Electrostatic Potential Force Research Articles

Fac-Tri-aqua-(1,10-phenanthroline-κ2 N,N')(sulfato-κO)cobalt(II): crystal structure, Hirshfeld surface analysis and computational study.

The CoII atom in the title complex, [Co(SO4)(C12H8N2)(H2O)3] (or C12H14CoN2O7S), is octa-hedrally coordinated within a cis-N2O4 donor set defined by the chelating N-donors of the 1,10-phenanthroline ligand, sulfate-O and three aqua-O atoms, the latter occupying an octa-hedral face. In the crystal, supra-molecular layers lying parallel to (110) are sustained by aqua-O-H⋯O(sulfate) hydrogen bonding. The layers stack along the c-axis direction with the closest directional inter-action between them being a weak phenanthroline-C-H⋯O(sulfate) contact. There are four significant types of contact contributing to the calculated Hirshfeld surface: at 44.5%, the major contribution comes from O-H⋯O contacts followed by H⋯H (28.6%), H⋯C/C⋯H (19.5%) and C⋯C (5.7%) contacts. The dominance of the electrostatic potential force in the mol-ecular packing is also evident in the calculated energy frameworks. The title complex is isostructural with its manganese, zinc and cadmium containing analogues and isomeric with its mer-tri-aqua analogue.

Macroscopic models for filtration and heterogeneous reactions in porous media

Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible (Valdés-Parada et al., 2011; Battiato and Tartakovsky, 2011a) due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in Allaire and Raphael (2007), Mauri (1991). The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue which represents the macroscopic effective reaction rate, and a non-reactive component. The latter can be then upscaled with a two-scale asymptotic expansion and the final macroscopic equation is obtained for the leading order. The same method can also be used to overcome another classical assumption, namely of non solenoidal velocity fields, such as the case of deposition of charged colloidal particles driven by electrostatic potential forces. The whole upscaling procedure, which consists in solving three cell problems, is implemented for arbitrarily complex two- and three-dimensional periodic structures using the open-source finite volume library OpenFOAM®. We provide details on the implementation and test the methodology for two-dimensional periodic arrays of spheres, and we compare the results against fully resolved numerical simulations, demonstrating the accuracy and generality of the upscaling approach. The effective velocity, dispersion and reaction coefficients are obtained for a wide range of Péclet and surface Damköhler numbers, and for Coulomb-like forces to the grains. Noticeably, all the effective transport parameters are significantly different from the non-reactive (conserved scalar) case, as the heterogeneity introduced by the reaction strongly affects the micro-scale profiles.

A sharp time-weighted inequality for the compressible Navier–Stokes–Poisson system in the critical Lp framework

The compressible Navier–Stokes–Poisson system takes the form of usual Navier–Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electrostatic potential force. In this paper, we focus on the large-time behavior of global strong solutions in the Lp critical Besov spaces. Inspired by the dissipative effect arising from Poisson potential, we formulate a new regularity assumption of low frequencies and then establish the sharp time-weighted inequality, which leads to the optimal time-decay estimates of strong solutions. Indeed, we see that the decay of density is faster at the half rate than that of velocity, which is a different ingredient in comparison with the situation of compressible Navier–Stokes equations. Our proof mainly depends on tricky and non classical Besov product estimates with respect to various Sobolev embeddings.

Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System

We investigate the nonlinear stability of the superposition of a viscous contact wave and two rarefaction waves for a one-dimensional (1D) bipolar Vlasov--Poisson--Boltzmann (VPB) system, which can be used to describe the transportation of charged particles under the additional electrostatic potential force. Based on a new micro-macro type of decomposition around the local Maxwellian related to the bipolar VPB system in the previous work [H.-L. Li, Y. Wang, T. Yang, and M.-Y. Zhong, Arch. Ration. Mech. Anal., 228 (2018), pp. 39--127], we prove that the superposition of a viscous contact wave and two rarefaction waves is time-asymptotically stable to the 1D bipolar VPB system under some smallness conditions on the initial perturbations and wave strength, which implies that this typical superposition wave pattern is nonlinearly stable under the combined effects of the binary collisions, the electrostatic potential force, and the mutual interactions of different charged particles. This is the first result about the nonlinear stability of the combination of two different wave patterns for the VPB system.

