Reduced basis method for the elastic scattering by multiple shape-parametric open arcs in two dimensions

We consider the elastic scattering problem by multiple disjoint arcs or cracks in two spatial dimensions. A key aspect of our approach lies in the parametric description of each arc’s shape, which is controlled by a potentially high-dimensional, possibly countably infinite, set of parameters. We are interested in the efficient approximation of the parameter-to-solution map employing model order reduction techniques, specifically the reduced basis method. Firstly, we use boundary potentials to transform the boundary value problem, originally posed in an unbounded domain, into a system of boundary integral equations set on the parametrically defined open arcs. We adopt the two-phase paradigm (offline and online) of the reduced basis method to construct a fast surrogate. In the offline phase, we construct a reduced order basis tailored to the single arc problem assuming a complete decoupling among arcs. In the online phase, when computing solutions for the multiple arc problem with a new parametric input, we use the aforementioned basis for each individual arc. We present a comprehensive theoretical analysis of the method, fundamentally based on our previous work [Pinto et al., J. Fourier Anal. Appl. 30 (2024) 14]. In particular, the results stated therein allow us to find appropriate bounds for the so-called Kolmogorov width. Finally, we present a series of numerical experiments demonstrating the advantages of our proposed method in terms of both accuracy and computational efficiency

Numerical approximation for stochastic nonlinear fractional diffusion equation driven by rough noise

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters H1, … , Hd+1 ∈ (0, ½] and d = 1, 2. We first provide the regularity of the solution. Then we employ the Wong–Zakai approximation to regularize the rough noise and discuss the convergence of the approximation. Next, the finite element and backward Euler convolution quadrature methods are used to discretize spatial and temporal operators for the obtained regularized equation, and the detailed error analyses are developed. Finally, some numerical examples are presented to confirm the theory

Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis

We study a linear model for the propagation of acoustic and surface gravity waves in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. In this paper, we introduce a new formulation written with a generalized potential. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well-posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides

Seed Oil (MOSEIL) Reduce CTGF (Connective Tissue Growth Factor) Gene Expression in Mice (

Liver fibrosis is a chronic liver disease that accounts for 45% of all causes of death in the world. Treatment for liver fibrosis until this day only uses synthetic drugs based on the cause. There are many side effects from synthetic drugs, so it is necessary to look for natural traditional medicines to treat liver fibrosis. One plant that has potential as an antifibrotic agent is Moringa oleifera seeds. This research aims to determine the effect of Moringa oleifera seed oil (MOSEIL) on mice (Mus musculus) with liver fibrosis models to develop drugs and prevent liver fibrosis. This study used 30 Balb/C mice that injected intraperitoneally with CCl4 and MOSEIL for 8 weeks. Body weight was measured once a week during treatment. The liver is weighed after dissection. Mice livers were taken to see the level of liver inflammation through histology and RT-qPCR tests to see CTGF gene expression. Data were analyzed using ANOVA with Duncan's post hoc test. Histological test results showed that MOSEIL could reduce necrosis and inflammation in the group given MOSEIL. CCl4 caused a significant reduction in the body weight of mice, while the results of the ANOVA on mice liver weight were not significant. Mice treated with MOSEIL had decreased CTGF gene expression compared to mice not treated with MOSEIL. This research requires further exploration and formulation of the active ingredients of Moringa oleifera seeds to prove further that MOSEIL has potential as an anti-liver fibrosis drugs

Robust optimization for multimodal route planning integrating shared taxi and bus under uncertain traveling time

Multimodal transportation that integrates multiple transport modes, such as buses, taxis, and subways, plays a crucial role in alleviating environmental pollution and improving mobility. However, unpredictable traffic conditions may disrupt the travel time. This work studies a robust multimodal route planning problem (RMRP), focusing on the integration of shared taxis and buses. It devises an innovative route planning approach for shared taxis to enable passengers to seamlessly transition between the two modes, while reducing the impact of uncertainty and allowing passengers to arrive on time. It establishes a multiobjective optimization model that considers travel time uncertainty. The objectives are minimizing the total travel distance traversed by shared taxis and maximizing the passenger satisfaction. A novel nondominated sorting genetic algorithm with uncertainty repair (NSGA-UR) is proposed to solve the problem. It incorporates innovative encoding and decoding methods, evolution strategies, and an uncertainty repair strategy. NSGA-UR demonstrates higher robustness compared to several widely used multiobjective optimization algorithms, including NSGA-II, MOPSO, and MOGWO. In addition, experimental results show the superiority of the algorithm in solving RMRP. This work can contribute to the advancement of intelligent public transportation services

Discovering four space dimensions for the organization of electronic orbitals in a neon atom

