Oscillatory Structure Research Articles

Parity effects in Rydberg-state excitation in intense laser fields

Conservation of parity plays a fundamental role in our understanding of various quantum processes. However, it is difficult to observe in atomic and molecular processes induced by a strong laser field due to their multiphoton character and the large number of states involved. Here we report an effect of parity in strong-field Rydberg-state excitation (RSE) by comparing the RSE probabilities of the N2 molecule and its companion atom Ar, which has a similar ionization potential but opposite parity of its ground state. Experimentally, we observe an oscillatory structure as a function of intensity with a period of about 50 TW/cm2 in the ratio between the RSE yields of the two species, which can be reproduced by simulations using the time-dependent Schrödinger equation (TDSE). We analyze a quantum-mechanical model, which allows for interference of electrons captured in different spatial regions of the Rydberg-state wave function. In the intensity-dependent RSE yield, it results in peaks with alternating heights with a spacing of 25 TW/cm2 and at the same intensity for both species. However, due to the opposite parities of their ground states, pronounced RSE peaks in Ar correspond to less pronounced peaks in N2 and vice versa, which leads to the period of 50 TW/cm2 in their ratio. Our work reveals a novel parity-related interference effect in the coherent-capture picture of the RSE process in intense laser fields.

Differential Cross-Sections for the Vibrationally Excited H + HOD(vOH = 1-4) → H2 + OD Reactions.

Using the time-dependent wave-packet approach, we calculate the first fully converged state-to-state differential cross-sections for the H + HOD(vOH = 1-4) → H2 + OD reactions on a highly accurate neural network PES. It is found that, unlike the loss of memory effect observed in the product distributions for low vibrational excitation reactions, high initial OH vibrational excitation significantly influences not only the product vibrational distribution but also the angular distribution. Furthermore, for the H + HOD(vOH = 3,4) reactions, the total integral cross-sections maintain the pronounced oscillatory structures in the J = 0 probabilities at low collision energies, which originate from the prereactive van der Waals resonances. Notably, the product angular distributions exhibit forward-backward peaked behavior at these energies, akin to those observed in the complex-forming system with deep potential wells. This is attributed to the much longer lifetimes of these resonances compared to those of conventional transition state resonances.

Comprehensive Insight into Regular Damped Oscillatory Structures from Effective Electromagnetic Form Factor Data of Some Mesons and Nucleons

Regular damped oscillatory structures from the “effective” electromagnetic form factors of the hadrons h=π±,K±,K0,p,n were investigated. The “effective” electromagnetic form factor behaviors were calculated from the experimental data on the total cross-sections σtot(e+e−→hh¯) with errors. The apparent oscillations were observed for the first time for the proton, and we show, also taking other hadrons into consideration, that they are an arbitrary artifact resulting from a very simplistic theoretical description based on an elementary three-parameter model. If the data are described by a more appropriate and physically well-founded Unitary and Analytic model, then the oscillations disappear. In spite of this, if the three-parameter model is used to describe the “effective” electromagnetic form factor data, an interesting phenomenon is observed. The oscillations are opposite for particles which form an isospin doublet. By using the physically well-founded Unitary and Analytic model, it is demonstrated that this feature originates from the special transformation properties of the electromagnetic current of the corresponding particles in the isotopic space.

Novel spectral methods for shock capturing and the removal of tygers in computational fluid dynamics

