Vibrational spectroscopy investigation using density functional theory on 7‐chloro‐3‐methyl‐2H‐1,2,4‐ benzothiadiazine 1,1‐dioxide

The solid phase Fourier transform infrared (FTIR) and Fourier transform (FT) Raman spectral analysis of 7‐chloro‐3‐methyl‐2H‐1,2,4‐benzothiadiazine 1,1‐dioxide (diazoxide), an antihypertensive agent was carried out along with density functional computations. The optimized geometry, wavenumber and intensity of the vibrational bands of diazoxide were obtained by DFT‐B3LYP level of theory with complete relaxation in the potential energy surface using 6‐31G(d,p) basis set. A complete vibrational assignment aided by the theoretical harmonic frequency analysis has been proposed. The harmonic vibrational wavenumbers calculated have been compared with experimental FTIR and FT Raman spectra. The observed and the calculated wavenumbers are found to be in good agreement. The experimental spectra coincide satisfactorily with those of calculated spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

The delay time of gravitational wave – gamma-ray burst associations

The first gravitational wave (GW) – gamma-ray burst (GRB) association, GW170817/GRB 170817A, had an offset in time, with the GRB trigger time delayed by ~1.7 s with respect to the merger time of the GW signal. We generally discuss the astrophysical origin of the delay time, Δt, of GW-GRB associations within the context of compact binary coalescence (CBC) – short GRB (sGRB) associations and GW burst – long GRB (lGRB) associations. In general, the delay time should include three terms, the time to launch a clean (relativistic) jet, Δt_jet; the time for the jet to break out from the surrounding medium, Δt_bo; and the time for the jet to reach the energy dissipation and GRB emission site, Δt_GRB. For CBC-sGRB associations, Δtjet and Δt_bo are correlated, and the final delay can be from 10 ms to a few seconds. For GWB-lGRB associations, Δt_jet and Δt_bo are independent. The latter is at least ~10 s, so that Δt of these associations is at least this long. For certain jet launching mechanisms of lGRBs, Δt can be minutes or even hours long due to the extended engine waiting time to launch a jet. We discuss the cases of GW170817/GRB 170817A and GW150914/GW150914-GBM within this theoretical framework and suggest that the delay times of future GW/GRB associations will shed light into the jet launching mechanisms of GRBs.     

Periodic solution of the generalized Rayleigh equation

The periodic solutions of a strongly cubic nonlinear oscillator whose motion is described with the generalized Rayleigh equation are studied. Approximate analytic solving methods are introduced. A new method based on homotopy and averaging is developed to determine the limit cycle motion. The obtained analytical solutions are compared with those calculated by the elliptic harmonic balance method with generalized Fourier series and Jacobian elliptic functions. Three types of cubic nonlinearity are considered: the coefficients of the linear and cubic terms are positive, the coefficient of the linear term is positive and that of the cubic term is negative and the opposite case. Comparisons of the analytical solution and numerical solution, obtained by using the Runge-Kutta method, are illustrated with examples.     

Ultrafast fiber lasers for strong‐field physics experiments

The recent demonstration of rare‐earth‐doped fiber lasers with a continuous‐wave output power approaching the 10‐kW level with diffraction‐limited beam quality proves that fiber lasers constitute a scalable solid‐state laser concept in terms of average power. In order to generate high peak power pulses from a fiber several fundamental limitations have to be overcome. This can be achieved by novel experimental strategies and fiber designs that offer an enormous potential towards ultrafast laser systems combining high average powers (> kW) and high peak power (> GW). In this paper the challenges, achievements and perspectives of ultrashort pulse generation and amplification in fibers are reviewed. This kind of laser system will have a tremendous impact on strong‐field physics experiments, such as the generation of coherent light by high‐harmonic generation. So far, applications in the interesting EUV spectral range suffer from the very low photon count leading to nonrelevant integration times with highly sophisticated detection schemes. High repetition rate high average power fiber lasers can potentially solve this issue. First demonstrations of high repetition‐rate strong‐field physics experiments using novel fiber laser systems will be discussed.     