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov–Poisson–Boltzmann System

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction wave for bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in [21, 23], we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as the applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction wave, are proved for the 1D bipolar Vlasov-Poisson-Boltzmann system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of rarefaction wave fan to compressible Euler equations is proved to 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in [18] sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

Spectrum structure and optimal decay rate of the relativistic Vlasov-Poisson-Landau system

It is interesting to analyze the mutual influence of relativistic effect and electrostatic potential force on the qualitative behaviors of charge particles simulated by the one-species relativistic Vlasov-Poisson-Landau (rVPL) system with the physical Coulombic interaction. In this paper, we first study the spectrum structure on the linearized rVPL system and obtain the optimal time decay rates of the solutions to the linearized system, and then we construct global strong solutions to the nonlinear system around a global relativistic Maxwellian. Finally we make use of time decay rates of the solutions to the linearized system and uniform energy estimates to establish the time decay of the global solution to the original Cauchy problem for the rVPL system to the absolute Maxwellian at the optimal convergence rate \begin{document}$(1+t)^{-3/4}$\end{document} . This time rate is faster than the optimal rate \begin{document}$(1+t)^{-1/4}$\end{document} of classical Vlasov-Poisson-Boltzmann [ 2 , 10 ] and Vlasov-Poisson-Landau system [ 7 , 8 , 17 ] and this fast time decay rate is caused by the combined influence of relativistic effect and electrostatic potential force.

A New Approach for Studying Bond Rupture/Closure of a Spiro Benzopyran Photochromic Material: Reactivity Descriptors Derived from Frontier Orbitals and DFT Computed Electrostatic Potential Energy Surface Maps

This paper focuses on computations technique within the framework of the TD-DFT theory for studying the relationship between structure-properties of reversible conversion of photochromic materials. Specifically, we report on 1′,3′-dihydro-8-methoxy-1′,3′,3′-trimethyl-6-nitrospiro[2H-1-benzopyran-2,2′-(2H)-indole] (SP) and its isomers. TD-DFT calculated UV-Vis electronic spectra of the closed and open isomers of this photochromic material are in excellent agreement with the experimental results. Moreover, this paper reports on the results of theoretical investigations of reactivity indices that may govern the conversion between spiropyrans and its isomers. In addition, the solvent and rigidity of the medium significantly control the thermal bleaching of the photogenerated colored isomers and hence the switch ability pattern of the photochromic material. The effect of molecular structure computed by DFT in gas-phase and solvents onCspiro-Obond length has been shown to correlate with photochromic properties. For this compound, DFT optimized geometry could be used to predict photochromism. Furthermore, in an attempt to predict the driving force for MC → SP, this work explores, for the first time, profitable exploitation of the calculated and visualized mapped electrostatic potential energy surfaces (ESP map). Interestingly, it seems that the electrostatic potential forces over the molecular fragments govern spirobond rupture/closure reactions. Thermodynamically, all-trans-colored isomer (CTT) is the most stable merocyanine-like form.

Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system

We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation. If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity, we show that the density converges to its equilibrium state at the L 2-rate $$(1 + t)^{ - \tfrac{7} {4}}$$ or L ∞-rate $$(1 + t)^{ - \tfrac{5} {2}}$$ , and the momentum decays at the L 2-rate $$(1 + t)^{ - \tfrac{5} {4}}$$ or L ∞-rate (1 + t)−2. These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system.

Optimal Decay Rate of the Compressible Navier–Stokes–Poisson System in $${\mathbb {R}^3}$$

The compressible Navier-Stokes-Poisson (NSP) system is considered in $R^3$ in the present paper and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the same $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ respectively as the compressible Navier-Stokes system, but the momentum of the NSP system decays at the $L^2$-rate $(1+t)^{-\frac14}$ or $L^\infty$-rate $(1+t)^{-1}$ respectively, which is slower than the $L^2$-rate $(1+t)^{-\frac34}$ or $L^\infty$-rate $(1+t)^{-3/2}$ for the compressible Navier-Stokes system. These convergence rates are also shown to be optimal for the compressible NSP system.

Transport Processes and Thermodynamic Equilibrium

THERE is an error in my article in Nature under the above title1. The error occurs at the point where the chemical potential μ is introduced as an undetermined multiplier and is in equation (7), the restriction on the volumes of the various parts of the system in a virtual reversible infinitesimal displacement of the system at constant total volume, mass, and entropy. The restriction given, that is, is appropriate when there are no long range gravitational or electrostatic potential forces, whereas for the increment in the total energy arising from such forces to be Σiφi δM i , a much stronger restriction must be applied, namely, for every region i,