treatment of transport

Detectable electromagnetic counterparts to gravitational waves from compact binary mergers can be produced by outflows from the black hole-accretion disk remnant during the first 10 s after the merger. Two-dimensional axisymmetric simulations with effective viscosity remain an efficient and informative way to model this late-time post-merger evolution. In addition to the inherent approximations of axisymmetry and modeling turbulent angular momentum transport by a viscosity, previous simulations often make other simplifications related to the treatment of the equation of state and turbulent transport effects. In this paper, we test the effect of these modeling choices. By evolving with the same viscosity the exact post-merger initial configuration previously evolved in Newtonian viscous hydrodynamics, we find that the Newtonian treatment provides a good estimate of the disk ejecta mass but underestimates the outflow velocity. We find that the inclusion of heavy nuclei causes a notable increase in ejecta mass. An approximate inclusion of r-process effects has a comparatively smaller effect, except for its designed effect on the composition. Diffusion of composition and entropy, modeling turbulent transport effects, has the overall effect of reducing ejecta mass and giving it a speed with lower average and more tightly-peaked distribution. Also, we find significant acceleration of outflow even at distances beyond 10 000 km, so that thermal wind velocities only asymptote beyond this radius and at higher values than often reported.

79 ASTRONOMY AND ASTROPHYSICS↗

Double-power-law Feature of Energetic Particles Accelerated at Coronal Shocks

Recent observations have shown that in many large solar energetic particle (SEP) events the event-integrated differential spectra resemble double power laws. We perform numerical modeling of particle acceleration at coronal shocks propagating through a streamer-like magnetic field by solving the Parker transport equation, including protons and heavier ions. We find that for all ion species the energy spectra integrated over the simulation domain can be described by a double power law, and the break energy depends on the ion charge-to-mass ratio as E B ~ (Q/A) α , with α varying from 0.16 to 1.2 by considering different turbulence spectral indices. We suggest that the double-power-law distribution may emerge as a result of the superposition of energetic particles from different source regions where the acceleration rates differ significantly due to particle diffusion. The diffusion and mixing of energetic particles could also provide an explanation for the increase of Fe/O at high energies as observed in some SEP events. Although further mixing processes may occur, our simulations indicate that either a power-law break or rollover can occur near the Sun and predict that the spectral forms vary significantly along the shock front, which may be examined by upcoming near-Sun SEP measurements from the Parker Solar Probe and Solar Orbiter.

79 ASTRONOMY AND ASTROPHYSICS↗

Analysis of cell-based diffusion acceleration for the slice balance approach

In this work, we perform analysis on the use of cell-based diffusion acceleration methodologies to accelerate the convergence of transport solutions discretized with the slice balance approach (SBA) on unstructured polygonal grids.We investigated both linear diffusion synthetic acceleration (DSA) and non linear diffusion acceleration (NDA), including its partial-current variant (pNDA). DSA and NDA were both shown to diverge for intermediate ranges of mesh optical thicknesses. However, pNDA and Krylov methods like GMRES and Broyden stabilized the acceleration schemes, including problems with degenerate cells formed by mesh refinement. (author)

42 ENGINEERING↗

On the evolution of scalar iso-surface area density in a turbulent mixing layer

In this paper, the transport equation for scalar iso-surface area density (Σ) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the Σ transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that Σ exhibits self-similar behaviour consistent with the development of the temporal mixing layer. Accordingly, each of the terms in the Σ transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of Σ (∂Σ/∂t) and the advection term scale with hλ Φ /ΔU, where h is the width of the mixing layer, λ Φ is the scalar Taylor length scale and ΔU is the velocity difference. The production and destruction terms are found to scale with an additional factor (ReSc) 1/2 . In contrast, the molecular diffusion term is found to scale with a factor (ReSc) –1/2 compared to ∂Σ/∂t. Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as ∂Σ/∂t and the advection term, which may have a significant impact on how the evolution of Σ is understood and modelled in turbulent flows.