Canonical transformations and exact invariants for time‐dependent Hamiltonian systems

An exact invariant is derived for n‐degree‐of‐freedom non‐relativistic Hamiltonian systems with general time‐dependent potentials. To work out the invariant, an infinitesimalcanonical transformation is performed in the framework of the extended phase‐space. We apply this approach to derive the invariant for a specific class of Hamiltonian systems. For the considered class of Hamiltonian systems, the invariant is obtained equivalently performing in the extended phase‐space a finitecanonical transformation of the initially time‐dependent Hamiltonian to a time‐independent one. It is furthermore shown that the invariant can be expressed as an integral of an energy balance equation. The invariant itself contains a time‐dependent auxiliary function ξ (t) that represents a solution of a linear third‐order differential equation, referred to as the auxiliary equation. The coefficients of the auxiliary equation depend in general on the explicitly known configuration space trajectory defined by the system's time evolution. This complexity of the auxiliary equation reflects the generally involved phase‐space symmetry associated with the conserved quantity of a time‐dependent non‐linear Hamiltonian system. Our results are applied to three examples of time‐dependent damped and undamped oscillators. The known invariants for time‐dependent and time‐independent harmonic oscillators are shown to follow directly from our generalized formulation.     

Increase of the Number of Detectable Gravitational Waves Signals Due to Gravitational Lensing

This article deals with the gravitational lensing (GL) of gravitational waves (GW). We compute the increase in the number of detected GW events due to GL. First, we check that geometrical optics is valid for the GW frequency range on which Earth-based detectors are sensitive, and that this is also partially true for what concerns the future space-based interferometer LISA. To infer this result, both the diffraction parameter and a cut-off frequency are computed. Then, the variation in the number of GW signals is estimated in the general case, and applied to some lens models: point mass lens and singular isothermal sphere (SIS profile). An estimation of the magnification factor has also been done for the softened isothermal sphere and for the King profile. The results appear to be strongly model-dependent, but in all cases the increase in the number of detected GW signals is negligible. The use of time delays among images is also investigated.     

Breather‐to‐soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers

We find that the sextic nonlinear Schrödinger (NLS) equation admits breather‐to‐soliton transitions. With the Darboux transformation, analytic breather solutions with imaginary eigenvalues up to the second order are explicitly presented. The condition for breather‐to‐soliton transitions is explicitly presented and several examples of transitions are shown. Interestingly, we show that the sextic NLS equation admits not only the breather‐to‐bright‐soliton transitions but also the breather‐to‐dark‐soliton transitions. We also show the interactions between two solitons on the constant backgrounds, as well as between breather and soliton.     

DFT simulations and Vibrational spectra of 4‐chloro and 4‐bromophenylboronic acid molecules

The experimental and theoretical vibrational spectra of 4‐chloro‐ and 4‐bromophenylboronic acids (abbreviated as 4Clpba and 4Brpba) were studied. The Fourier transform Raman and Fourier transform infrared (FTIR) spectra of 4Clpba and 4Brpba molecules were recorded in the solid phase. The structural and spectroscopic analyses of the molecules were made by using Hartree–Fock and density functional harmonic calculations. In both 4Clpba and 4Brpba only one form was most stable using B3LYP level with the 6–311 + + G(d,p) basis set. Selected experimental bands were assigned and characterized on the basis of the scaled theoretical wavenumbers by their total energy distribution (TED). Finally, geometric parameters as well as infrared (IR) and Raman bands were compared with the experimental data of the molecules. Copyright © 2008 John Wiley & Sons, Ltd.     

On‐axis shaping of second‐harmonic beams

We report complete spatial shaping (both phase and amplitude) of the second‐harmonic beam generated in a nonlinear photonic crystal. Using a collinear second‐order process in a nonlinear computer generated hologram imprinted on the crystal, the desired beam is generated on‐axis and in the near field. This enables compact and efficient one‐dimensional beam shaping in comparison to previously demonstrated off‐axis Fourier holograms. We experimentally demonstrate the second‐harmonic generation of high‐order Hermite–Gauss, top hats and arbitrary skyline‐shaped beams.

