The 2-D 3-T heat conduction equations can approximate the propagation of energy in the material, as well as the energy exchange process of electrons, ions and photons. In many cases, the computational time to solve th...
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In this paper,the authors consider the local well-posedness for the derivative Schrödinger equation in higher dimension ut-iΔu+|u|^(2)(→γ·▽u)+u^(2)(→λ·▽-u)=0,(x,t)∈R^(n)×R,→γ,→λ∈R^(n);...
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In this paper,the authors consider the local well-posedness for the derivative Schrödinger equation in higher dimension ut-iΔu+|u|^(2)(→γ·▽u)+u^(2)(→λ·▽-u)=0,(x,t)∈R^(n)×R,→γ,→λ∈R^(n);n≥2 It is shown that the Cauchy problem of the derivative Schrödinger equation in higher dimension is locally well-posed in H^(s)(R^(n))(s>n/2)for any large initial *** this result can compare with that in one dimension except for the endpoint space H^(n/2).
The Universal Approximation Theorem posits that neural networks can theoretically possess unlimited approximation capacity with a suitable activation function and a freely chosen or trained set of parameters. However,...
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The present work is motivated by the mixing mechanism in inertial confinement fusion (ICF), which remarkably degrades the ignition performance. The mixing is a direct result of velocity disequilibrium and affected by ...
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In this work,the pulsation analysis is performed on 83 high-amplitudeδScuti stars(HADS),which have been observed by the Transiting Exoplanet Survey *** results show that 49 of these HADS show single-mode pulsation,27...
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In this work,the pulsation analysis is performed on 83 high-amplitudeδScuti stars(HADS),which have been observed by the Transiting Exoplanet Survey *** results show that 49 of these HADS show single-mode pulsation,27 of them show radial double-modes pulsation(in which 22 of them pulsate with the fundamental and first overtone modes and five of them pulsate with the first and second overtone modes),and seven of them show radial triple-modes pulsation(three of which are newly confirmed triple-mode HADS).The histogram of the fundamental periods and the ratios between the fundamental and first overtone periods show bimodal structures,which might be caused by the stellar evolution in this specific *** of the radial triple-mode HADS have a fundamental amplitude of 41-54 mmag,and 50%of them have similar amplitudes of the fundamental and first overtone pulsation *** these hints require further confirmation not only in observations with more HADS samples,but also in theoretical models with suitable treatments of stellar evolution and pulsation.
Hydrous phases play a fundamental role in the deep-water cycle on Earth. Understanding their stability and thermoelastic properties is essential for constraining their abundance using seismic tomography. However, dete...
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Hydrous phases play a fundamental role in the deep-water cycle on Earth. Understanding their stability and thermoelastic properties is essential for constraining their abundance using seismic tomography. However, determining their elastic properties at extreme conditions is notoriously challenging. The challenges stem from the complex behavior of hydrogen bonds under high pressures and temperatures (P,Ts). In this study, we evaluate how advanced molecular dynamics simulation techniques can address these challenges by investigating the adiabatic elasticity and acoustic velocities of δ−AlOOH, a critical and prototypical high-pressure hydrous phase. We compared the performances of three methods to assess their viability and accuracy. The thermoelastic tensor was computed up to 140 GPa and temperatures up to 2700 K using molecular dynamics with a DeePMD machine-learning interatomic potential based on the SCAN meta-GGA functional. The excellent agreement with ambient condition single-crystal ultrasound measurements and the correct description of velocity changes induced by H-bond disorder-symmetrization transition observed at 10 GPa in Brillouin scattering measurements underscores the accuracy and efficacy of our approach.
The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this *** the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to...
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The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this *** the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev *** the careful energy estimates,a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error *** convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.
Let γ(t) = (P1(t), . . ., Pn(t)) where Pi is a real polynomial with zero constant term for each 1 ≤ i ≤ n. We will show the existence of the configuration {x, x + γ(t)} in sets of positive density ǫ in [0, 1]n wit...
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This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical *** algorithm has half-face fluxes and a nodal velocity solver,which can ensure t...
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This paper presents a second-order direct arbitrary Lagrangian Eulerian(ALE)method for compressible flow in two-dimensional cylindrical *** algorithm has half-face fluxes and a nodal velocity solver,which can ensure the compatibility between edge fluxes and the nodal flow *** two-dimensional cylindrical geometry,the control volume scheme and the area-weighted scheme are used respectively,which are distinguished by the discretizations for the source term in the momentum *** two-dimensional second-order extensions of these schemes are constructed by employing the monotone upwind scheme of conservation law(MUSCL)on unstructured *** results are provided to assess the robustness and accuracy of these new schemes.
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