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At least 343 records · Page 19

Density Large Deviations for Multidimensional Stochastic Hyperbolic Conservation Laws

We investigate the density large deviation function for a multidimensional conservation law in the vanishing viscosity limit, when the probability concentrates on weak solutions of a hyperbolic conservation law. When the mobility and diffusivity matrices are proportional, i.e. an Einstein-like relation is satisfied, the problem has been solved in Bellettini and Mariani (Bull Greek Math Soc 57:31–45, 2010). When this proportionality does not hold, we compute explicitly the large deviation function for a step-like density profile, and we show that the associated optimal current has a non trivial structure. We also derive a lower bound for the large deviation function, valid for a more general weak solution, and leave the general large deviation function upper bound as a conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Homology modeling and docking of AahII-Nanobody complexes reveal the epitope binding site on AahII scorpion toxin

Highlights: • AahII specific nanobodies share common CDRs sequence patterns. • Residues forming sequences' pattern interact specifically with AahII. • CDR1 Tyr27, Tyr29 and Ser30 polar residues are involved in AahII neutralization. • Interacting AahII Arg62/NbAahII10 CDR3 Asp112 charged residues are crucial. • AahII-NbAahII10 trapping involves a distinct toxin 3D orientation. Scorpion envenoming and its treatment is a public health problem in many parts of the world due to highly toxic venom polypeptides diffusing rapidly within the body of severely envenomed victims. Recently, 38 AahII-specific Nanobody sequences (Nbs) were retrieved from which the performance of NbAahII10 nanobody candidate, to neutralize the most poisonous venom compound namely AahII acting on sodium channels, was established. Herein, structural computational approach is conducted to elucidate the Nb-AahII interactions that support the biological characteristics, using Nb multiple sequence alignment (MSA) followed by modeling and molecular docking investigations (RosettaAntibody, ZDOCK software tools). Sequence and structural analysis showed two dissimilar residues of NbAahII10 CDR1 (Tyr27 and Tyr29) and an inserted polar residue Ser30 that appear to play an important role. Indeed, CDR3 region of NbAahII10 is characterized by a specific Met104 and two negatively charged residues Asp115 and Asp117. Complex dockings reveal that NbAahII17 and NbAahII38 share one common binding site on the surface of the AahII toxin divergent from the NbAahII10 one's. At least, a couple of NbAahII10 – AahII residue interactions (Gln38 – Asn44 and Arg62, His64, respectively) are mainly involved in the toxic AahII binding site. Altogether, this study gives valuable insights in the design and development of next generation of antivenom.

60 APPLIED LIFE SCIENCES↗

Metastability of stratified magnetohydrostatic equilibria and their relaxation

Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Investigating the crust of neutron stars with neural-network quantum states

An accurate description of low-density nuclear matter is crucial for explaining the physics of neutron star crusts. In the density range between approximately 0.01 fm −3 and 0.1 fm −3 , matter transitions from neutron-rich nuclei to various higher-density pasta shapes, before ultimately reaching a uniform liquid. In this work, we introduce a variational Monte Carlo method based on a neural Pfaffian-Jastrow quantum state, which allows us to model the transition from the liquid phase to neutron-rich nuclei microscopically. At low densities, nuclear clusters dynamically emerge from the microscopic interactions among protons and neutrons, which we model based on pionless effective field theory. Our variational Monte Carlo approach represents a significant improvement over the state-of-the-art auxiliary-field diffusion Monte Carlo method, which is severely hindered by the fermion-sign problem in this low-density regime and cannot capture the onset of clusters. In addition to computing the energy per particle of symmetric nuclear matter and pure neutron matter, we analyze an intermediate isospin-asymmetry configuration to elucidate the formation of nuclear clusters. We also provide evidence that the presence of such nuclear clusters influences the amount of protons in the crust compared to protons in beta-equilibrated, neutrino-transparent matter.

Nuclear astrophysics↗

Atwood effects on nonlocality of the scalar transport closure in Rayleigh-Taylor mixing

The importance of nonlocality is assessed in modeling mean scalar transport for turbulent Rayleigh-Taylor (RT) mixing at different Atwood numbers. Building on the two-dimensional incompressible work of Lavacot et al. [J. Fluid Mech. 985, A47 (2024)], the present work extends the macroscopic forcing method to variable density problems in three-dimensional space to measure moments of the generalized eddy diffusivity kernel in RT mixing for increasing Atwood numbers (𝐴 = 0.05, 0.3, 0.5, 0.8). It is found that as 𝐴 increases, (1) the eddy diffusivity moments become asymmetric and (2) the higher-order eddy diffusivity moments become larger relative to the leading-order diffusivity, indicating that nonlocality becomes more important at higher 𝐴. There is a particularly strong temporal nonlocality at higher 𝐴, suggesting stronger history effects. In conclusion, the implications of these findings for closure modeling for finite-Atwood RT are discussed.