Spectral methods yield numerical solutions of the Galerkin-truncated versions of nonlinear partial differential equations (PDEs) involved especially in fluid dynamics. In the presence of discontinuities, such as shocks, spectral approximations develop Gibbs oscillations near the discontinuity. This causes the numerical solution to deviate quickly from the true solution. For spectral approximations of the inviscid Burgers equation in one-dimension (1D), nonlinear wave resonances lead to the formation of localised oscillatory structures called tygers in well-resolved areas of the flow, far from the shock. Recently, the author of [1] has proposed novel spectral relaxation (SR) and spectral purging (SP) schemes for the removal of tygers and Gibbs oscillations in spectral approximations of nonlinear conservation laws. For the 1D inviscid Burgers equation, it is shown in [1] that the novel SR and SP approximations of the solution converge strongly in L2 norm to the entropic weak solution, under an appropriate choice of kernels and related parameters. In this work, we carry out a detailed numerical investigation of SR and SP schemes when applied to the 1D inviscid Burgers equation and report the efficiency of shock capture and the removal of tygers. We then extend our study to systems of nonlinear hyperbolic conservation laws, such as the 2×2 system of the shallow water equations and the standard 3×3 system of 1D compressible Euler equations. For the latter, we generalise the implementation of SR methods to non-periodic problems using Chebyshev polynomials. We then turn to singular flow in the 1D wall approximation of the 3D-axisymmetric wall-bounded incompressible Euler equation [2]. Here, in order to determine the blowup time of the solution, we compare the decay of the width of the analyticity strip, obtained from the pure pseudospectral method (PPS), with the improved estimate obtained using the novel spectral relaxation scheme.

Mathematical Structure of RelB Dynamics in the NF-κB Non-Canonical Pathway

This study analyzed the non-canonical NF-κB pathway, which controls functions distinct from those of the canonical pathway. Although oscillations of NF-κB have been observed in the non-canonical pathway, a detailed mechanism explaining the observed behavior remains elusive, owing to the different behaviors observed across cell types. This study demonstrated that oscillations cannot be produced by the experimentally observed pathway alone, thereby suggesting the existence of an unknown reaction pathway. Assuming this pathway, it became evident that the oscillatory structure of the non-canonical pathway was caused by stable periodic orbits. In addition, we demonstrated that altering the expression levels of specific proteins reproduced various behaviors. By fitting 14 parameters, excluding those measured in previous studies, this study successfully reproduce nuclear retention (saturation), oscillation, and singular events that had been experimentally confirmed. The analysis also provided a comprehensive understanding of the dynamics of the RelB protein and suggested a potential inhibitory role for the unknown factor. These findings indicate that the unknown factor may be an isoform of IκB, contributing to the regulation of NF-κB signaling. Based on these models, we gained invaluable understanding of biological systems, paving the way for the development of new strategies to manipulate specific biological processes.

Frequency conversion interposer with no-internal stress curved-beam for MEMS vibrational energy harvesters

The generating efficiency of an micro electro mechanical system vibrational energy harvester (MEMS VEH), which converts vibrational energy into electrical energy, is maximized at resonance. However, because the resonance frequency of an MEMS VEH is an order of magnitude higher than the vibrational frequency in the environment and not only has a high Q value, but the frequency of vibration in the environment changes randomly, it is difficult for MEMS VEHs to harvest vibrational energy efficiently. In this study, we propose a method to improve the generation efficiency of MEMS VEHs using a Frequency Conversion Interposer (FCI) that vibrates nonlinearly with its bistable no-internal stress curved-beam. As a simulation model combining FCI with the MEMS VEH, we fabricated a Two-Dimensional Monolithic Structure (TDMS) with a curved-beam and a straight beam that mimicked the FCI and oscillatory structure of the MEMS VEH, respectively. It was observed that the vibration of the straight beam induced snap-through (ST) of the curved-beam of the FCI, and the measured acceleration was more than 1.3 times the applied acceleration applied from the FCI to the MEMS VEH. As the power generation of the MEMS VEH is proportional to the square of the applied acceleration, the FCI is useful for improving the generating efficiency of the MEMS VEH.

The single-phase solution and Whitham modulation equations of the defocusing self-induced transparency system

Under investigation in this paper is the defocusing self-induced transparency system which can describe propagation characters of short pulses in Erbium doped fibers with a two-level medium. The single-phase periodic solution and Whitham modulation equations will be derived via finite-gap integration method and Whitham modulation theory. In addition, the oscillatory structure of dispersive shock waves will be constructed and analyzed.