     

High‐efficiency coherence‐preserving harmonic rejection with crystal optics

This work reports a harmonic‐rejection scheme based on the combination of Si(111) monochromator and Si(220) harmonic‐rejection crystal optics. This approach is of importance to a wide range of X‐ray applications in all three major branches of modern X‐ray science (scattering, spectroscopy, imaging) based at major facilities, and especially relevant to the capabilities offered by the new diffraction‐limited storage rings. It was demonstrated both theoretically and experimentally that, when used with a synchrotron undulator source over a broad range of X‐ray energies of interest, the harmonic‐rejection crystals transmit the incident harmonic X‐rays on the order of 10^?6. Considering the flux ratio of fundamental and harmonic X‐rays in the incident beam, this scheme achieves a total flux ratio of harmonic radiation to fundamental radiation on the order of 10^?10. The spatial coherence of the undulator beam is preserved in the transmitted fundamental radiation while the harmonic radiation is suppressed, making this scheme suitable not only for current third‐generation synchrotron sources but also for the new diffraction‐limited storage rings where coherence preservation is an even higher priority. Compared with conventional harmonic‐rejection mirrors, where coherence is poorly preserved and harmonic rejection is less effective, this scheme has the added advantage of lower cost and footprint. This approach has been successfully utilized at the ultra‐small‐angle X‐ray scattering instrument at the Advanced Photon Source for scattering, imaging and coherent X‐ray photon correlation spectroscopy experiments. With minor modification, the harmonic rejection can be improved by a further five orders of magnitude, enabling even more performance capabilities.     

Resonance Raman spectroscopic and density functional theory investigation of the excited state structural dynamics of 2‐mercapto‐1‐methylimidazole

The resonance Raman spectroscopy in conjunction with the density functional theory calculations were used to study the excited state structural dynamics of 2‐mercapto‐1‐methylimidazole (MMI). The experimental UV absorption bands were assigned according to the time‐dependent density functional calculations. The vibrational assignments were done for the A‐band resonance Raman spectra of MMI in water and acetonitrile on the basis of the Fourier transform infrared (FT‐IR) and FT‐Raman measurements in solid, in water and in acetonitrile and the corresponding B3LYP/6‐311+G(d, p) computations. The dynamic structures of MMI were obtained by analysis of the resonance Raman intensity pattern and normal mode analysis. The differences in the dynamic structures of MMI and thiourea were revealed and explained. The structural dynamic of MMI was found to be similar to that of 2‐thiopyrimidone in terms of major reaction coordinates and thus favored the intra‐molecular proton transfer reaction. Copyright © 2012 John Wiley & Sons, Ltd.     

The effective action of D‐branes in Calabi‐Yau orientifold compactifications

In this review article we study type IIB superstring compactifications in the presence of space‐time filling D‐branes while preserving 𝒩=1 supersymmetry in the effective four‐dimensional theory. This amount of unbroken supersymmetry and the requirement to fulfill the consistency conditions imposed by the space‐time filling D‐branes lead to Calabi‐Yau orientifold compactifications. For a generic Calabi‐Yau orientifold theory with space‐time filling D3‐ or D7‐branes we derive the low‐energy spectrum. In a second step we compute the effective 𝒩=1 supergravity action which describes in the low‐energy regime the massless open and closed string modes of the underlying type IIB Calabi‐Yau orientifold string theory. These 𝒩=1 supergravity theories are analyzed and in particular spontaneous supersymmetry breaking induced by non‐trivial background fluxes is studied. For D3‐brane scenarios we compute soft‐supersymmetry breaking terms resulting from bulk background fluxes whereas for D7‐brane systems we investigate the structure of D‐ and F‐terms originating from worldvolume D7‐brane background fluxes. Finally we relate the geometric structure of D7‐brane Calabi‐Yau orientifold compactifications to 𝒩=1 special geometry.     

非线性晶体内腔倍频的温度模式分布

为了提高谐波转换效率和消除温升引起的晶体走离效应，对于非线性晶体温度场分布特点进行了分析与计算.同时研究了基波偏心辐射对KTP晶体温度场的影响.通过对腔内倍频KTP晶体工作特点的分析，建立了方形非线性晶体热模型并首次引入了方形晶体辐射偏心度的定义.基于热传导方程，得到了温度场分布的一般解析表达式.     