42 ENGINEERING↗

Development and Applications of an eReaxFF Force Field for Graphitic Anodes of Lithium-Ion Batteries

Graphene is one of the most promising materials for lithium-ion battery anodes due to its superior electronic conductivity, high surface area for lithium intercalation, fast ionic diffusivity and enhanced specific capacity. A reliable description of many battery processes requires an explicit description of electrochemical interactions involving electrons. A detailed atomistic modeling of electronic conduction and non-zero voltage simulations of graphitic materials require the inclusion of an explicit electronic degree of freedom. To enable large length- and time-scale simulations of electron conduction in graphitic anodes, we developed an eReaxFF force field concept describing graphitic materials with an explicit electron. The newly developed force field, verified against quantum chemistry-based data describing, amongst others, electron affinities and equation of states, reproduces the qualitative behavior of electron conductivity in pristine and imperfect graphitic materials at different applied temperatures and voltages. In addition, excess electron localization near a defect site estimated from eReaxFF simulations agree quite well with the corresponding density functional theory calculations. Here, our eReaxFF simulations show the initiation of lithium-metal-plating driven by electron transfer from the graphene surface to the exposed lithium ions demonstrating the method’s potential for studying lithium-graphene interactions with explicit electrons and explain many unresolved electrode and electrode-electrolyte interface processes.

25 ENERGY STORAGE↗

Radiation GRMHD Models of Accretion onto Stellar-mass Black Holes. II. Super-Eddington Accretion

We present a comprehensive analysis of super-Eddington black hole accretion simulations that solve the GRMHD equations coupled with angle-discretized radiation transport. The simulations span a range of accretion rates, two black hole spins, and two magnetic field topologies, and include resolution studies as well as comparisons with nonradiative models. Super-Eddington accretion flows consistently develop geometrically thick disks supported by radiation pressure, regardless of magnetic field configuration. Radiation generated in the inner disk drives substantial outflows, forming conical funnel regions that limit photon escape and result in very low radiation efficiency. The accretion flows are highly turbulent, with thermal energy transport dominated by radiation advection rather than diffusion. Angular momentum is primarily carried outward by Maxwell stress, with turbulent Reynolds stress playing a subdominant role. Both strong and weak jets are produced. Strong jets arise from sufficient net vertical magnetic flux and rapid black hole spin, and they can effectively evacuate the funnel, enabling radiation to escape through strong geometric beaming. In contrast, weak jets fail to clear the funnel, which becomes obscured by radiation-driven outflows and leads to distinct observational signatures. Spiral structures are observed in the plunging region, behaving like density waves. These super-Eddington models are applicable to a variety of astronomical systems, including ultraluminous X-ray sources, little red dots, and black hole transients.

79 ASTRONOMY AND ASTROPHYSICS↗

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES↗

Modelling a compressible packed bed flow-through washing and deacetylation reactor for corn stover pretreatment

The deacetylation process is a key step in the lignocellulosic biomass pretreatment process that currently is done in batch reactors. A flow-through diffuser type reactor is a promising approach to make the process more efficient and economically favorable. A washing step before deacetylation can further reduce chemical usage and increase the process efficiency. However, the highly compacted biomass particles can cause significant pressure-drop for fluid flow through the bed, which in the worst case can cause self-enhancing pressure-drop leading to reactor blocking. Detailed understanding of the fundamentals of flow through a compressible packed bed is necessary to scale up the washing and deacetylation process. This work closely examines the classical Kozeny Carman equation and proposes modifications to accurately predict the pressure-drop at different compaction states. Here, a compressible packed bed model is further developed based on the interaction between solid mechanics and fluid dynamics. Experimental measurements of water flow through a packed bed of corn stover show good agreement with the developed model. Corn stover washing process scale up simulations show that smaller reactor diameter, higher friction lining material, lower process throughput, and higher process temperature is favorable in stabilizing the bed from extensive compression when the bed height is fixed.