general physics↗

Boundary Effects in the Diffusion of New Products on Cartesian Networks

The Role of Boundaries in the Spreading of Solar Peer effects by neighbors play a key role in the spreading of residential solar. Thus, people are more likely to install a solar system on their roof if some of their neighbors have already done so. Because people who live near the municipality boundary have fewer neighbors, does this imply that they are less likely to adopt solar? In “Boundary Effects in the Diffusion of New Products on Cartesian Networks,” Fibich, Levin, and Gillingham analyze this problem analytically using the Bass model on two-dimensional networks and empirically using data on installations of solar systems. They show that boundaries have a significant impact on the adoption of residential units near the municipality boundary. Their effect on the aggregate adoption in the municipality, however, is negligible.

Business & Economics↗

Inpainting Galactic Foreground Intensity and Polarization Maps Using Convolutional Neural Networks

The Deep Convolutional Neural Networks (DCNNs) have been a popular tool for image generation and restoration. In this work, we applied DCNNs to the problem of inpainting non-Gaussian astrophysical signal, in the context of Galactic diffuse emissions at the millimetric and submillimetric regimes, specifically Synchrotron and Thermal Dust emissions. Both signals are affected by contamination at small angular scales due to extragalactic radio sources (the former) and dusty star-forming galaxies (the latter). Furthermore, we compare the performance of the standard diffusive inpainting with that of two novel methodologies relying on DCNNs, namely Generative Adversarial Networks and Deep-Prior. We show that the methods based on the DCNNs are able to reproduce the statistical properties of the ground-truth signal more consistently with a higher confidence level.

79 ASTRONOMY AND ASTROPHYSICS↗

A fast implicit solver for semiconductor models in one space dimension

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in semiconductor devices under a low-density assumption. At each implicit time step, the discretized system is formulated as a fixed-point problem, which can then be solved with a variety of methods. A key algorithmic component in all the approaches considered here is a recently developed sweeping algorithm for Vlasov-Poisson systems. A synthetic acceleration scheme has been implemented to accelerate the convergence of iterative solvers by using the solution to a drift-diffusion equation as a preconditioner. The performance of four iterative solvers and their accelerated variants has been compared on problems modeling semiconductor devices with various electron mean-free-path.

97 MATHEMATICS AND COMPUTING↗

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗

Interface learning in fluid dynamics: Statistical inference of closures within micro–macro-coupling models

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of the solution is governed by how the information is exchanged between these solvers at the interface and several methods have been devised for such coupling problems. In this article, we construct a data-driven model by spatially coupling a microscale lattice Boltzmann method (LBM) solver and macroscale finite difference method (FDM) solver for reaction-diffusion systems. The coupling between the micro-macro solvers has one to many mapping at the interface leading to the interface closure problem, and we propose a statistical inference method based on neural networks to learn this closure relation. The performance of the proposed framework in a bifidelity setting partitioned between the FDM and LBM domain shows its promise for complex systems where analytical relations between micro-macro solvers are not available.

42 ENGINEERING↗

An Efficient Numerical Algorithm for Solving Data Driven Feedback Control Problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. In this work, we call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

97 MATHEMATICS AND COMPUTING↗

Detecting inter-aquifer leakage in areas with limited data using hydraulics and multiple environmental tracers, including {sup 4}He, {sup 36}Cl/Cl, {sup 14}C and {sup 87}Sr/{sup 86}Sr

The investigation of regionally extensive groundwater systems in remote areas is hindered by a shortage of data due to a sparse observation network, which limits our understanding of the hydrogeological processes in arid regions. The study used a multidisciplinary approach to determine hydraulic connectivity between the Great Artesian Basin (GAB) and the underlying Arckaringa Basin in the desert region of Central Australia. In order to manage the impacts of groundwater abstraction from the Arckaringa Basin, it is vital to understand its connectivity with the GAB (upper aquifer), as the latter supports local pastoral stations and groundwater-dependent springs with unique endemic flora and fauna. The study is based on the collation of available geological information, a detailed analysis of hydraulic data, and data on environmental tracers. Enhanced inter-aquifer leakage in the centre of the study area was identified, as well as recharge to the GAB from ephemeral rivers and waterholes. Throughout the rest of the study area, inter-aquifer leakage is likely controlled by diffuse inter-aquifer leakage, but the coarse spatial resolution means that the presence of additional enhanced inter-aquifer leakage sites cannot be excluded. This study makes the case that a multi-tracer approach along with groundwater hydraulics and geology provides a tool-set to investigate enhanced inter-aquifer leakage even in a groundwater basin with a paucity of data. A particular problem encountered in this study was the ambiguous interpretation of different age tracers, which is attributed to diffusive transport across flow paths caused by low recharge rates.

