Oscillatory Structure Research Articles

Effect of internal excitations of reagent diatom on initial state-selected dynamics of C + OH reaction on its second excited (14A″) electronic state

ABSTRACTInitial state-selected total reaction probabilities and integral reaction cross sections (ICSs) of, C(3P) + OH (X2Π) → CO(a3Π) + H (2S), reaction on its second excited electronic state (14A″) are calculated with the aid of a time-dependent wave packet propagation method within the coupled states approximation. Partial wave contributions for the total angular momentum quantum number, J=0–48, were necessary to obtain converged ICSs for OH (v=0, j=0) upto a collision energy of ∼0.25 eV. In case of rotationally and vibrationally excited OH, many more partial wave contributions had to be included. Dense oscillatory structures are found in total reaction probabilities due to the formation of quasibound collision complexes inside the wells (of depth ∼2.25 eV and ∼1.85 eV) present on the potential energy surface. While reagent vibrational excitation promotes the reaction, no such general trend is found with rotational excitation. The results of the present study are compared with the literature data. Mechanistic details of the C + OH reaction occurring on its ground, first and second excited electronic states are compared and discussed.

Characterization of spatiotemporal chaos in a Kerr optical frequency comb and in all fiber cavities.

Complex spatiotemporal dynamics have been a subject of recent experimental investigations in optical frequency comb microresonators and in driven fiber cavities with Kerr-type media. We show that this complex behavior has a spatiotemporal chaotic nature. We determine numerically the Lyapunov spectra, allowing us to characterize different dynamical behavior occurring in these simple devices. The Yorke-Kaplan dimension is used as an order parameter to characterize the bifurcation diagram. We identify a wide regime of parameters where the system exhibits a coexistence between the spatiotemporal chaos, the oscillatory localized structure, and the homogeneous steady state. The destabilization of an oscillatory localized state through radiation of counter-propagating fronts between the homogeneous and the spatiotemporal chaotic states is analyzed. To characterize better the spatiotemporal chaos, we estimate the front speed as a function of the pump intensity.

Photodetachment dynamics in a time-dependent oscillating electric field

Using the time-dependent form of closed orbit theory, as developed by Haggerty and Delos [M.R. Haggerty, J.B. Delos, Phys. Rev. A 61, 053406 (2000)], and by Yang and Robicheaux [B.C. Yang, F. Robicheaux, Phys. Rev. A 93, 053413 (2016)], we study the photodetachment dynamics of a hydrogen negative ion in a time-dependent oscillating electric field. Compared to the photodetachment in a static electric field, the photodetachment dynamics of a negative ion in the time-dependent oscillating electric field become much more complicated but more interesting. Since the applied electric field is oscillating with time, the photodetachment cross section of the negative ion in the oscillating electric field is time-dependent. In a time-dependent framework, we put forward an analytical formula for calculating the instantaneous photodetachment cross section of this system. Our study suggests that the instantaneous photodetachment cross section exhibits oscillatory structure, which depends sensitively on the frequency of the oscillating electric field. With increasing frequency of the oscillating electric field, the number of closed orbits increases and the oscillatory structure in the photodetachment cross section becomes much more complicated. The connection between the detached electron’s closed orbit with the oscillating cross section is analyzed quantitatively. This study provides a clear and intuitive picture for the photodetachment processes of a negative ion in the presence of an oscillating electric field. We hope that our work will be useful in guiding future experimental research.

A full-dimensional time-dependent wave packet study of the H + CO2 → OH + CO reaction

A full dimensional quantum dynamics calculation has been carried out to study the prototypical complex forming H+CO2→OH+CO reaction. The total reaction probability is converged with a propagation time much shorter than the reverse reaction, and only exhibits very small oscillatory structures, indicating the reaction proceeds mainly through a direct mechanism. The strong Fermi resonance between the (020) and (100) vibrationally excited states makes it hard to define their efficacy for reactivity, although it is conceivable that the bending excitation is much more effective than the symmetric excitation according to the geometry of the transition state in the entrance channel.