Premixed flames in narrow heated channels of circular cross-section: Steady-state solutions, their linear stability analysis and the multiplicity of stable dynamic modes

Premixed flames in narrow heated circular channels subjected to a Poiseuille flow are investigated within the constant density model for various Lewis numbers using irreversible one-step Arrhenius kinetics. A global stability analysis of steady-state axisymmetric solutions is carried out, together with time-dependent direct numerical simulations. The analysis reveals the criteria for the appearance of oscillatory and three-dimensional cellular flame structures. The problem is also studied separately within the framework of the narrow-channel approximation.Among the results obtained, the following can be singled out as the main ones. First, the multiplicity of stable dynamic modes, oscillatory and steady-state, taking place for the same set of parameters for flames with Le<1 is demonstrated. The actual occurrence of one mode or another depends on the initial conditions. Second, the appearance of chaotic regimes is shown for flames with Le>1. The chaotic dynamics occurs in a narrow range of values of the flow rate, with Feigenbaum period-doubling cascades taking place both before and after this interval. The results of this study could be useful in the development and use of small-scale combustion devices.Novelty and significance statement: A systematic study of premixed flames in narrow heated circular channels in the presence of Poiseuille flow is carried out for various Lewis numbers using irreversible one-step Arrhenius kinetics. One of the novelties presented in the paper is the linear global stability analysis of steady state axisymmetric solutions of this problem, which has not been reported before. Also, for the first time, the existence of multiple stable dynamic modes, oscillatory and time-independent, which occurs at the same parameter values, is demonstrated for flames with Lewis number smaller than one. For flames with a Lewis number greater than one, cases with chaotic dynamics are found that manifest themselves in a narrow range of the flow rate. Finally, it is demonstrated that the Feigenbaum cycle-doubling cascade can appear before and after this interval of chaotic dynamics. Such analysis has not been reported before for this problem of flames in partially heated channels.

Highly localized horseshoe ripplons and solitons in positive dispersion media

In this study, we systematically review various ripplon solutions to the Kadomtsev–Petviashvili equation with positive dispersion (KP1 equation). We show that there are mappings that allow one to transform the horseshoe solitons and curved lump chains of the KP1 equation into circular solitons of the cylindrical Korteweg–de Vries (cKdV) equation and two-dimensional solitons of the cylindrical Kadomtsev–Petviashvili (cKP) equation. Then, we present analytical solutions that describe new nonlinear highly localized ripplons of a horseshoe shape. Ripplons are two-dimensional waves with an oscillatory structure in space and a decaying character in time; they are similar to lumps but non-stationary. In the limiting case, the horseshoe ripplons reduce to solitons decaying with time and having bent fronts. Such entities can play an important role in the description of strong turbulence in plasma and other media.

Ultrafast Spectroscopy under Vibrational Strong Coupling in Diphenylphosphoryl Azide.

Strong coupling of cavity photons and molecular vibrations creates vibrational polaritons that have been shown to modify chemical reactivity and alter material properties. While ultrafast spectroscopy of vibrational polaritons has been performed intensively in metal complexes, ultrafast dynamics in vibrationally strongly coupled organic molecules remain unexplored. Here, we report ultrafast pump-probe measurement and two-dimensional infrared spectroscopy in diphenylphosphoryl azide under vibrational strong coupling. Early time oscillatory structures indicate coherent energy exchange between the two polariton modes, which decays in ∼2 ps. We observe a large transient absorptive feature around the lower polariton, which can be explained by the overlapped excited-state absorption and derivative-shaped structures around the lower and upper polaritons. The latter feature is explained by the Rabi splitting contraction, which is ascribed to a reduced population in the ground state. These results reassure the previously reported spectroscopic theory to describe nonlinear spectroscopy of vibrational polaritons. We have also noticed the influence of the complicated layer structure of the cavity mirrors. The penetration of the electric field distribution into the layered structure of the dielectric-mirror cavities can significantly affect the Rabi splitting and the decay time constant of polaritonic systems.

