Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

Topological Space of the Chemical Elements and its Properties

We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table     

Cobalt Ion Incorporation into Periodic Mesoporous Organosilica Materials Synthesized by Co-condensation of 1,2-Bistrimethoxysilylethane with 3-Glycidoxypropyltriethoxysilane

Bifunctional periodic mesoporous organosilica materials with and without cobalt ion incorporation were synthesized by co-condensation of 1,2-bistrimethoxysilylethane (BTME) with 3-glycidoxypropyltriethoxysilane (GPTS) in the presence of cetyltrimethylammonium bromide. Nitrogen gas adsorption on samples with varying ratios of BTME:GPTS revealed that increasing the amount of GPTS affects pore size, surface area and pore volume as well as shapes of the isotherms and hysteresis loops. The hysteresis loops of the Type IV isotherms obtained for GPTS-modified ethane silica materials (without cobalt ion) change from Type H3 to Type H4 with increasing GPTS content. There is a tendency for pore sizes to change from mesopore to micropore when the amount of GPTS is increased. Isotherms of cobalt ion incorporated GPTS-modified ethane silica materials change from Type IV to Type I with increasing GPTS content. The surface area, pore volume and pore diameter decrease with increasing loading of GPTS as well as after cobalt ion incorporation. Thermogravimetric analysis and differential thermal analysis show that the surfactant is removed by solvent extraction. Cobalt ion incorporation is confirmed by powder X-ray diffraction and Raman spectroscopy.     

The application of the reaction calorimetry to investigate reactions involving unstable compounds

The RC1 calorimeter revealed itself a suitable instrument to obtain information about safety and mechanisms involved in the reaction between cyclohexanecarboxylic acid (AEB) and oleum. A previous hypothesis about the existence of an unstable intermediate was confirmed and its heat of formation was calculated. The heat of sulphonation related to undesirable by-products production and the heat of protonation of AEB with H₂SO₄ were also evaluated. Therefore, it was possible to distinguish the reactions involved in the process and, through their thermal behaviour, to determine the limit conditions to avoid the by-products formation.

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Zusammenfassung Das RC1 Kalorimeter erwies sich als ein geeignetes Instrument, um Informationen über Sicherheit und Mechanismen bei der Reaktion von Cyclohexancarbonsäure (AEB) und Oleum zu gewinnen. Eine bereits bestehende Hypothese über die Existenz eines instabilen Zwischenproduktes konnte bestätigt und dessen Bildungswärme berechnet werden. Weiterhin wurde auch die Sulphonierungswärme bezogen auf die Entstehung von unerwünschten Nebenprodukten und die Protonierungswärme von AEB durch H₂SO₄ ermittelt. Es ist deshalb möglich, die einzelnen Reaktionen innerhalb dieses Prozesses über ihr thermisches Verhalten voneinander zu unterscheiden, um die Grenzbedingungen zur Vermei-dung der Bildung von Nebenprodukten zu ermitteln.

     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

Reflecting a single attosecond pulse by using periodic Mo/Si multilayer mirrors with different layers

The reflecting of a single attosecond pulse from a periodic Mo/Si multilayer was investigated. By changing the number of bi-layers, the periodic multilayer showed greatly different spectral and temporal responses of the attosecond pulse reflection, which has been discussed in detail in this paper. The capability of attosecond pulse reflection of the periodic multilayers with different bi-layer numbers has been evaluated using suitable temporal parameters. In addition, the condition for obtaining high-efficiency reflected pulses has been analyzed by comparing the pulse responses of the periodic multilayer with different layers. The transfer-matrix method together with the fast Fourier transform has been used in our simulation.     

On the construction of periodic solutions of kaplan-yorke type for some differential delay equations

In this paper we point out the main idea to yield periodic solutions of Kaplan-Yorke type of differential delay equations. Some new sufficient conditions for the existence of Kaplan-Yorke type periodic solutions have been given. Many interesting examples are also disscused.     

Lagrangian actions for elliptical solutions of 2-body and 3-body problems with fixed energies

Based on the works of Gordon (1977) and Zhang and Zhou (2001) on the variational minimizing properties for Keplerian orbits and Lagrangian solutions of Newtonian 2-body and 3-body problems, we use the constrained variational principle of Ambrosetti and Coti Zelati (1990) to compute the Lagrangian actions on Keplerian and Lagrangian elliptical solutions with fixed energies. We also find an interesting relation between the period and the energy for Lagrangian elliptical solutions with Newtonian potentials.     

DFT Simulations as Valuable Tool to Support NMR Characterization of Halide Perovskites: the Case of Pure and Mixed Halide Perovskites

Solid state NMR spectroscopy is swiftly emerging as useful tool to characterize the structure, composition and dynamic properties of lead halide perovskites. On the other hand, interpretation of solid state NMR signatures is often challenging, because of the potential presence of many overlapping signals in small range of chemical shifts, hence complicating the extraction of detailed structural features. Here, we demonstrate the reliability of periodic Density Functional Theory in providing theoretical support for the NMR characterization of halide perovskite compounds, considering nuclei with spin I=1/2. For light ¹H and ¹³C nuclei, we predict NMR chemical shifts in good agreement with experiment, further highlighting the effects of motional narrowing. Accurate prediction of the NMR response of ²⁰⁷Pb nuclei is comparably more challenging, but we successfully reproduce the downshift in frequency when changing the halide composition from pure iodine to pure bromine. Furthermore, we confirm NMR as ideal tool to study mixed halide perovskite compounds, currently at the limelight for tandem solar cells and color-tunable light emission.     

Further advances on low-energy lunar impact dynamics

We extend the analysis, started in a previous work [1], concerning the formation of lunar impact craters due to low-energy trajectories. First, we adopt the Circular Restricted Three-Body Problem and consider different choices of initial conditions inside the stable invariant manifold associated with the central invariant one in the neighborhood of the L₂ equilibrium point in the Earth-Moon system. Then we move to the Bicircular Restricted Four-Body Problem to study the effect of the Sun on the distribution of impacts on the Moon’s surface.