Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians

2021 ◽  
Vol 273 (1339) ◽  
Author(s):  
Gong Chen
Keyword(s):  
Wave Equation ◽  
Charge Transfer ◽  
Wave Equations ◽  
Linear Models ◽  
Energy Estimate ◽  
Strichartz Estimates ◽  
Content Type ◽  
Scattering States ◽  
Scattering State ◽  
A Charge

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R 3 \mathbb {R}^{3} : \[ ∂ t t u − Δ u + ∑ j = 1 m V j ( x − v → j t ) u = 0. \partial _{tt}u-\Delta u+\sum _{j=1}^{m}V_{j}\left (x-\vec {v}_{j}t\right )u=0. \] The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [Comm. Math. Phys. 364 (2018), no. 1, pp. 45–82].

A comparative study of modified cubic B-spline differential quadrature methods for a class of nonlinear viscous wave equations

2018 ◽  
Vol 35 (1) ◽  
pp. 315-333
Author(s):  
Ramesh Chand Mittal ◽  
Sumita Dahiya
Keyword(s):  
Wave Equation ◽  
Comparative Study ◽  
Wave Equations ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Nonlinear Odes ◽  
Content Type ◽  
B Spline ◽  
Cpu Time ◽  
Quadrature Methods

Purpose In this study, a second-order standard wave equation extended to a two-dimensional viscous wave equation with timely differentiated advection-diffusion terms has been solved by differential quadrature methods (DQM) using a modification of cubic B-spline functions. Two numerical schemes are proposed and compared to achieve numerical approximations for the solutions of nonlinear viscous wave equations. Design/methodology/approach Two schemes are adopted to reduce the given system into two systems of nonlinear first-order partial differential equations (PDE). For each scheme, modified cubic B-spline (MCB)-DQM is used for calculating the spatial variables and their derivatives that reduces the system of PDEs into a system of nonlinear ODEs. The solutions of these systems of ODEs are determined by SSP-RK43 scheme. The CPU time is also calculated and compared. Matrix stability analysis has been performed for each scheme and both are found to be unconditionally stable. The results of both schemes have been extensively discussed and compared. The accuracy and reliability of the methods have been successfully tested on several examples. Findings A comparative study has been carried out for two different schemes. Results from both schemes are also compared with analytical solutions and the results available in literature. Experiments show that MCB-DQM with Scheme II yield more accurate and reliable results in solving viscous wave equations. But Scheme I is comparatively less expensive in terms of CPU time. For MCB-DQM, less depository requirements lead to less aggregation of approximation errors which in turn enhances the correctness and readiness of the numerical techniques. Approximate solutions to the two-dimensional nonlinear viscous wave equation have been found without linearizing the equation. Ease of implementation and low computation cost are the strengths of the method. Originality/value For the first time, a comparative study has been carried out for the solution of nonlinear viscous wave equation. Comparisons are done in terms of accuracy and CPU time. It is concluded that Scheme II is more suitable.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Determination of Epsilon Aminocaproic Acid Based on Charge Transfer Complexation with p-Nitrophenlol by Spectrophotometry

2020 ◽  
Vol 16 ◽  
Author(s):  
Sheng-Yun Li ◽  
Fang Tian
Keyword(s):  
Charge Transfer ◽  
Aminocaproic Acid ◽  
Concentration Limit ◽  
Official Method ◽  
Good Precision ◽  
Pharmaceutical Dosage Forms ◽  
Relative Standard ◽  
A Charge ◽  
Epsilon Aminocaproic Acid

: A spectrophotometry was investigated for the determination of epsilon aminocaproic acid (EACA) with p-nitrophenol (PNP). The method was based on a charge transfer (CT) complexation of this drug as n-electron donor with π-acceptor PNP. Experiment indicated that the CT complexation was carried out at room temperature for 10 minutes in dimethyl sulfoxide solvent. The spectrum obtained for EACA/PNP system showed the maximum absorption band at wavelength of 425 nm. The stoichiometry of the CT complex was found to be 1:1 ratio by Job’s method between the donor and the acceptor. Different variables affecting the complexation were carefully studied and optimized. At the optimum reaction conditions, Beer’s law was obeyed in a concentration limit of 1～6 µg mL-1. The relative standard deviation was less than 2.9%. The apparent molar absoptivity was determined to be 1.86×104 L mol-1cm-1 at 425 nm. The CT complexation was also confirmed by both FTIR and 1H NMR measurements. The thermodynamic properties and reaction mechanism of the CT complexation have been discussed. The developed method could be applied successfully for the determination of the studied compound in its pharmaceutical dosage forms with a good precision and accuracy compared to official method as revealed by t- and F-tests.