A variant of the discrete gradient method for the solution of the semilinear wave equation under different boundary conditions

In this paper, energy-preserving schemes based upon the discrete gradient are used to numerically solve the semilinear wave equation under periodic boundary conditions, Dirichlet boundary conditions and Neumann boundary conditions. Both the integral form and the evolutionary behaviour of the energy depend on the associated boundary conditions. The wave equations are semi-discretized in different manners for different boundary conditions such that the Hamiltonian functions of the resulting semi-discrete Hamiltonian systems are the discrete analogue of the original energy. Furthermore, the Hamiltonian functions of the resulting semi-discrete systems have similar evolutionary behaviours as the original energy. It is noted that the semi-discrete system exhibits an oscillatory structure. Subsequently, the semi-discrete approximation of the energy evolution as well as the oscillatory structure is passed to the fully-discrete problem by applying extended discrete gradient formula in the temporal direction. Numerical experiments are carried out to show the effectiveness of the new schemes.

Phonon thermal transport shaped by strong spin-phonon scattering in a Kitaev material Na2Co2TeO6

The report of a half-quantized thermal Hall effect and oscillatory structures in the magnetothermal conductivity in the Kitaev material α-RuCl3 have sparked a strong debate on whether it is generated by Majorana fermion edge currents, spinon Fermi surface, or whether other more conventional mechanisms are at its origin. Here, we report low temperature thermal conductivity (κ) of another candidate Kitaev material, Na2Co2TeO6. The application of a magnetic field (B) along different principal axes of the crystal reveals a strong directional-dependent B impact on κ, while no evidence for mobile quasiparticles except phonons can be concluded at any field. Instead, severely scattered phonon transport prevails across the B−T phase diagram, revealing cascades of phase transitions for all B directions. Our results thus cast doubt on recent proposals for significant itinerant magnetic excitations in Na2Co2TeO6, and emphasize the importance of discriminating true spin liquid transport properties from scattered phonons in candidate materials.

Quantum State-Resolved Nonadiabatic Dynamics of the H+NaF → Na+HF Reaction

The H + NaF reaction is investigated at the quantum state-resolved level using the time-dependent wave-packet method based on a set of accurate diabatic potential energy surfaces. Oscillatory structures in the total reaction probability indicate the presence of the short-lived intermediate complex, attributed to a shallow potential well and exothermicity. Ro-vibrational state-resolved integral cross sections reveal the inverted population distributions of the product. The HF product favors an angular distribution in the forward hemisphere of 30°–60° within the collision energy range from the threshold to 0.50 eV, which is related to the nonlinear approach of the H atom to the NaF molecule. Quantum generalized deflection functions show that the low-J partial waves contribute primarily to the backward scattering, while the high-J partial waves govern the forward scattering. The correlation between the partial wave J and the scattering angle ϑ proves that the reaction follows a predominant direct reaction mechanism.

Observing quantum matter-wave diffraction in the energetic He2+-He collisions

We present an experiment combined with numerical simulations to study single and double electron capture processes induced during the collisions between the He target and the He2+ projectile in the energy range 2–20 keV/u. According to our experimental observations, measuring the angular distribution of the scattered projectile He2+ reveals a clear oscillatory structure. The latter records an imprint of the collision dynamics, specifically, a signature of the matter-wave scattering and the internal electronic structure of the collisional system He2+-He. We found that this feature is sensitive to the incident projectile's energy and the nature of the involved process. With the help of four-body semiclassical close coupling and classical trajectory Monte Carlo methods, we show that the observed structure is of a quantum nature. This is further supported by a simple mathematical model based on Fraunhofer-type diffraction of light, to which the oscillations are attributed. Our findings thus provide insights into the role of quantum phenomena in characterizing collision dynamics. Published by the American Physical Society 2024

High vibrational excitation of the reagent transforms the late-barrier H + HOD reaction into an early-barrier reaction.

