Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation
Not Available
97 MATHEMATICS AND COMPUTING↗
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Solving the 3d Ising Model with the Conformal Bootstrap II. c -Minimization and Precise Critical Exponents
Here, we use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge \(c\) in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are even able to precisely reconstruct the first several \(\mathbb {Z}_2\) -even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension \(\Delta _\sigma = 0.518154(15)\) , and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Ken Wilson: Solving the Strong Interactions
Abstract Not Provided
Phenomenology-HEP, General Physics, Theory-HEP,HEP↗
On the Behavior of Solutions of Some Systems of Differential Equations Partially Solved with Respect to the Derivatives in the Presence of a Pole
We study the existence of analytic solutions for some systems of ordinary differential equations partially solvable with respect to the derivatives. We establish sufficient conditions for the existence of analytic solutions of the Cauchy problem in the presence of a pole. An estimate for these solutions is obtained in a certain domain and the problem of the number of solutions is investigated.
97 MATHEMATICS AND COMPUTING↗
Solving Recent Challenges for Wrought Ni-Base Superalloys
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.
36 MATERIALS SCIENCE↗
Improving Joint Formation and Tensile Properties of Dissimilar Friction Stir Welding of Aluminum and Magnesium Alloys by Solving the Pin Adhesion Problem
Friction stir welding (FSW), as a solid-state welding technology invented by TWI in 1991, has potential to join dissimilar Al/Mg alloys. In this study, the pin adhesion phenomenon affecting joint quality during FSW of 6061-T6 aluminum and AZ31B magnesium alloys was investigated. The adhesion phenomenon induced by higher heat input easily transformed the tapered-and-screwed pin into a tapered pin, which greatly reduced the tool’s ability to drive the plasticized materials and further deteriorated joint formation. Under the condition without the pin adhesion, the complex intercalated interlayer at the bottom of stir zone was beneficial to mechanical interlocking of Al/Mg alloys, improving tensile properties. However, the formation of intermetallic compounds was still the main reason of the joint fracture, significantly deteriorating tensile properties. Under the welding speed of 60 mm/min without the pin adhesion phenomenon, the maximum tensile strength of 107 MPa and elongation of 1.2% were achieved.
36 MATERIALS SCIENCE↗
Solving equilibrium problems using extended mathematical programming
We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and (quasi-) variational inequalities, and computing solutions of them from modeling languages. We define a new set of constructs with which users annotate variables and equations of the model to describe equilibrium and variational problems. Our constructs enable a natural translation of the model from one formulation to another more computationally tractable form without requiring the modeler to supply derivatives. In the context of many independent agents in the equilibrium, we facilitate expression of sophisticated structures such as shared constraints and additional constraints on their solutions. We define shared variables and demonstrate their uses for sparse reformulation, economic equilibrium problems sharing economic states, mixed pricing behavior of agents, and so on. We give some equilibrium and variational examples from the literature and describe how to formulate them using our framework. Experimental results comparing performance of various complementarity formulations for shared variables are provided. Our framework has been implemented and is available within GAMS/EMP.
Equilibrium programming↗
Crystal structure of a novel non-Pfam protein PF2046 solved using low resolution B-factor sharpening and multi-crystal averaging methods
Sometimes crystals cannot diffract X-rays beyond 3.0 {angstrom} resolution due to the intrinsic flexibility associated with the protein. Low resolution diffraction data not only pose a challenge to structure determination, but also hamper interpretation of mechanistic details. Crystals of a 25.6 kDa non-Pfam, hypothetical protein, PF2046, diffracted X-rays to 3.38 {angstrom} resolution. A combination of Se-Met derived heavy atom positions with multiple cycles of B-factor sharpening, multi-crystal averaging, restrained refinement followed by manual inspection of electron density and model building resulted in a final model with a R value of 23.5 (R{sub free} = 24.7). The asymmetric unit was large and consisted of six molecules arranged as a homodimer of trimers. Analysis of the structure revealed the presence of a RNA binding domain suggesting a role for PF2046 in the processing of nucleic acids.
59 BASIC BIOLOGICAL SCIENCES↗
Solving macroscopic and microscopic pin-fin heat sink problems by adapted spectral method
In this paper, simulation of heat transfer in a heat sink with macroscopic and microscopic scales when one pin-fin is added to the system is investigated by the proposed spectral method. In the microscopic problems, heat transfer model uses dual-phase lag formulas in contrast with macroscopic problems when Fourier law is used to formulate the governing equation. In macroscopic problem, the results are compared with COMSOL multiphysics software results and a good agreement between the results are shown. In microscopic problems, 3D Gaussian heat source is used and boundary conditions obey the Newton law. Comparisons show the efficiency of the current method, while the results are compared with existed literature. It is shown that: by adding one pin fin to the heat sink problem, temperature of the system will decrease. Numerical results are given and graphs of the temperature for various kinds of pin-fin heat sink problems are depicted.
97 MATHEMATICS AND COMPUTING↗
Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations
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.
97 MATHEMATICS AND COMPUTING↗
An active learning high-throughput microstructure calibration framework for solving inverse structure–process problems in materials informatics
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.
36 MATERIALS SCIENCE↗
A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes
Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithms for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.
97 MATHEMATICS AND COMPUTING↗
A new fast method of solving the high dimensional elliptic eigenvalue problem
Not Available
Huang, Ruihao↗
Development of a set of benchmark problems to verify numerical methods for solving burnup equations
Not Available
Lago, Daniel↗
Solving non-Markovian open quantum systems with multi-channel reservoir coupling
We extend the non-Markovian quantum state diffusion (QSD) equation to open quantum systems which exhibit multi-channel coupling to a harmonic oscillator reservoir. Open quantum systems which have multi-channel reservoir coupling are those in which canonical transformation of reservoir modes cannot reduce the number of reservoir operators appearing in the interaction Hamiltonian to one. We show that the non-Markovian QSD equation for multi-channel reservoir coupling can, in some cases, lead to an exact master equation which we derive. We then derive the exact master equation for the three-level system in a vee-type configuration which has multi-channel reservoir coupling and give the analytical solution. Finally, we examine the evolution of the three-level vee-type system with generalized Ornstein-Uhlenbeck reservoir correlations numerically. - Highlights: Black-Right-Pointing-Pointer The concept of multi-channel vs. single-channel reservoir coupling is rigorously defined. Black-Right-Pointing-Pointer The non-Markovian quantum state diffusion equation for arbitrary multi-channel reservoir coupling is derived. Black-Right-Pointing-Pointer An exact time-local master equation is derived under certain conditions. Black-Right-Pointing-Pointer The analytical solution to the three-level system in a vee-type configuration is found. Black-Right-Pointing-Pointer The evolution of the three-level system under generalized Ornstein-Uhlenbeck noise is plotted for many parameter regimes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