Shilnikov lemma for a nondegenerate critical manifold of a Hamiltonian system

Let M be a normally hyperbolic symplectic critical manifold of a Hamiltonian system. Suppose M consists of equilibria with real eigenvalues. We prove an analog of the Shilnikov lemma (strong version of the λ-lemma) describing the behavior of trajectories near M. Using this result, trajectories shadowing chains of homoclinic orbits to M are represented as extremals of a discrete variational problem. Then the existence of shadowing periodic orbits is proved. This paper is motivated by applications to the Poincaré’s second species solutions of the 3 body problem with 2 masses small of order µ. As µ → 0, double collisions of small bodies correspond to a symplectic critical manifold M of the regularized Hamiltonian system. Thus our results imply the existence of Poincaré’s second species (nearly collision) periodic solutions for the unrestricted 3 body problem.     

Layered solutions with multiple asymptotes for non autonomous Allen–Cahn equations in {\mathbb {R}^{3}}

We consider a class of semilinear elliptic equations of the form $$ \label{eq:abs}-\Delta u(x,y,z)+a(x)W'(u(x,y,z))=0,\quad (x,y,z)\in\mathbb {R}^{3},$$ where ${a:\mathbb {R} \to \mathbb {R}}$ is a periodic, positive, even function and, in the simplest case, ${W : \mathbb {R} \to \mathbb {R}}$ is a double well even potential. Under non degeneracy conditions on the set of minimal solutions to the one dimensional heteroclinic problem $$-\ddot q(x)+a(x)W^{\prime}(q(x))=0,\ x\in\mathbb {R},\quad q(x)\to\pm1\,{\rm as}\, x\to \pm\infty,$$ we show, via variational methods the existence of infinitely many geometrically distinct solutions u of (0.1) verifying u(x, y, z) → ± 1 as x → ± ∞ uniformly with respect to ${(y, z) \in \mathbb {R}^{2}}$ and such that ${\partial_{y}u \not \equiv0, \partial_{z}u \not\equiv 0}$ in ${\mathbb {R}^{3}}$ .     

Vibrationally resolved K-shell photoionization cross sections of methane

We use an extension of the static-exchange density functional theory (DFT) method, previously reported in [E. Plésiat et al., Phys. Rev. A 2, 023409 (2012), E. Plésiat, P. Decleva, F. Martín, Phys. Chem. Chem. Phys. 31, 10853 (2012)], to evaluate vibrationally resolved (total and angular) K-shell photoelectron cross sections of methane. The calculated cross sections are in very good agreement with the existing experimental measurements at low photoelectron energies. We show that, in contrast with the rich interference patterns previously observed in molecular frame C(1s) photoelectron angular distributions of methane at both low and high photoelectron energy, no interference effects are observed in the calculated β parameters, even at high photon energies.     

A perturbation-based super-CI approach for the orbital optimization of a CASSCF wave function

A perturbation theory-based algorithm for the iterative orbital update in complete active space self-consistent-field (CASSCF) calculations is presented. Following Angeli et al. (J. Chem. Phys. 2002, 117, 10525), the first-order contribution of singly excited configurations to the CASSCF wave function is evaluated using the Dyall Hamiltonian for the determination of a zeroth-order Hamiltonian. These authors employ an iterative diagonalization of the first-order density matrix including the first-order correction arising from single excitations, whereas the present approach uses the single-excitation amplitudes directly for the construction of the exponential of an anti-Hermitian matrix resulting in a unitary matrix which can be used for the orbital update. At convergence, the single-excitation amplitudes vanish as a consequence of the generalized Brillouin's theorem. It is shown that this approach in combination with direct inversion of the iterative subspace (DIIS) leads to very rapid convergence of the CASSCF iteration procedure. © 2019 Wiley Periodicals, Inc.     

Studies of phononlike low-energy excitations of protein molecules by inelastic x-ray scattering

Molecular dynamics simulations and neutron scattering experiments have shown that many hydrated globular proteins exhibit a universal dynamic transition at TD = 220 K, below which the biological activity of a protein sharply diminishes. We studied the phononlike low-energy excitations of two structurally very different proteins, lysozyme and bovine serum albumin, using inelastic x-ray scattering above and below TD. We found that the excitation energies of the high-Q phonons show a marked softening above TD. This suggests that the large amplitude motions of wavelengths corresponding to this specific Q range are intimately correlated with the increase of biological activities of the proteins.     

Ring Opening Polymerization of Lactide under Solvent‐Free Conditions Catalyzed by a Chlorotitanium Calix[4]arene Complex

A novel chlorotitanium calix[4]arene complex was synthesized and tested, without activator, as catalyst for the polymerization of L ‐ and rac‐lactide under solvent‐free conditions. The catalyst displayed high activity, which depended on the monomer‐to‐catalyst molar ratio, and led to highly isotactic PLLA. Despite concomitant transesterification during the polymerization, polylactide formation was well‐controlled, the molar mass distribution indexes remaining in the restricted range of 1.2–1.4.

     

Investigation of gel porosity clogging during glass leaching

A 5-oxide glass (62.5SiO₂, 16.6B₂O₃, 13.1Na₂O, 6.0CaO, 1.8ZrO₂) was leached at 90 °C at a high glass-surface-area-to-solution-volume ratio (SA/V = 80 cm^?1). Its dissolution rate diminished over time until it became unmeasurable. The alteration layer was characterized by ²⁹Si isotopic tracing in the leaching solution. ToF-SIMS elemental profiles showed that glass dissolution ceased due to clogging of the gel porosity at the gel/solution interface. One of the hypotheses proposed to account for the rate drop observed during borosilicate glass alteration is based on morphological changes in the alteration gel over time. Monte Carlo modeling of glass alteration, especially with simple glasses, indicates a clogging of the porosity on the external portion of the gel (near the solution/gel interface) after densification of the layer by silicon precipitation, but this phenomenon had never previously been directly observed experimentally. The initial results obtained by isotopic tracing provide new data that appears to confirm this hypothesis.     

A mechanical model for heat conduction

Continuum Mechanics and Thermodynamics - A theory of heat conduction in rigid heat conductors based entirely on mechanical concepts is proposed and compared with the traditional thermodynamic...