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An immersed boundary method for the compressible Navier-Stokes equations can be used for moving boundary problems as well as fully coupled fluid-structure interaction is presented. The underlying Cartesian immersed boundary method of the Launch Ascent and Vehicle Aerodynamics (LAVA) framework, based on the locally stabilized immersed boundary method previously presented by the authors, is extended to account for unsteady boundary motion and coupled to linear and geometrically nonlinear structural finite element solvers. The approach is validated for moving boundary problems with prescribed body motion and fully coupled fluid structure interaction problems. Keywords: Immersed Boundary Method, Higher-Order Finite Difference Method, Fluid Structure Interaction.
Abstract A Mn(II) salt and A + CN − under anaerobic conditions react to form 2‐D and 3‐D extended structured compounds of A m Mn II n (CN) m+2n stoichiometry. Here, the creation and characterization of this large family of compounds, for example AMn II 3 (CN) 7 , A 2 Mn II 3 (CN) 8 , A 2 Mn II 5 (CN) 12 , A 3 Mn II 5 (CN) 13 , and A 2 Mn II [Mn II (CN) 6 ], where A represents alkali and tetraalkylammonium cations, is reviewed. Cs 2 Mn II [Mn II (CN) 6 ] has the typical Prussian blue face centered cubic unit cell. However, the other alkali salts are monoclinic or rhombohedral. This is in accord with smaller alkali cation radii creating void space that is minimized by increasing the van der Waals stabilization energy by reducing ∠Mn−N≡C, which, strengthens the magnetic coupling and increases the magnetic ordering temperatures. This is attributed to the non‐rigidity of the framework structure due the significant ionic character associated with the high‐spin Mn II sites. For larger tetraalkylammonium cations, the high‐spin Mn sites lack sufficient electrostatic A + ⋅⋅⋅NC stabilization and form unexpected 4‐ and 5‐coordinated Mn sites within a flexible, extended framework around the cation; hence, the size, shape, and charge of the cation dictate the unprecedented stoichio‐metry and unpredictable cation adaptive structures. Antiferromagnetic coupling between adjacent Mn II sites leads to ferrimagnetic ordering, but in some cases antiferromagnetic coupling of ferrimagnetic layers are compensated and synthetic antiferromagnets are observed. The magnetic ordering temperatures for ferrimagnetic A 2 Mn II [Mn II (CN) 6 ] with both octahedral high‐ and low‐spin Mn II sites increase with decreasing ∠Mn−N≡C. The crystal structures for all of the extended structured materials were obtained by powder diffraction.
The 2020 Smoky Mountains Computational Sciences and Engineering Conference enlists research scientists from across Oak Ridge National Laboratory (ORNL) to be data sponsors and help create data analytics challenges for eminent data sets at the laboratory. This work describes the significance of each of the seven data sets and their as- sociated challenge questions. The challenge questions for each data set were required to cover multiple difficulty levels. An international call for participation was sent to students, and researchers asking them to form teams of up to four people to apply novel data analytics techniques to these data sets.
We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a $\mathbb{Z}$ 2 -symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $\overline{g}$, and is expected to have a critical point at a tuned value ${\overline{g}}_{\ast }$ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the $\mathbb{Z}$ 2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $\overline{g}$ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C -function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.
We propose a solution to the strong CP problem that specifically relies on massless quarks and has no light axion. The QCD color group SU(3) c is embedded into a larger, simple gauge group (grand-color) where one of the massless, colored fermions enjoys an anomalous chiral symmetry, rendering the strong CP phase unphysical. The grand-color gauge group G GC is Higgsed down to SU(3) c × ${G}_{c^{\prime }}$, after which ${G}_{c^{\prime }}$ eventually confines at a lower scale, spontaneously breaking the chiral symmetry and generating a real, positive mass to the massless, colored fermion. Since the chiral symmetry has a ${G}_{c^{\prime }}$ anomaly, there is no corresponding light Nambu-Goldstone boson. The anomalous chiral symmetry can be an accidental symmetry that arises from an exact discrete symmetry without introducing a domain wall problem. Potential experimental signals of our mechanism include vector-like quarks near the TeV scale, pseudo Nambu-Goldstone bosons below the 10 GeV scale, light dark matter decay, and primordial gravitational waves from the new strong dynamics.
Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.