58 GEOSCIENCES↗

Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (CBED) enables determination of aspherical valence electron distributions through refinement of low-order structure factors, which are highly sensitive to chemical bonding and charge density variations. However, conventional quantitative CBED (QCBED) requires solving a highly nonlinear inverse problem with many coupled parameters, and computationally intensive dynamical diffraction calculations, making it time-consuming and difficult to apply to complex systems. More broadly, reconstructing charge density and orbital electron distribution from diffraction data has long been a central challenge in both x-ray and electron crystallography. Here, in this study, we introduce an artificial-intelligence (AI)-based framework that replaces traditional refinement with a data-driven inverse solver. Using a large synthetic CBED dataset generated by Bloch-wave simulations, we train a conditional diffusion model to directly infer crystal structural parameters and multipole density formalism parameters, and hence valence electron distributions, from CBED patterns alone. By learning from forward simulations across realistic parameter space, the model effectively solves the inverse problem. Compared with direct regression approaches, the diffusion-based framework provides posterior parameter distributions for rigorous uncertainty quantification while preserving quantitative fidelity and reducing analysis time by orders of magnitude. By eliminating the need for external single-crystal x-ray diffraction data and complex nonlinear refinement, this approach enables practical, high-throughput, and in situ quantitative CBED, enabling real-time mapping of valence electron distributions and their correlation with functional responses in quantum and energy materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

High-order two-fluid plasma solver for direct numerical simulations of plasma flows with full transport phenomena

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating terms, have been implemented in the CFDNS code and solved by using sixth-order non-dissipative compact finite differences for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales, while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. Non-dimensional analysis of the two-fluid plasma equations shows that, by varying the characteristic/background number density, length scale, temperature, and magnetic strength, the corresponding Hall, resistive, and ideal magnetohydrodynamic equations can be recovered as limiting cases. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows in different regimes have been validated against four canonical problems: Alfven and whistler dispersion relations, electromagnetic plasma shock, and magnetic reconnection. For all test cases, by using physical dissipation and diffusion, with negligible numerical dissipation/diffusion, fully converged Direct Numerical Simulation (DNS)-like solutions are obtained when the ion Reynolds number based on the grid size is smaller than a threshold value which is about 2.3. For the magnetic reconnection problem, the results show that the magnetic flux saturation time and value converge when the ion and magnetic Reynolds numbers are large enough. Thus, the DNS-like results become relevant to practical problems with much larger Reynolds numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗

AutoTandemML: Active Learning Enhanced Tandem Neural Networks for Inverse Design Problems

Inverse design in science and engineering involves determining optimal design parameters that achieve desired performance outcomes, a process often hindered by the complexity and high dimensionality of design spaces, leading to significant computational costs. To tackle this challenge, we propose a novel hybrid approach that combines active learning with Tandem Neural Networks to enhance the efficiency and effectiveness of solving inverse design problems. Active learning allows to selectively sample the most informative data points, reducing the required dataset size without compromising accuracy. We investigate this approach using three benchmark problems: airfoil inverse design, photonic surface inverse design, and scalar boundary condition reconstruction in diffusion partial differential equations. We demonstrate that integrating active learning with Tandem Neural Networks outperforms standard approaches across the benchmark suite, achieving better accuracy with fewer training samples.

97 MATHEMATICS AND COMPUTING↗

Shape effect on drying behavior of cement-based materials: Mechanisms and numerical analysis

The shape of the specimen or structure has a direct impact on the behavior of drying concrete. This effect is not taken into account in most of shrinkage models and codes. Only the current B4 model and its previous version B3 model incorporate a shape factor. The determination of this coefficient is based on the nonlinear moisture diffusion analysis, which can explain the shape effect on the shrinkage rate. However, the model integrates this coefficient in the ultimate shrinkage values as well. An experimental study has been performed to confirm and understand this behavior. The mass loss and drying shrinkage of cylinders showed higher rate and ultimate values than the prisms, for the same effective cross section thickness. To explain this result, the drying, the differential shrinkage, the internal stress and the damaged depth were determined for both shapes through numerical modeling. The main input data of the model were the measured mass loss and shrinkage. The calculated desorption isotherm curve of the cylinder was below that of the prism, which is consistent with its higher ultimate mass-loss. The determination of stress profiles indicates slower stress mitigation for the cylinder. The cylinder develops a larger relative damaged area, defined as the part of the specimen where cracking is likely to occur due to tensile stresses. The results actually show that differential shrinkage between the edge and the core is more pronounced for the cylinder and decreases with time.

36 MATERIALS SCIENCE↗