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Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation

A n-dimensional quasiliner wave equation with nonlinear boundary dissipation is considered. Global existence, uniqueness and uniform decay rates are established for the model, under the assumption that the H¹(Ω)xL₂(Ω') norms of the initial data are sufficiently small. The result presented in this paper extends/generalizes those obtained those obtained recently in (13), where, by contrast, interior nonlinear damping was considered; and those obtained in (31), where the one-dimensional wave equation with linear boundary damping was treated.     

The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees

Atomic partial charges are among the most commonly used interpretive tools in quantum chemistry. Dozens of different ‘population analyses’ are in use, which are best seen as proxies (indirect gauges) rather than measurements of a ‘general ionicity’. For the GMTKN55 benchmark of nearly 2,500 main-group molecules, which span a broad swathe of chemical space, some two dozen different charge distributions were evaluated at the PBE0 level near the 1-particle basis set limit. The correlation matrix between the different charge distributions exhibits a block structure; blocking is, broadly speaking, by charge distribution class. A principal component analysis on the entire dataset suggests that nearly all variation can be accounted for by just two ‘principal components of ionicity’: one has all the distributions going in sync, while the second corresponds mainly to Bader QTAIM vs. all others. A weaker third component corresponds to electrostatic charge models in opposition to the orbital-based ones. The single charge distributions that have the greatest statistical similarity to the first principal component are iterated Hirshfeld (Hirshfeld-I) and a minimal-basis projected modification of Bickelhaupt charges. If three individual variables, rather than three principal components, are to be identified that contain most of the information in the whole dataset, one representative for each of the three classes of Corminboeuf et al. is needed: one based on partitioning of the density (such as QTAIM), a second based on orbital partitioning (such as NPA), and a third based on the molecular electrostatic potential (such as HLY or CHELPG).     

Relaxation of physical systems in relative-number state representation

The relaxation properties of physical systems in the Liouville space are investigated in terms of the relative-number state representation. An arbitrary state can be expressed by superposition of relative-number states. In the absence of an time-dependent external field, all components with non-zero relative-numbers decay to zero with time, and any stationary state can be expressed only in terms of zero relative-number states. The phase canonically conjugate to the relative-number is completely uncertain in a stationary state. It is thought that relaxation from an arbitrary initial state to a stationary state is described as some kind of phase relaxation process. Such a phase relaxation process is explicitly described by the phase operator formalism within the framework of the relative-number state representation.     

Design and optimisation of multimode 1D photonic band gap waveguide

The modal characteristics of planar waveguides with photonic band gap guiding properties are studied. It is demonstrated that a slight deviation from the periodicity in the photonic band gap multilayers can result in multimode transmission within the guiding layer. Possible applications of the results for avoiding single mode regime destruction due to fabrication process imperfection, as well as for designing such waveguides for conventional and emerging new applications of multimode photonic devices, are pointed out.     

A solvable model of microscopic frequency modulation: II. Rigorous treatment of the damping operator

The solvable model of quantum-statistical mechanical frequency modulation, which was proposed previously by the authors, is solved exactly by rigorous treatment of the damping operator for the cases of boson and two-state irrelevant subsystems to obtain the intensity distribution and the response function for a certain operator of the relevant subsystem. The results are compared with the previous ones which were obtained within the conventional treatment of the damping operator.     

Characterization of the microscopic surface structure of the octadecylsilica stationary phase using a molecular-dynamics simulation.

The influence of the mobile-phase composition and temperature on the surface structure of the octadecylsilica (ODS) stationary-phase was investigated by applying a molecular-dynamics (MD) simulation. The molecular model to which the MD simulation was applied consisted of three parts: an amorphous silica base, dimethyloctadecylsilyl ligands and mobile-phase solvents. More detailed information on the effect of the mobile-phase composition was obtained by constructing larger molecular models than those used in our previous study. The thickness of the hydrocarbon layer of the stationary phase could be estimated based on the distance between the carbon atom located at the terminal end of the ODS ligand and the silica gel surface. The structural information obtained by the calculation showed good consistency with the experimentally observed values. The gauche fraction in the ODS ligand conformation could be also estimated to obtain a more detailed ligand conformation for each molecular model. It was found that as the temperature increased, the ligand conformation collapsed more. This trend was the same as the experimentally observed trends obtained by NMR, FT-IR, and Raman spectroscopic techniques.