Nonlinear Self‐Gravitational Solar Plasma Fluctuations with Electron Inertia

A theoretical evolutionary model for new nonlinear self‐gravitational fluctuations associated with the solar plasma system is developed. The lowest‐order inertial correction of the plasma thermal electrons is considered. We try to present our calculation scheme leading to the fluctuation patterns evolving as a new class of nonlinear coherent structures. It is demonstrated that they are mainly monotonous shock‐like eigenmodes governed by a unique type of driven Korteweg‐de Vries Burger (d ‐KdVB) equation obtained by multiscale analysis over the gravito‐electrostatic equilibrium structure equations. The self‐consistent new and unique nonlinear driving source here appears due to the inclusion of weak electron inertia. The d ‐KdVB system is studied analytically, graphically and numerically in detail to show the detailed features of the eigenmodes. Our conclusions are in good qualitative agreement with multispace satellite and imaging detections made by others. Main results significant to diverse solar, stellar and other astrophysical contexts along with future directions are summarily highlighted. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Semiclassical expansion of quantum characteristics for many‐body potential scattering problem

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star‐product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many‐body potential scattering problem simplifies to a statistical‐mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ?. We present semiclassical expansion of quantum characteristics for many‐body scattering problem and provide tools for calculation of average values of time‐dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non‐locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum‐mechanical extensions of the Liouville theorem on conservation of the phase‐space volume and the Poincaré theorem on conservation of 2p‐forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for someparametric moving boundaries as well.     

Time-domain analytic solutions of two-wire transmission line excited by a plane-wave field

This paper reports that an analytic method is used to calculate the load responses of the two-wire transmission line excited by a plane-wave directly in the time domain. By the frequency-domain Baum Liu-Tesehe （BLT） equation, the time-domain analytic solutions are obtained and expressed in an infinite geometric series. Moreover, it is shown that there exist only finite nonzero terms in the infinite geometric series if the time variate is at a finite interval. In other word, the time-domain analytic solutions are expanded in a finite geometric series indeed if the time variate is at a finite interval. The computed results are subsequently compared with transient responses obtained by using the frequency-domain BLT equation via a fast Fourier transform, and the agreement is excellent.     

FT‐Raman spectroscopy—a rapid and reliable quantification protocol for the determination of natural indigo dye in Polygonum tinctorium

In the recent years, Raman and IR spectroscopies have attracted increasing attention as fast, non‐invasive and widely applicable alternative analytical approaches for a variety of materials. Vibrational spectroscopy has been used in the analysis of herbal products, dyes and sensitive art objects, besides complex and aqueous biomaterials such as biopolymers or mammalian tissue. Compared to conventional analytical methods based on high‐performance liquid chromatography (HPLC) or gas chromatography, which often involves extensive and time‐consuming sample preparation, Raman or IR spectroscopy can avoid these procedures. The present work introduces a fast and reliable quantification method for the determination of naturally occurring indigo dye in dyer's knotweed (Polygonum tinctorium) based on Fourier transform (FT) Raman spectroscopy. The results were validated by HPLC‐UV, and the merits and drawbacks of the present method are elaborated. Besides the qualitative aspects of signal assignment and comparison to appropriate attenuated total reflectance Fourier transform infrared (ATR‐FT‐IR) measurements, the Raman spectrum of dihydro indigo, an important intermediate in the indigo dying process, is presented for the first time and discussed with regard to its spectroscopic behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

Third‐order nonlinear and linear time‐dependent dynamical diffraction of X‐rays in crystals

For the first time the third‐order nonlinear time‐dependent Takagi's equations of X‐rays in crystals are obtained and investigated. The third‐order nonlinear and linear time‐dependent dynamical diffraction of X‐rays spatially restricted in the diffraction plane pulses in crystals is investigated theoretically. A method of solving the linear and the third‐order nonlinear time‐dependent Takagi's equations is proposed. Based on this method, results of analytical and numerical calculations for both linear and nonlinear diffraction cases are presented and compared.