Time-dependent formulation of the two-dimensional model of resonant electron collisions with diatomic molecules and interpretation of the vibrational excitation cross sections

A two-dimensional model of the resonant electron-molecule collision processes with one nuclear and one electronic degree of freedom introduced by K. Houfek, T. N. Rescigno, and C. W. McCurdy [Phys. Rev. A 73, 032721 (2006)] is reformulated within the time-dependent framework and solved numerically using the finite-element method with the discrete variable representation basis, the exterior complex scaling method, and the generalized Crank-Nicolson method. On this model we illustrate how the time-dependent calculations can provide deep insight into the origin of oscillatory structures in the vibrational excitation cross sections if one evaluates the cross sections not only at sufficiently large time to obtain the final cross sections, but also at several characteristic times which are given by the evolution of the system. It is shown that all details of these structures, especially asymmetrical peaks, can be understood as quantum interference of several experimentally indistinguishable processes separated in time due to a resonant capture of the electron and the subsequent vibrational motion of the negative molecular ion. Numerical results are presented for the ${\mathrm{N}}_{2}$-like, NO-like, and ${\mathrm{F}}_{2}$-like models and compared with ones obtained within the time-independent approach and within the local complex potential approximation.

Time-Dependent Quantum Wave Packet Study of the Si + OH → SiO + H Reaction: Cross Sections and Rate Constants.

The dynamics of the Si(3P) + OH(X2Π) → SiO(X1Σ+) + H(2S) reaction is investigated by means of the time-dependent wave packet (TDWP) approach using an ab initio potential energy surface recently developed by Dayou et al. ( J. Chem. Phys. 2013 , 139 , 204305 ) for the ground X2A' electronic state. Total reaction probabilities have been calculated for the first 15 rotational states j = 0-14 of OH(v=0,j) at a total angular momentum J = 0 up to a collision energy of 1 eV. Integral cross sections and state-selected rate constants for the temperature range 10-500 K were obtained within the J-shifting approximation. The reaction probabilities display highly oscillatory structures indicating the contribution of long-lived quasibound states supported by the deep SiOH/HSiO wells. The cross sections behave with collision energies as expected for a barrierless reaction and are slightly sensitive to the initial rotational excitation of OH. The thermal rate constants show a marked temperature dependence below 200 K with a maximum value around 15 K. The TDWP results globally agree with the results of earlier quasi-classical trajectory (QCT) calculations carried out by Rivero-Santamaria et al. ( Chem. Phys. Lett. 2014 , 610-611 , 335 - 340 ) with the same potential energy surface. In particular, the thermal rate constants display a similar temperature dependence, with TDWP values smaller than the QCT ones over the whole temperature range.

Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. II. Dispersion dependencies

The dielectric permeability tensor for spin polarized plasmas derived in terms of the spin-1/2 quantum kinetic model in six-dimensional phase space in Part I of this work is applied for study of spectra of high-frequency transverse and transverse-longitudinal waves propagating perpendicular to the external magnetic field. Cyclotron waves are studied at consideration of waves with electric field directed parallel to the external magnetic field. It is found that the separate spin evolution modifies the spectrum of cyclotron waves. These modifications increase with the increase of the spin polarization and the number of the cyclotron resonance. Spin dynamics with no account of the anomalous magnetic moment gives a considerable modification of spectra either. The account of anomalous magnetic moment leads to a fine structure of each cyclotron resonance. So, each cyclotron resonance splits on three waves. Details of this spectrum and its changes with the change of spin polarization are studied for the first and second cyclotron waves. A cyclotron resonance existing at $\omega\approx0.001\mid\Omega_{e}\mid$ due to the anomalous magnetic moment is also described, where $\mid\Omega_{e}\mid$ is the cyclotron frequency. The ordinary waves does not have any considerable modification. The electrostatic and electromagnetic Berstein modes are studied during the analysis of waves propagating perpendicular to the external magnetic field with the electric field perturbation directed perpendicular to the external field. A modification of the oscillatory structure caused by the equilibrium spin polarization is found in both regimes. Similar modification is found for the extraordinary wave spectrum.

