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The pretrained large language models have been widely tested for their performance on some challenging tasks including arithmetic, commonsense, and symbolic reasoning. Recently how to combine LLMs with prompting techniques has attracted lots of researchers to propose their models to automatically solve math word problems. However, most research works focus on solving math problems at the elementary school level and few works aim to solve problems in science disciplines, e.g., Physics. In this exploratory study, we discussed the potential pedagogical benefits of using ChatGPT in physics and demonstrated how to prompt ChatGPT in solving physics problems. The results suggest that ChatGPT is able to solve some physics calculation problems, explain solutions, and generate new exercises at a human level.

Simulating discontinuities has been a long-standing challenge, especially when dealing with shock waves characterized by strong nonlinear features. Despite their promise, the recently developed physics-informed neural networks (PINNs) have not yet fully demonstrated their effectiveness in handling discontinuities when compared to traditional shock-capturing methods. In this study, we reveal a paradoxical phenomenon during the training of PINNs when computing problems with strong nonlinear discontinuities. To address this issue and enhance the PINNs’ ability to capture shocks, we propose PINNs-WE (Physics-Informed Neural Networks with Equation Weight) method by introducing three novel strategies. Firstly, we attenuate the neural network’s expression locally at ‘transition points’ within the shock waves by introducing a physics-dependent weight into the governing equations. Consequently, the neural network will concentrate on training the smoother parts of the solutions. As a result, due to the compressible property, sharp discontinuities emerge, with transition points being compressed into well-trained smooth regions akin to passive particles. Secondly, we also introduce the Rankine–Hugoniot (RH) relation, which is equivalent to the weak form of the conservation laws near the discontinuity, in order to improve the shock-capturing preformance. Lastly, we construct a global physical conservation constraint to enhance the conservation properties of PINNs which is key to resolve the right position of the discontinuity. To illustrate the impact of our novel approach, we investigate the behavior of the one-dimensional Burgers’ equation, as well as the one- and two-dimensional Euler equations. In our numerical experiments, we compare our proposed PINNs-WE method with a traditional high-order weighted essential non-oscillatory (WENO) approach. The results of our study highlight the significant enhancement in discontinuity computing by the PINNs-WE method when compared to traditional PINNs.

The Non-Symmetrized Hyperspherical Harmonics method (NSHH) is introduced in the hypernuclear sector and benchmarked with three different ab-initio methods, namely the Auxiliary Field Diffusion Monte Carlo method, the Faddeev–Yakubovsky approach and the Gaussian Expansion Method. Binding energies and hyperon separation energies of three- to five-body hypernuclei are calculated by employing the two-body Λ N component of the phenomenological Bodmer–Usmani potential (Bodmer and Usmani in Nucl Phys A 477:621, 1988 ; Usmani and Khanna in J Phys G 35:025105, 2008 ), and a hyperon-nucleon interaction (Hiyama et al. in Phus Rev C 65:011301, 2001 ) simulating the scattering phase shifts given by NSC97f (Rijken et al. in Phys Rev C 59:21, 1999 ). The range of applicability of the NSHH method is briefly discussed.

X‐ray diffraction imaging (XDI) is utilized for visualizing the structures of non‐crystalline particles in material sciences and biology. In the structural analysis, phase‐retrieval (PR) algorithms are applied to the diffraction amplitude data alone to reconstruct the electron density map of a specimen particle projected along the direction of the incident X‐rays. However, PR calculations may not lead to good convergence because of a lack of diffraction patterns in small‐angle regions and Poisson noise in X‐ray detection. Therefore, the PR calculation is still a bottleneck for the efficient application of XDI in the structural analyses of non‐crystalline particles. For screening maps from hundreds of trial PR calculations, we have been using a score and measuring the similarity between a pair of retrieved maps. Empirically, probable maps approximating the particle structures gave a score smaller than a threshold value, but the reasons for the effectiveness of the score are still unclear. In this study, the score is characterized in terms of the phase differences between the structure factors of the retrieved maps, the usefulness of the score in screening the maps retrieved from experimental diffraction patterns is demonstrated, and the effective resolution of similarity‐score‐selected maps is discussed. The similarity score is a useful metric for screening electron density maps from phase‐retrieval calculations in X‐ray diffraction imaging. The characteristics of the score have been studied in reciprocal space and are described here.

Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles such as neutrons or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging and extremely valuable. In this paper, we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.

In this paper we study the well-posedness and the asymptotic stability of a one-dimensional thermoelastic Bresse system, where the heat conduction is given by Cattaneo’s law effective in the shear angle displacements. We establish the well-posedness of the system and prove that the system is exponentially stable depending on the parameters of the system. Furthermore, we show that in general, the system is not exponential stable. In this regards, we prove that the solution decays polynomially.

The thermal properties of pavement layers made of concrete with varying bulk densities are a particularly interesting topic in the context of development road technologies. If a hybrid layer system is used as a starting point, with thin asphalt layers (from 1 cm to 4 cm) laid on top of a foam concrete layer, thermal properties begin to play a crucial role. The main research problem was to create a test method enabling the assessment of the influence of solar heating on the thermal parameters of the building material, especially cement concrete. For this reason, this paper is concerned specifically with the assessment of a new methodology for testing and calculating the value of the thermal diffusivity coefficient of samples made of concrete varying bulk densities. In this case, using the proprietary concept the authors built a solar simulator using a multi-source lighting system. The analysis of the results of laboratory tests and numerical analyses allowed the authors to observe that there is a strong correlation between the bulk density of samples heated and the thermal diffusivity parameter, which appears in the unidirectional heat transfer equation. The strength of this relationship has been expressed with the coefficient of determination and amounts to 99%. The calculated values of the coefficient of thermal diffusivity for samples made of foam concrete range from 0.16×10−6m2s to 0.52×10−6m2s and are lower (from 2.5 to 8 times) than the value determined for samples made of typical cement concrete.

This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, \"imperfections\" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry.

The electrodynamic model of interaction of electromagnetic waves with multilayer graphene–dielectric metamaterials in the terahertz (THz) frequency range is constructed based on solving the diffraction problem for the Maxwell equations by using the method of autonomous blocks with Floquet channels. An imitation probabilistic model has been developed and the results of probabilistic calculation of characteristics of THz metamaterial-based filters have been obtained taking into account random variations in parameters (the surface conductivity of graphene and the thickness of dielectric layers).

The feasibility of generation of powerful x-ray radiation by a cascade free-electron laser (FEL) with amplification of higher harmonics using a two-frequency undulator is studied. To analyze the FEL operation, a complex phenomenological single-pass FEL model is developed and used. It describes linear and nonlinear generation of harmonics in the FEL with seed laser that takes into account initial electron beam noise and describes all main losses of each harmonic in each FEL cascade. The model is also calibrated against and approved by the experimental FEL data and available results of three-dimensional numerical simulation. The electron beam in the undulator is assumed to be matched and focused, and the dynamics of power in the singlepass FEL with cascade harmonic multipliers is investigated to obtain x-ray laser radiation in the FEL having the shortest length, beam energy, and frequency of the seed laser as low as possible. In this context, the advantages of the two-frequency undulator used for generation of harmonics are demonstrated. The evolution of harmonics in a multicascade FEL with multiplication of harmonics is investigated. The operation of the cascade FEL at the wavelength λ = 1.14 nm, generating ~30 MW already on 38 m with the seed laser operating at a wavelength of 11.43 nm corresponding to the maximal reflectivity of the multilayered mirror MoRu/Be coating is investigated. In addition, the operation of the multicascade FEL with accessible seed UVlaser operating at a wavelength of 157 nm (F2 excimer UV-laser) and electron beam with energy of ~0.5 GeV is investigated. X-ray radiation simulated in it at the wavelength λ ~ 3.9 nm reaches power of ~50 MW already at ~27 m, which is by two orders of magnitude shorter than 3.4 km of the x-ray FEL recently put into operation in Europe.