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This paper reviews the status of technology in design and manufacture of new wrought 21 polycrystalline Ni-base superalloys for critical engineering applications. There is a strong 22 motivation to develop new alloys that are capable of operating at higher temperatures to 23 realise improvements in thermal efficiency, which are necessary to achieve environmental 24 targets for reduced emissions of harmful green-house gases. From the aerospace sector, 25 the development of new powder metallurgy and ingot metallurgy alloys are discussed for 26 disk rotor and static applications. New compositions for powder metallurgy contain about 27 50-55% of gamma prime (γ') strengthening precipitates to ensure components operate 28 successfully at temperatures up to 788°C (1450°F). In contrast, new compositions for ingot 29 metallurgy aim to occupy a design space in temperature capability between Alloy 718 and 30 current powder alloys that are in-service, and show levels of γ' of about 30-44%. The focus 31 in developing these alloys was design for manufacturability. To complement the aerospace 32 developments, a review of work to understand the suitability of candidate alloys for multiple 33 applications in Advanced-Ultra Supercritical (AUSC) power plants has been undertaken by 34 Detrois, Jablonski and Hawk from the National Energy Technology Laboratory. In these 35 power plants, steam temperatures are required to reach 700-760°C. The common thread is 36 to develop alloys that demonstrate a combination of high temperature properties, which are 37 reliant on both the alloy composition and microstructure and can be produced readily at the 38 right price. For the AUSC applications, the emphasis is on high temperature strength, long 39 term creep life, phase stability, oxidation resistance and robust welding for fabrications. 40 Whereas for powder disk rotors in aircraft engines, the priority is enhanced resistance to 41 time dependent crack growth, phase stability and resistance to environmental damage, while 42 extending the current strength levels, which are shown by existing alloys, to higher 43 temperatures.
In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.
Determining a process–structure–property relationship is the holy grail of materials science, where both computational prediction in the forward direction and materials design in the inverse direction are essential. Problems in materials design are often considered in the context of process–property linkage by bypassing the materials structure, or in the context of structure–property linkage as in microstructure-sensitive design problems. However, there is a lack of research effort in studying materials design problems in the context of process–structure linkage, which has a great implication in reverse engineering. In this paper, given a target microstructure, we propose an active learning high-throughput microstructure calibration framework to derive a set of processing parameters, which can produce an optimal microstructure that is statistically equivalent to the target microstructure. The proposed framework is formulated as a noisy multi-objective optimization problem, where each objective function measures a deterministic or statistical difference of the same microstructure descriptor between a candidate microstructure and a target microstructure. Furthermore, to significantly reduce the physical waiting wall-time, we enable the high-throughput feature of the microstructure calibration framework by adopting an asynchronously parallel Bayesian optimization to exploit high-performance computing resources. Case studies in additive manufacturing and grain growth are used to demonstrate the applicability of the proposed framework, where kinetic Monte Carlo (kMC) simulation is used as a forward predictive model, such that for a given target microstructure, the target processing parameters that produced this microstructure are successfully recovered.
We reduce the solution of the scattering problem defined on the half-line [0,∞) by a real or complex potential v(x) and a general homogeneous boundary condition at x=0 to that of the extension of v(x) to the full line that vanishes for x<0. We find an explicit expression for the reflection amplitude of the former problem in terms of the reflection and transmission amplitudes of the latter. We obtain a set of conditions on these amplitudes under which the potential in the half-line develops bound states, spectral singularities, and time-reversed spectral singularities where the potential acts as a perfect absorber. We examine the application of these results in the study of the scattering properties of a δ-function potential and a finite barrier potential defined in [0,∞), discuss optical systems modeled by these potentials, and explore the configurations in which these systems act as a laser or perfect absorber. In particular, we derive an explicit formula for the laser threshold condition for a slab laser with a single mirror and establish the surprising fact that a nearly perfect mirror gives rise to a lower threshold gain than a perfect mirror. We also offer a nonlinear extension of our approach which allows for utilizing a recently developed nonlinear transfer matrix method in the full line to deal with finite-range nonlinear scattering interactions defined in the half-line.
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Physics-informed neural networks (PINNs) are demonstrating remarkable promise in integrating physical models with gappy and noisy observational data, but they still struggle in cases where the target functions to be approximated exhibit high-frequency or multi-scale features. Here in this work we investigate this limitation through the lens of Neural Tangent Kernel (NTK) theory and elucidate how PINNs are biased towards learning functions along the dominant eigen-directions of their limiting NTK. Using this observation, we construct novel architectures that employ spatio-temporal and multi-scale random Fourier features, and justify how such coordinate embedding layers can lead to robust and accurate PINN models. Numerical examples are presented for several challenging cases where conventional PINN models fail, including wave propagation and reaction–diffusion dynamics, illustrating how the proposed methods can be used to effectively tackle both forward and inverse problems involving partial differential equations with multi-scale behavior.