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1. thornado-transport: IMEX schemes for two-moment neutrino transport respecting Fermi-Dirac statistics

   Chu, R; Endeve, E; Hauck, C; Mezzacappa, A; Messer, B (July 2019, Journal of physics Conference series)

   We develop implicit-explicit (IMEX) schemes for neutrino transport in a background material in the context of a two-moment model that evolves the angular moments of a neutrino phase-space distribution function. Considering the upper and lower bounds that are introduced by Pauli’s exclusion principle on the moments, an algebraic moment closure based on Fermi-Dirac statistics and a convex-invariant time integrator both are demanded. A finite-volume/first-order discontinuous Galerkin(DG) method is used to illustrate how an algebraic moment closure based on Fermi-Dirac statistics is needed to satisfy the bounds. Several algebraic closures are compared with these bounds in mind, and the Cernohorsky and Bludman closure, which satisfies the bounds, is chosen for our IMEX schemes. For the convex-invariant time integrator, two IMEX schemes named PD-ARS have been proposed. PD-ARS denotes a convex-invariant IMEX Runge-Kutta scheme that is high-order accurate in the streaming limit, and works well in the diffusion limit. Our two PD-ARS schemes use second- and third-order, explicit, strong-stability-preserving Runge-Kutta methods as their explicit part, respectively, and therefore are second- and third-order accurate in the streaming limit, respectively. The accuracy and convex-invariance of our PD-ARS schemes are demonstrated in the numerical tests with a third-order DG method for spatial discretization and a simple Lax-Friedrichs flux. The method has been implemented in our high-order neutrino-radiation hydrodynamics (thornado) toolkit. We show preliminary results employing tabulated neutrino opacities. 

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2. Real-time Height-field Simulation of Sand and Water Mixtures

   https://doi.org/10.1145/3610548.3618159  

   Su, Haozhe; Zhang, Siyu; Pan, Zherong; Aanjaneya, Mridul; Gao, Xifeng; Wu, Kui (December 2023, ACM)

   We propose a height-field-based real-time simulation method for sand and water mixtures. Inspired by the shallow-water assumption, our approach extends the governing equations to handle two-phase flows of sand and water using height fields. Our depth-integrated governing equations can model the elastoplastic behavior of sand, as well as sand-water-mixing phenomena such as friction, diffusion, saturation, and momentum exchange. We further propose an operator-splitting time integrator that is both GPU-friendly and stable under moderate time step sizes. We have evaluated our method on a set of benchmark scenarios involving large bodies of heterogeneous materials, where our GPU-based algorithm runs at real-time frame rates. Our method achieves a desirable trade-off between fidelity and performance, bringing an unprecedentedly immersive experience for real-time applications. 

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3. A Numerical Integrator for Kinetostatic Folding of Protein Molecules Modeled as Robots with Hyper Degrees of Freedom

   https://doi.org/10.3390/robotics13100150  

   Kacem, Amal; Zbiss, Khalil; Mohammadi, Alireza (October 2024, Robotics (Special Issue Bioinspired Robotics: Toward Softer, Smarter and Safer))

   The kinetostatic compliance method (KCM) models protein molecules as nanomechanisms consisting of numerous rigid peptide plane linkages. These linkages articulate with respect to each other through changes in the molecule dihedral angles, resulting in a kinematic mechanism with hyper degrees of freedom. Within the KCM framework, nonlinear interatomic forces drive protein folding by guiding the molecule’s dihedral angle vector towards its lowest energy state in a kinetostatic manner. This paper proposes a numerical integrator that is well suited to KCM-based protein folding and overcomes the limitations of traditional explicit Euler methods with fixed step size. Our proposed integration scheme is based on pseudo-transient continuation with an adaptive step size updating rule that can efficiently compute protein folding pathways, namely, the transient three-dimensional configurations of protein molecules during folding. Numerical simulations utilizing the KCM approach on protein backbones confirm the effectiveness of the proposed integrator. 

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4. A fast local embedded boundary method suitable for high power electromagnetic sources

   https://doi.org/10.1063/5.0019210  

   Thavappiragasam, Mathialakan; Christlieb, Andrew; Luginsland, John; Guthrey, Pierson (November 2020, AIP Advances)

   High power sources of electromagnetic energy often require complicated structures to support electromagnetic modes and shape electromagnetic fields to maximize the coupling of the field energy to intense relativistic electron beams. Geometric fidelity is critical to the accurate simulation of these High Power Electromagnetic (HPEM) sources. Here, we present a fast and geometrically flexible approach to calculate the solution to Maxwell’s equations in vector potential form under the Lorenz gauge. The scheme is an implicit, linear-time, high-order, A-stable method that is based on the method of lines transpose (MOLT). As presented, the method is fourth order in time and second order in space, but the A-stable formulation could be extended to both high order in time and space. An O(n) fast convolution is employed for space-integration. The main focus of this work is to develop an approach to impose perfectly electrically conducting (PEC) boundary conditions in MOLT by extending our past work on embedded boundary methods. As the method is A-stable, it does not suffer from small time step limitations that are found in explicit finite difference time domain methods when using either embedded boundary or cut-cell methods to capture geometry. This is a major advance for the simulation of HPEM devices. While there is no conceptual limitation to develop this in 3D, our initial work has centered on 2D. The extension to 3D requires validation that the proposed fixed point iteration will converge and is the subject of our follow-up work. The eventual goal is to combine this method with particle methods for the simulations of plasma. In the current work, the scheme is evaluated for EM wave propagation within an object that is bounded by PEC. The consistency and performance of the scheme are confirmed using the ping test and frequency mode analysis for rotated square cavities—a standard test in the HPEM community. We then demonstrate the diffraction Q value test and the use of this method for simulating an A6 magnetron. The ability to handle both PEC and open boundaries in a standard device test problem, such as the A6, gives confidence on the robustness of this new method. 

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5. Explicit Polynomial Sequences with Maximal Spaces of Partial Derivatives and a Question of K. Mulmuley

   https://doi.org/10.4086/toc.2019.v015a003  

   Gesmundo, Fulvio; Landsberg, Joseph M. (January 2019, Theory of Computing)

   null (Ed.)

   We answer a question of K. Mulmuley. Efremenko et al. (Math. Comp., 2018) have shown that the method of shifted partial derivatives cannot be used to separate the padded permanent from the determinant. Mulmuley asked if this “no-go” result could be extended to a model without padding. We prove this is indeed the case using the iterated matrix multiplication polynomial. We also provide several examples of polynomials with maximal space of partial derivatives, including the complete symmetric polynomials. We apply Koszul flattenings to these polynomials to have the first explicit sequence of polynomials with symmetric border rank lower bounds higher than the bounds attainable via partial derivatives. 

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