State-selective electron capture in 30- and 100-keVHe++Hecollisions

A combined experimental and theoretical study on single capture in 30- and 100-keV ${\mathrm{He}}^{+}$ on He collisions was performed. By using a reaction microscope, we obtained the state selective cross sections and the angular-differential cross sections. It was found that the experimental state-selective cross sections were in good agreement with the dynamic screening classical trajectory Monte Carlo calculation for 100-keV ${\mathrm{He}}^{+}$ incident. The comparisons with various versions of such calculations reveal the roles played by different electron-electron correlation effects. Moreover, a prominent oscillatory structure was observed in the angular-differential cross sections for both projectile energies. With the single capture probability distribution obtained from the classical trajectory Monte Carlo calculation, the oscillation structures can be well explained by atomic-size Fraunhofer-type diffraction.

Solitons, compactons and undular bores in Benjamin–Bona–Mahony-like systems

We examine the effect of dissipation on travelling waves in nonlinear dispersive systems modelled by Benjamin–Bona–Mahony (BBM)-like equations. In the absence of dissipation, the BBM-like equations are found to support soliton and compacton /anticompacton solutions depending on whether the dispersive term is linear or nonlinear. We study the influence of increasing nonlinearity of the medium on the soliton and compacton dynamics. The dissipative effect is found to convert the solitons either to undular bores or to shock-like waves depending on the degree of nonlinearity of the equations. The anticompacton solutions are also transformed to undular bores by the effect of dissipation. But the compactons tend to vanish due to viscous effects. The local oscillatory structures behind the bores and /or shock-like waves in the case of solitons and anticompactons are found to depend sensitively both on the coefficient of viscosity and solution of the unperturbed problem.

Automatic Detection of Optic Disc and Blood Vessel in Retinal Images using Morphological Operations and Ipachi Model

Automated detection of Optic disc and blood vessel fabrication is becoming of virtual interest for better management of diabetic disease. In this paper, we propose morphology technique and new infinite active contour model that uses hybrid region information of image to approach this problem. For optic disc detection scheme utilizes operations such as edge detection, binary threshold and morphological operation. For vessel detection we use an infinite perimeter regularize, provided by using L2 Lebesgue measure of the boundaries, allows for better detection of small oscillatory structures than the models based on length of a feature’s boundaries. The advantage of using different types of region information, Eigen based enhancement, such as the combination of image intensity information and local phase based enhancement. The local phase based enhancement map is used for preserving vessel edges while the given intensity information will give a correct feature’s segmentation.

Sleep Neurophysiological Dynamics Through the Lens of Multitaper Spectral Analysis.

During sleep, cortical and subcortical structures within the brain engage in highly structured oscillatory dynamics that can be observed in the electroencephalogram (EEG). The ability to accurately describe changes in sleep state from these oscillations has thus been a major goal of sleep medicine. While numerous studies over the past 50 years have shown sleep to be a continuous, multifocal, dynamic process, long-standing clinical practice categorizes sleep EEG into discrete stages through visual inspection of 30-s epochs. By representing sleep as a coarsely discretized progression of stages, vital neurophysiological information on the dynamic interplay between sleep and arousal is lost. However, by using principled time-frequency spectral analysis methods, the rich dynamics of the sleep EEG are immediately visible-elegantly depicted and quantified at time scales ranging from a full night down to individual microevents. In this paper, we review the neurophysiology of sleep through this lens of dynamic spectral analysis. We begin by reviewing spectral estimation techniques traditionally used in sleep EEG analysis and introduce multitaper spectral analysis, a method that makes EEG spectral estimates clearer and more accurate than traditional approaches. Through the lens of the multitaper spectrogram, we review the oscillations and mechanisms underlying the traditional sleep stages. In doing so, we will demonstrate how multitaper spectral analysis makes the oscillatory structure of traditional sleep states instantaneously visible, closely paralleling the traditional hypnogram, but with a richness of information that suggests novel insights into the neural mechanisms of sleep, as well as novel clinical and research applications.