A neon atom includes a helium shell and a neon shell. The helium sphere is isotropic and may be regarded as a one-dimensional point whereas the neon spherical layer contains four basic space dimensions: two symmetric periphery points, two complementary semicircular arcs, two opposite hemispherical surfaces, and an outer solid sphere minus an inner sphere. While 2s electronic orbital pair are a four-dimensional hollow ball in shape, three types of 2p electronic orbitals in the X, Y, and Z directions are anisotropic because they are points, arcs, and surfaces respectively. The atomic structure with dimension stairs must have been the theoretical ground of orbital quantization in quantum mechanics. We suggest that electronic motion should be characterized by dimensional transformation through continuous dynamic calculus of electromagnetism instead of discrete linear algebra of mechanics. Eight electrons in a neon shell are undergoing general harmonic oscillations in their respective dimensions, forming a continuous octet cycle that encapsulates both 1s electrons in the middle. We delineate this exquisite order of electronic orbitals in a neon atom by geometry, trigonometry, calculus, and differential equations in conformity with the Schrödinger equations in a coherent manner. Experimental results from various aspects are furnished to support this fresh view of atomic structure

Nuclear Astrophysics with RI Beams at CRIB

Radioactive-isotope (RI) beams are essential for studies on relevant astrophysical reactions involving RIs. RIs play important roles in high-temperature stellar environments, but the experimental study of RI-involving astrophysical reactions is still challenging for many cases, mainly due to the limited intensity of the RI beam. Researchers have devised several methods to overcome this difficulty. Here we discuss the development of the RI beams at the low-energy RI beam separator CRIB, operated by Center for Nuclear Study, the University of Tokyo. We also introduce recent successful cases of astrophysical reaction study at CRIB. One is a study on the 22Mg(α, p), which is a relevant reaction in high-temperature stellar environment such as X-ray bursts. Another is an experiment on the 7Be(n, p) and 7Be(n, α) reactions in the Big-Bang nucleosynthesis with the “Trojan-horse” method, performed for investigating the 7Li abundance problem in the primordial universe

Probing the heating of the neutral atomic interstellar medium in the Dwarf Galaxy Survey through infrared cooling lines

Context. Star formation in galaxies is regulated by dynamical and thermal processes. In the Milky Way and star-forming galaxies with similar metallicity, the photoelectric effect on small dust grains usually dominates the heating of the neutral atomic gas, which constitutes the main star-forming gas reservoir. In more metal-poor galaxies, the lower dust-to-gas mass ratio together with the higher occurrence and luminosity of X-ray sources suggest that other heating mechanisms may be at play. Aims. We aim to determine the contribution of the photoelectric effect, photoionization by UV and X-ray photons, and ionization by cosmic rays to the total heating of the neutral gas in a sample of 37 low-metallicity galaxies. In particular, we wish to assess whether X-ray sources can be a significant source of heating. We also attempt to recover the intrinsic X-ray fluxes and compare them with observations when available. Methods. We used the statistical code MULTIGRIS together with a photoionization grid of Cloudy models propagating radiation from stellar clusters and potential X-ray sources to the ionized and neutral gas. This grid includes physical parameters such as metallicity, gas density, ionization parameter, and radiative source properties. We describe a galaxy as a combination of many 1D components linked by a few physical hyperparameters. We used infrared cooling lines as constraints to evaluate the most likely combinations and parameters. Results. We constrained the heating fractions for the main mechanisms for the first time in a low-metallicity galaxy sample. We show that for the higher metallicity galaxies, the photoelectric effect dominates the neutral gas heating. At metallicities below 1 /8 the Milky Way value, cosmic rays and photoionization can become predominant. We computed an observational proxy for the photoelectric effect heating efficiency on polycyclic aromatic hydrocarbons (PAHs) using the total cooling traced by [CI

Evolving massive stars to core collapse with GENEC: Extension of equation of state, opacities and effective nuclear network

Context. Stars with initial mass above roughly 8 M⊙ will evolve to form a core made of iron group elements, at which point no further exothermic nuclear reactions between charged nuclei may prevent the core collapse. Electron capture, neutrino losses, and the photo-disintegration of heavy nuclei trigger the collapse of these stars. Models at the brink of core collapse are produced using stellar evolution codes, and these pre-collapse models may be used in the study of the subsequent dynamical evolution (including their explosion as supernovae and the formation of compact remnants such as neutron stars or black holes). Aims. We upgraded the physical ingredients employed by the GENeva stellar Evolution Code, GENEC, so that it covers the regime of high-temperatures and high-densities required to produce the progenitors of core-collapse. Our ultimate goal is producing pre-supernova models with GENEC, not only right before collapse, but also during the late phases (silicon and oxygen burning). Methods. We have improved GENEC in three directions: equation of state, the nuclear reaction network, and the radiative and conductive opacities adapted for the computation of the advanced phases of evolution. We produce a small grid of pre-supernova models of stars with zero age main sequence masses of 15 M⊙, 20 M⊙, and 25 M⊙ at solar and less than half solar metallicities. The results are compared with analogous models produced with the MESA code. Results. The global properties of our new models, particularly of their inner cores, are comparable to models computed with MESA and pre-existing progenitors in the literature. Between codes the exact shell structure varies, and impacts explosion predictions. Conclusions. Using GENEC with state-of-the-art physics, we have produced massive stellar progenitors prior to collapse. These progenitors are suitable for follow-up studies, including the dynamical collapse and supernova phases. Larger grids of supernova progenitors are now feasible, with the potential for further dynamical evolution

The impact of disk-locking on convective turnover times of low-mass pre-main sequence and main sequence stars

Aims. The impact of disk-locking on the stellar properties related to magnetic activity from the theoretical point of view is investigated. Methods. We use the ATO