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1. Revisiting the Replica Trick: Competition Between Spin Glass and Conventional Order

   https://doi.org/10.1007/s10955-023-03135-1  

   Baldwin, Christopher L.; Swingle, Brian (July 2023, Journal of Statistical Physics)

   There is an ambiguity in how to apply the replica trick to spin glass models which have additional order parameters unrelated to spin glass order—with respect to which quantities does one minimize vs maximize the action, and in what sequence? Here we show that the correct procedure is to first maximize with respect to “replica” order parameters, and then minimize with respect to “conventional” order parameters. With this result, we further elucidate the relationship between quenched free energies, annealed free energies, and replica order—it is possible for the quenched and annealed free energies to differ even while all replica order parameters remain zero. 

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2. DIRK Schemes with High Weak Stage Order

   https://doi.org/10.1007/978-3-030-39647-3_36  

   Ketcheson, D.; Seibold, B.; Shirokoff, D.; Zhou, D. (August 2020, Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering. Springer.)

   Sherwin, S.; Moxey, D.; Peiro, J.; Vincent, P.; Schwab, C. (Ed.)

   Runge-Kutta time-stepping methods in general suffer from order reduction: the observed order of convergence may be less than the formal order when applied to certain stiff problems. Order reduction can be avoided by using methods with high stage order. However, diagonally-implicit Runge-Kutta (DIRK) schemes are limited to low stage order. In this paper we explore a weak stage order criterion, which for initial boundary value problems also serves to avoid order reduction, and which is compatible with a DIRK structure. We provide specific DIRK schemes of weak stage order up to 3, and demonstrate their performance in various examples. 

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3. Development and Calibration of Reduced-order Building Energy Models by coupling with High-order Simulations

   https://doi.org/10.5281/zenodo.3689397  

   Zhang, R.; Karaguzel, O. T. (February 2020, Global journal of advanced engineering technologies and sciences)

   Building energy modeling and simulation is an effective approach to evaluate building performance and energy system operations to achieve higher building energy efficiency. The high-order building models can offer exceptional simulation capacity and accuracy, however, its high level of complexity does not allow it to directly work with the optimization algorithms and methods that require a complete differential-algebraic-equations-based mathematical description of the physical model. In order to fill in the gap, the study presents a systematic approach to develop and calibrate the reduced-order building models. A notable feature of the approach is its coupling with high-order building simulations in order to pre-process the input information and support the calibration of the reduced model. A case study on a representative office building shows that the developed reduced-order model can present acceptable simulation accuracy compared with high-order simulations and significantly reduce the modeling complexity. 

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4. On the first-order parts of problems in the Weihrauch degrees

   https://doi.org/10.3233/COM-230446  

   Dzhafarov, Damir D; Solomon, Reed; Yokoyama, Keita (January 2024, Computability)

   We introduce the notion of the first-order part of a problem in the Weihrauch degrees. Informally, the first-order part of a problem P is the strongest problem with codomaixn ω that is Weihrauch reducible to P. We show that the first-order part is always well-defined, examine some of the basic properties of this notion, and characterize the first-order parts of several well-known problems from the literature. 

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5. High-order strongly nonlinear long wave approximation and solitary wave solution. Part 2. Internal waves

   https://doi.org/10.1017/jfm.2022.950  

   Choi, Wooyoung (December 2022, Journal of Fluid Mechanics)

   A strongly nonlinear long-wave approximation is adopted to obtain a high-order model for large-amplitude long internal waves in a two-layer system by assuming the water depth is much smaller than the typical wavelength. When truncated at the first order, the model can be reduced to the regularized strongly nonlinear model of Choiet al.(J. Fluid Mech., vol. 629, 2009, pp. 73–85), which lessens the Kelvin–Helmholtz instability excited by the tangential velocity jump across the interface in the inviscid Miyata–Choi–Camassa (MCC) equations. Using the second-order model, the next-order correction to the internal solitary wave solution of the MCC equations is found and its validity is examined with the Euler solution in terms of the wave profile, the effective wavelength and the velocity profile. It is shown that the correction greatly improves the comparison with the Euler solution for the whole range of wave amplitudes and no further correction is necessary for practical applications. Based on a local stability analysis, the region of stability for the second-order long-wave model is identified in the physical parameter space so that the efficient numerical scheme developed for the first-order model can be used for the second-order model. 

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