Geometric phase effects in the ultracold D + HD D + HD and D + HD H + D2 reactions

The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0) D + HD(, ), D + HD(v = 4, j = 0) H + D2(, ) and H + D2(v = 4, j = 0) D + HD(, ) reactions are presented for collision energies between and . The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1– energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Thus, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.

Ionization of N2 in collisions with fast electrons: Evidence of an interference effect

Absolute double differential cross sections (DDCS) of electron emission were measured for ionization of ${\mathrm{N}}_{2}$ by fast electrons with energy 7 keV. Measurements were performed for different electron emission angles and energies. Evidence of oscillation due to Young-type interference was observed in the DDCS ratios for all angles. The frequency for large backward angle is found to be larger compared to that for small forward angle. Consequently, the forward-backward asymmetry parameter reveals the oscillatory structure even more clearly. The oscillations observed for both experimental-to-theoretical DDCS ratios and forward-backward asymmetry were well explained by the Cohen-Fano model of interference in a molecular double slit. A periodic deviation of the Cohen-Fano model from the asymmetry parameter data reveals the presence of a higher-frequency component. The first Born model was employed to explain the results of molecular nitrogen for which a complete-neglect-of-differential-overlap approximation was used along with an effective atomic number.

Quantum multiscattering interferences in collision-induced coherent electron emission from diatomic molecules by swift ion impact

In the intramolecular scattering process, the interference between the rescattered electron waves emanating from each atomic center gives rise to additional oscillations superimposed on the Young-type oscillatory structure in the observed electron intensity. Here we explore numerically this behavior for coherent electron emission from the dimer ${{\mathrm{Rb}}_{2}}^{+}$ by fast-moving highly charged ions, which is achieved by solving the two-dimensional time-dependent Schr\odinger equation. Well-defined modulations with higher frequency are observed in the momentum distribution of the ejected electron, which are well reproduced by additional quantitative calculations based on the third-order Born series. This demonstrates without ambiguity the dynamic interference induced by multiple scattering paths of the electron prior to emission. Furthermore, the dependence of the phenomenon on the emission direction of the electron and the orientation of the molecular axis also is investigated. The phenomenon is not specific to ${{\mathrm{Rb}}_{2}}^{+}$ as investigated in the present study, but is broadly applicable to other systems with sufficiently large internuclear distances, thus opening new prospects for the investigation of electron emission process from large systems.

Geometric phase effects in the ultracold H + H2 reaction.

The H3 system has served as a prototype for geometric phase (GP) effects in bimolecular chemical reactions for over three decades. Despite a large number of theoretical and experimental efforts, no conclusive evidence of GP effects in the integral cross section or reaction rate has been presented until recently [B. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Here we report a more detailed account of GP effects in the H + H2(v = 4, j = 0) → H + H2(v', j') (para-para) reaction rate coefficients for temperatures between 1 μK (8.6 × 10-11 eV) and 100 K (8.6 × 10-3 eV). The GP effect is found to persist in both vibrationally resolved and total rate coefficients for collision energies up to about 10 K. The GP effect also appears in rotationally resolved differential cross sections leading to a very different oscillatory structure in both energy and scattering angle. It is shown to suppress a prominent shape resonance near 1 K and enhance a shape resonance near 8 K, providing new experimentally verifiable signatures of the GP effect in the fundamental hydrogen exchange reaction. The GP effect in the D + D2 and T + T2 reactions is also examined in the ultracold limit and its sensitivity to the potential energy surface is explored.