09 BIOMASS FUELS↗

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells’ location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells’ diffusion and immune cells’ influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes’ diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

60 APPLIED LIFE SCIENCES↗

Phase-field simulations of fission gas bubble growth and interconnection in U-(Pu)-Zr nuclear fuel

Abstract The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection. Surface area increased rapidly during the initial stages of growth, then slowed and finally decreased as bubble interconnection began and coarsening acted to reduce surface area. The fraction of the bubbles vented to a simulation domain boundary, f V , was quantified as a measure of the microstructure’s interconnectivity and plotted as a function of porosity p . The defect species diffusivity was varied; although changes in diffusivity significantly affected the microstructure, the plots of f V vs. p did not change significantly. The percolation threshold p c was calculated to be approximately 0.26, depending on the assumed diffusivity and using an initial bubble number density based on experimental observations. This is slightly smaller than the percolation threshold for continuum percolation of overlapping 3D spheres. The simulation results were used to parameterize two different engineering-scale swelling models for U-(Pu)-Zr in the nuclear fuel performance code BISON.

Aagesen, Larry K. (ORCID:000000034936676X)↗

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗

Perturbative treatment of nonlocal chiral interactions in auxiliary-field diffusion Monte Carlo calculations

Nuclear many-body systems, ranging from nuclei to neutron stars, are some of the most interesting physical phenomena in our universe, and quantum Monte Carlo (QMC) approaches are among the most accurate many-body methods currently available to study them. In recent decades, interactions derived from chiral effective field theory (EFT) have been widely adopted in the study of nuclear many-body systems. One drawback of the QMC approach is the requirement that the nuclear interactions need to be local, whereas chiral EFT interactions usually contain nonlocalities. In this work, we leverage the capability of computing second-order perturbative corrections to the ground-state energy in order to develop a self-consistent approach to including nonlocal operators in QMC calculations. In conclusion, we investigate both the deuteron and the neutron-matter equation of state in order to show the robustness of our technique and pave the way for future QMC calculations at higher orders in the EFT, where nonlocal operators cannot be avoided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Micro-continuum approach for mineral precipitation

Abstract Rates and extents of mineral precipitation in porous media are difficult to predict, in part because laboratory experiments are problematic. It is similarly challenging to implement numerical methods that model this process due to the need to dynamically evolve the interface of solid material. We developed a multiphase solver that implements a micro-continuum simulation approach based on the Darcy–Brinkman–Stokes equation to study mineral precipitation. We used the volume-of-fluid technique in sharp interface implementation to capture the propagation of the solid mineral surface. Additionally, we utilize an adaptive mesh refinement method to improve the resolution of near interface simulation domain dynamically. The developed solver was validated against both analytical solution and Arbitrary Lagrangian–Eulerian approach to ensure its accuracy on simulating the propagation of the solid interface. The precipitation of barite (BaSO 4 ) was chosen as a model system to test the solver using variety of simulation parameters: different geometrical constraints, flow conditions, reaction rate and ion diffusion. The growth of a single barite crystal was simulated to demonstrate the solver’s capability to capture the crystal face specific directional growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulation of plasma transport in MPS-LD linear plasma device by using BOUT++