Fluorescence Quenching of Aminodiphenylamines with Chloromethanes

2002 ◽  
Vol 67 (8) ◽  
pp. 1154-1164 ◽  
Author(s):  
Nachiappan Radha ◽  
Meenakshisundaram Swaminathan
Keyword(s):  
Charge Transfer ◽  
Fluorescence Quenching ◽  
Ground State ◽  
Rate Constants ◽  
Quenching Mechanism ◽  
Quenching Rate ◽  
Charge Transfer Interaction ◽  
Electronically Excited ◽  
A Charge

The fluorescence quenching of 2-aminodiphenylamine (2ADPA), 4-aminodiphenylamine (4ADPA) and 4,4'-diaminodiphenylamine (DADPA) with tetrachloromethane, chloroform and dichloromethane have been studied in hexane, dioxane, acetonitrile and methanol as solvents. The quenching rate constants for the process have also been obtained by measuring the lifetimes of the fluorophores. The quenching was found to be dynamic in all cases. For 2ADPA and 4ADPA, the quenching rate constants of CCl4 and CHCl3 depend on the viscosity, whereas in the case of CH2Cl2, kq depends on polarity. The quenching rate constants for DADPA with CCl4 are viscosity-dependent but the quenching with CHCl3 and CH2Cl2 depends on the polarity of the solvents. From the results, the quenching mechanism is explained by the formation of a non-emissive complex involving a charge-transfer interaction between the electronically excited fluorophores and ground-state chloromethanes.

Charge-transfer induced multifunctional BCP:Ag complexes for semi-transparent perovskite solar cells with a record fill factor of 80.1%

2021 ◽  
Author(s):  
Zhiqin Ying ◽  
Xi Yang ◽  
Jingming Zheng ◽  
Yudong Zhu ◽  
Jingwei Xiu ◽  
...  
Keyword(s):  
Solar Cells ◽  
Charge Transfer ◽  
Buffer Layer ◽  
Fill Factor ◽  
Perovskite Solar Cells ◽  
A Charge

A charge-transfer induced BCP:Ag complex is employed as a multifunctional buffer layer for efficient inverted semi-transparent perovskite solar cells.

scholarly journals Multi-configurational Ehrenfest simulations of ultrafast nonadiabatic dynamics in a charge-transfer complex

2018 ◽  
Vol 149 (24) ◽  
pp. 244107 ◽  
Author(s):  
Tianji Ma ◽  
Matteo Bonfanti ◽  
Pierre Eisenbrandt ◽  
Rocco Martinazzo ◽  
Irene Burghardt
Keyword(s):  
Charge Transfer ◽  
Charge Transfer Complex ◽  
Nonadiabatic Dynamics ◽  
A Charge

scholarly journals Synthesis and Photobehavior of a NewDehydrobenzoannulene-Based HOF with Fluorine Atoms: From Solution to Single Crystals Observation

2021 ◽  
Vol 22 (9) ◽  
pp. 4803
Author(s):  
Eduardo Gomez ◽  
Ichiro Hisaki ◽  
Abderrazzak Douhal
Keyword(s):  
Charge Transfer ◽  
Single Crystals ◽  
Parent Compound ◽  
Time Resolved ◽  
Strong Basis ◽  
Triplet Structure ◽  
Carboxylic Groups ◽  
Potential Applications ◽  
A Charge ◽  
Further Development

Hydrogen-bonded organic frameworks (HOFs) are the focus of intense scientific research due their potential applications in science and technology. Here, we report on the synthesis, characterization, and photobehavior of a new HOF (T12F-1(124TCB)) based on a dehydrobenzoannulene derivative containing fluorine atoms (T12F-COOH). This HOF exhibits a 2D porous sheet, which is hexagonally networked via H-bonds between the carboxylic groups, and has an interlayers distance (4.3 Å) that is longer than that of a typical π–π interaction. The presence of the fluorine atoms in the DBA molecular units largely increases the emission quantum yield in DMF (0.33, T12F-COOH) when compared to the parent compound (0.02, T12-COOH). The time-resolved dynamics of T12F-COOH in DMF is governed by the emission from a locally excited state (S1, ~ 0.4 ns), a charge-transfer state (S1(CT), ~ 2 ns), and a room temperature emissive triplet state (T1, ~ 20 ns), in addition to a non-emissive triplet structure with a charge-transfer character (T1(CT), τ = 0.75 µs). We also report on the results using T12F-ester. Interestingly, FLIM experiments on single crystals unravel that the emission lifetimes of the crystalline HOF are almost twice those of the amorphous ones or the solid T12F-ester sample. This shows the relevance of the H-bonds in the photodynamics of the HOF and provides a strong basis for further development and study of HOFs based on DBAs for potential applications in photonics.

The Reagent Diphenyldiselane/Iodine: No Phenylselenenyl Iodide but a Charge Transfer Complex with Cyclic Moieties

1988 ◽  
Vol 27 (3) ◽  
pp. 431-433 ◽  
Author(s):  
Silvia Kubiniok ◽  
Wolf-Walther du Mont ◽  
Siegfried Pohl ◽  
Wolfgang Saak
Keyword(s):  
Charge Transfer ◽  
Charge Transfer Complex ◽  
A Charge
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