Fabry-Pérot interference in a triple-gated quantum point contact

We demonstrated that a triple-gated GaAs quantum point contact, which has an additional surface gate between a pair of split gates to strengthen the lateral confinement, produces the well-defined quantized conductance and Fabry-Pérot-type (FP-type) oscillations on it even using a relatively low mobility wafer. A one-dimensional phenomenological model potential was developed to explain the oscillatory behavior. By combining the model calculations and dc bias spectroscopy, we obtained a detailed information about the energy scales of the oscillatory structures. The relationships between the FP-type oscillations and the anomaly below the first plateau will be addressed.

Photodetachment of the H− ion in a linear time-dependent electric field

Using the time-dependent closed orbit theory, we study the photodetachment of the H− ion in a linear time-dependent electric field for the first time. An analytical formula for calculating the time-dependent photodetachment cross section of this system has been put forward. It is found when the external electric field changes very slowly with time, there is only one closed orbit of the detached electron and the photodetachment cross section is quite stable. However, when the electric field changes quickly with time, three different types of closed orbits are found and the photodetachment cross section oscillates in a much more complex way. The connection of each type of closed orbit with the oscillatory structure in the photodetachment cross section is analyzed quantitatively. In addition, the photon energy and the laser field parameters can also have great influence on the time-dependent photodetachment cross section of this system. This study provides a clear and intuitive picture for the photodetachment dynamics of a negative ion in the presence of a time-dependent electric field and may guide future experimental studies exploring the quantum effect in the photodetachment dynamics of negative ions from a time-dependent viewpoint.

A family of improved Falkner-type methods for oscillatory systems

For solving general second-order initial value problems u′′(t)=f(t,u(t),u′(t)), the classical Falkner methods can date back to Falkner’s work in 1936. In this paper, we propose and study a family of improved Falkner-type methods for the oscillatory system u′′(t)+Mu(t)=g(t,u(t)), where g: R × Rd → Rd, in which the first derivative does not appear explicitly, and M ∈ Rd × d is a symmetric positive semi-definite matrix. The new methods take into account the oscillatory structures of the problem and exactly integrate the unperturbed problem u′′(t)+Mu(t)=0. The global error bounds of the new methods are presented. Numerical experiments are performed to show that the new methods are more efficient than other effective methods appeared in the scientific literature.

Temperature-dependent optical phonon replicas characteristics of MgxZn1−xO alloy nanowires

MgxZn1−xO alloy nanowires have been synthesized through high temperature vapor-solid deposition process. The temperature-dependent optical phonon replicas characteristics of MgxZn1−xO alloy nanowires under 10K to 300K were investigated. The results show that a strong near-band-edge (NBE) ultraviolet (UV) and multi-peak emissions situated at the region (about 3.4eV ~ 3.0eV) was observed under low temperature. The UV emission shows an obvious redshift with the increasing temperature. The multi-peaks emission has an energy periodicity about 70meV. The oscillatory structure is mainly attributed to longitudinal optical phonon replicas of free exciton. The Mg composition can be estimated from the near-band-edge PL emission peak of MgxZn1−xO alloy nanowires, in agreement with previously reported results for MgxZn1−xO nanorods.

Infrared refractive index dispersion of polymethyl methacrylate spheres from Mie ripples in Fourier-transform infrared microscopy extinction spectra.

We performed high-resolution Fourier-transform infrared (FTIR) spectroscopy of a polymethyl methacrylate (PMMA) sphere of unknown size in the Mie scattering region. Apart from a slow, oscillatory structure (wiggles), which is due to an interference effect, the measured FTIR extinction spectrum exhibits a ripple structure, which is due to electromagnetic resonances. We fully characterize the underlying electromagnetic mode structure of the spectrum by assigning mode numbers to each of the ripples in the measured spectrum. We show that analyzing the ripple structure in the spectrum in the wavenumber region from about 3000 cm-1 to 8000 cm-1 allows us to determine both the unknown radius of the sphere and the PMMA index of refraction, which shows a strong frequency dependence in this infrared spectral region. While in this paper we focus on examining a PMMA sphere as an example, our method of determining the refractive index and its dispersion from infrared extinction spectra is generally applicable for the determination of the index of refraction of any transparent substance that can be shaped into micron-sized spheres.