We derive the global existence of weak solutions of the Shigesada–Kawasaki–Teramoto systems in any space dimension d≥1 with a rather general condition on the coefficients. The existence is ...established using finite differences in time with truncations and an argument of Stampacchia’s maximum principle to show the positivity of the solutions. We derive also the existence of a weak global attractor.
In this paper, an h∕p spectral element method with least-square formulation for parabolic interface problem will be presented. The regularity result of the parabolic interface problem is proven for ...non-homogeneous interface data. The differentiability estimates and the main stability estimate theorem, using non-conforming spectral element functions, are proven. Error estimates are derived for h and p versions of the proposed method. Specific numerical examples are given to validate the theory.
•An h∕p least-squares SEM for parabolic interface problem will be presented.•The regularity result is proven for non-homogeneous interface data.•Stability estimates and error estimates are discussed rigorously.•Specific numerical examples are given to validate the theory.
We present the physical properties of V404 Lyr exhibiting eclipse timing variations and multiperiodic pulsations from all historical data including the Kepler and SuperWASP observations. Detailed ...analyses of 2922 minimum epochs showed that the orbital period has varied through a combination of an upward-opening parabola and two sinusoidal variations, with periods of P sub(3) = 649 days and P sub(4) = 2154 days and semi-amplitudes of K sub(3) 193 s and K sub(4) = 49 s, respectively. A satisfactory model for the Kepler light curves was obtained by applying a cool spot to the secondary component. The results demonstrate that the close eclipsing pair is in a semi-detached, but near-contact, configuration; the primary fills approximately 93% of its limiting lobe and is larger than the lobe-filling secondary. Only eight eclipsing binaries have been known to contain gamma Dor pulsating components and, therefore, V404 Lyr will be an important test bed for investigating these rare and interesting objects.
The parabolic Radon transform has been widely used in multiple attenuation. To further improve the accuracy and efficiency of the Radon transform, we developed the lambda-f domain high-resolution ...Radon transform based on the fast and modified parabolic Radon transform presented by Abbad. The introduction of a new variable lambda makes the transform operator frequency-independent. Thus, we need to calculate the transform operator and its inverse operator only once, which greatly improves the computational efficiency. Besides, because the primaries and multiples are distributed on straight lines with different slopes in the lambda-f domain, we can easily choose the filtering operator to suppress the multiples. At the same time, the proposed method offers the advantage of high-resolution Radon transform, which can greatly improve the precision of attenuating the multiples. Numerical experiments suggest that the multiples are well suppressed and the amplitude versus offset characteristics of the primaries are well maintained. Real data processing results further verify the effectiveness and feasibility of the method.PUBLICATION ABSTRACT
A compact scintillator-based electron–ion Thomson Parabola Spectrometer (ei-TPS) is designed and built up, which is able to measure the spectrum of electron and ion beams simultaneously in the same ...angular axis and real-time mode. The energy range of electrons is around 0.27–3.8 MeV with a relative energy resolution better than 2.5%, and the energy range of proton is around 0.16–21 MeV with a relative energy resolution better than 4% at the kinetic energy of 1 MeV, which makes it suitable for laser-driven ion acceleration experiments with 100-TW level laser. Detailed mathematical modeling is performed to reveal the dependence of properties, such as energy range and resolution, response, and detection threshold, on various parameters of ei-TPS, which is useful to modify the parameters according to specific requirements of electrons and ions.
Reactions of concerted decomposition of cyclic molecules (Diels—Alder retro-reactions) were studied using quantum chemical modeling and the method of intersecting parabolas (M3IP model). According to ...results of quantum chemical calculations and topological analysis of transition states (TSs) of five concerted decomposition reactions of cyclic molecules, all TSs represent six-membered rings in which the bonds being cleaved are weak covalent ones. The presence of ring heteroatoms (N, O, or S) has a strong impact on the TS geometry and on the energy characteristics of the reactions. The M3IP model was used to process the experimental results to develop an algorithm for calculating the activation energies (
E
) of the reactions in question and the classical potential barriers to thermally neutral reaction (
E
e
0
). Factors influencing the energies
E
were determined and assessed. These include the enthalpy of reaction, substituents, ring heteroatoms, the force constants of bonds, and the bond dissociation energies. A comparison of the activation energies
E
and the enthalpies of reaction Δ
H
obtained from the M3IP and density functional B3LYP/6-311++G** calculations revealed good agreement between them.
In 1657, the Oxford University student William Neile, using infinitesimal techniques developed by Bonaventura Cavalieri, Evangelista Torricelli, and John Wallis, successfully found the arc length of ...the semicubical parabola. We give an exposition and modern interpretation of his result and discuss some of the historical outcomes that stemmed from it.
Decomposition reactions of azoalkanes of different structure were studied by quantum chemistry methods (MP2/6-311++G** calculations) and by the method of three intersecting parabolas (M3IP). The MP2 ...method was used to obtain the transition-state geometries, the bond lengths in the molecules under study, and the activation energies. Possible mechanisms of decomposition are discussed. Concerted decomposition of branched azoalkanes was shown to be the most probable mechanism of the process. The M3IP method was used to calculate the kinetic and thermodynamic parameters of concerted decomposition of azoalkanes and to determine and evaluate the main factors affecting the activation energy (
E
). The stabilization energy of the radical being formed in the decomposition reaction is one of the key factors determining the concerted mechanism. The kinetic parameters calculated by the two independent methods are in good agreement.
Modelling the dynamics of wildfires is very computationally challenging. Although three-dimensional computational fluid dynamics (CFD) models have been successfully applied to wildfires, the ...computational time required makes them currently impractical for operational usage. In this study, we develop a two-dimensional propagation model coupled to a ‘pyrogenic’ potential flow formulation representing the inflow of air generated by the fire. This model can accurately replicate features of fires previously unable to be simulated using current two-dimensional models, including development of a fire line into a parabolic shape, attraction between nearby fires and the observed closing behaviour of ‘V’ shaped fires. The model is compared to experimental results with good agreement. The pyrogenic potential model is orders of magnitude faster than a full CFD model, and could be used for improved operational wildfire prediction.
•Development of a coupled ‘pyrogenic’ model for fire propagation with inflowing air generated by the fire.•Very good fit between a generalised rate-of-spread model utilising pyrogenic feedback and small-scale experimental fires.•Two-dimensional formulation runs at a fraction of the cost of a full three-dimensional model.
Isochrony in 3D Radial Potentials Simon-Petit, Alicia; Perez, Jérôme; Duval, Guillaume
Communications in mathematical physics,
01/2018, Letnik:
363, Številka:
2
Journal Article
Recenzirano
Revisiting and extending an old idea of Michel Hénon, we geometrically and algebraically characterize the whole set of isochrone potentials. Such potentials are fundamental in potential theory. They ...appear in spherically symmetrical systems formed by a large amount of charges (electrical or gravitational) of the same type considered in mean-field theory. Such potentials are defined by the fact that the radial period of a test charge in such potentials, provided that it exists, depends only on its energy and not on its angular momentum. Our characterization of the isochrone set is based on the action of a real affine subgroup on isochrone potentials related to parabolas in the R2 plane. Furthermore, any isochrone orbits are mapped onto associated Keplerian elliptic ones by a generalization of the Bohlin transformation. This mapping allows us to understand the isochrony property of a given potential as relative to the reference frame in which its parabola is represented. We detail this isochrone relativity in the special relativity formalism. We eventually exploit the completeness of our characterization and the relativity of isochrony to propose a deeper understanding of general symmetries such as Kepler’s Third Law and Bertrand’s theorem.
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