Here a linear plasma device (LPD) module based on the 2D transport module under the BOUT++ framework is developed in this paper to simulate plasma transport in the LPD. The LPD module includes three parts, i.e. magnetic field calculation, simulation mesh generation and plasma transport setup. The magnetic field is calculated with the circular current loop using the location and current information of each coil. The mesh generation code can produce a simulation mesh for LPD by employing the magnetic field. The plasma transport model is based on the reduced Braginskii equations, which consist of the continuity equation, momentum equation, and energy equation. The fluid neutral model is applied for neutral particle simulation. Deuterium (D) and helium (He) ions and atoms can be simulated by the model. The first attempt to simulate plasma transport in the new LPD, called multiple plasma simulation linear plasma device (MPS-LD), is presented using the developed model. The D plasma transport in the MPS-LD is simulated and benchmarked against the two-point model, showing the validation of the BOUT++ simulation. The effects of radial transport on the heat load to the target are studied, which illustrates the significant impact of the radial diffusivities $D_⟂$ and $\mathcal{X}_{⟂i,e}$ on the plasma. Moreover, the He impurity injection process during the discharge is studied with emphasis on plasma–impurity interactions. The simulation results show that He injection can reduce the plasma energy load to the target significantly, and the efficiency depends on the He source density and injection velocity. The present work provides an alternative and flexible simulation tool for plasma transport in LPDs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Transient heat transfer of superfluid He 4 in nonhomogeneous geometries: Second sound, rarefaction, and thermal layer

Transient heat transfer in superfluid 4 He (He II) is a complex process that involves the interplay of the unique counterflow heat-transfer mode, the emission of second-sound waves, and the creation of quantized vortices. Many past researches focused on homogeneous heat transfer of He II in a uniform channel driven by a planar heater. Here, we report our systematic study of He II transient heat transfer in nonhomogeneous geometries that are pertinent to emergent applications. By solving the He II two-fluid equations of motion coupled with Vinen's equation for vortex-line density, we examine and compare the characteristics of transient heat transfer from planar, cylindrical, and spherical heaters in He II. Our results show that as the heater turns on, an outgoing second-sound pulse emerges, within which the vortex-line density grows rapidly. These vortices attenuate the second sound and result in a heated He II layer in front of the heater, i.e., the thermal layer. In the planar case where the vortices are created throughout the space, the second-sound pulse is continuously attenuated, leading to a thick thermal layer that diffusely spreads following the heat pulse. On the contrary, in the cylindrical and the spherical heater cases, vortices are created mainly in a thin thermal layer near the heater surface. As the heat pulse ends, a rarefaction tail develops following the second-sound pulse, in which the temperature drops. This rarefaction tail can promptly suppress the thermal layer and take away the deposited thermal energy. The effects of the heater size, heat flux, pulse duration, and temperature on the thermal-layer dynamics are discussed. We also show how the peak heat flux for the onset of boiling in He II can be studied in our model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Enabling high rate capability, low internal resistance, and excellent cyclability for vanadium redox flow batteries utilizing ultrafast laser-structured graphite felt

The electrochemical performance of vanadium redox flow batteries (VRFBs) was enhanced via laser-patterned graphite felt (GF) electrodes. The laser-structured GF electrodes engineered via preparing a series of well-ordered microscopic channel structures with an average width of 200 μm, creating a three-dimensional carbon framework. The ultrafast laser patterning increased the porosity by 10%, as compared to pristine electrode. The analysis of the overpotential distribution using electrochemical impedance spectroscopy revealed that the electrode polarization involving charge transfer and diffusion resistance is strongly alleviated with the aid of carbon micro-perforation. The advanced design of laser-structured GF electrode also exhibits high rate capability, low internal resistance, and excellent cyclability. The improved performance was attributed to the synergistic effect involving (i) high electrochemically active surface area for rapid electrochemical reactions (i.e., V(II)/V(III) and V(IV)/V(V) redox couples) and (ii) excellent transport properties for facile electron/ion/species transport. The micro-scale channels created with the laser-ablation technique act as capillary structures and enabled homogeneous and rapid wetting of GF electrodes as formulated with the classical Washburn equation. The VRFB equipped with the laser-structured GF electrodes delivered a high discharge capacity with exceptional capacity retention upon extended cycling (>84.9%). In conclusion, accordingly, the design of laser-structured electrode paves the pathway towards finely tuning the electrode internal microstructure for improved cyclability, durability, and capacity retention in various electrochemical energy storage/conversion devices (e.g. all-vanadium redox flow batteries).

25 ENERGY STORAGE↗