Polanyi's rules predict that a late-barrier reaction yields vibrationally cold products; however, experimental studies showed that the H2 product from the late-barrier H + H2O(|04⟩-) and H + HOD(vOH = 4) reactions is vibrationally hot. Here, we report a potential-averaged five-dimensional state-to-state quantum dynamics study for the H + HOD(vOH = 0-4) → H2 + OD reactions on a highly accurate potential energy surface with the total angular momentum J = 0. It is found that with the HOD vibration excitation increasing from vOH = 1 to 4, the product H2 becomes increasingly vibrationally excited and manifests a typical characteristic of an early barrier reaction for vOH = 3 to 4. Analysis of the scattering wave functions revealed that vibrational excitation in the breaking OH bond moves the location of dynamical saddle point from product side to reactant side, transforming the reaction into an early barrier reaction. Interestingly, pronounced oscillatory structures in the total and product vibrational-state-resolved reaction probabilities were observed for the H + HOD(vOH = 3, 4) reactions, in particular at low collision energies, which originate from the Feshbach resonance states trapped in the bending/torsion excited vibrational adiabatic potential wells in the entrance region due to van der Waals interactions.

Quantum dynamics study of reaction H+SiH using a new potential energy surface of SiH&lt;sub&gt;2&lt;/sub&gt;(1&lt;sup&gt;1&lt;/sup&gt;A′)

Initial state-selected and energy-resolved reaction probabilities, integral cross sections(ICSs), and thermal rate constants of the &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ \text{H}{(}^{2}\text{S})+S\text{iH}({\text{X}}^{2}\Pi; \nu = 0\text{ },j = 0)\to \text{Si}{(}^{1}\text{D})+{\text{H}}_{2}({\text{X}}^{1} \Sigma_{g}^{+}) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; reaction are calculated within the coupled state(CS) approximation and accurate calculation with full Coriolis coupling(CC) by a time-dependent wave packet propagation method (Chebyshev wave packet method). Therefore, a new ab initio global potential energy surface (PES) of the electronic ground state (1&lt;sup&gt;1&lt;/sup&gt;A′) of the system, which was recently reported by Li et al. [&lt;ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://pubs.rsc.org/en/content/articlelanding/2022/cp/d1cp05432e"&gt; &lt;i&gt;Phys. Chem. Chem. Phys.&lt;/i&gt; 2022 &lt;b&gt;24&lt;/b&gt; 7759&lt;/ext-link&gt;], is employed. The contributions of all partial waves to the total angular momentum &lt;i&gt;J&lt;/i&gt; = 80 for CS approximation and &lt;i&gt;J&lt;/i&gt; = 90 for CC calculation are considered to obtain the converged ICSs in a collision energy range of 1.0 ×10&lt;sup&gt;–3&lt;/sup&gt;－1.0 eV. The calculated probabilities and ICSs display a decreasing trend with the increase of the collision energy and show an oscillatory structure due to the SiH&lt;sub&gt;2&lt;/sub&gt; well on the reaction path. The neglect of CC effect will lead to underestimation of the ICS and the rate constant due to the formation of an SiH&lt;sub&gt;2&lt;/sub&gt; complex supported by the stationary points of the SiH&lt;sub&gt;2&lt;/sub&gt;(1&lt;sup&gt;1&lt;/sup&gt;A′) PES. In addition, the results of the exact calculation including CC effect are compared with those calculated in the CS approximation. For the reaction probability, CC and CS calculations change with similar tends, shown by their observations at small total angular momentum &lt;i&gt;J&lt;/i&gt; = 10, 20 and 30, and the CC results are larger than the CS results almost in the whole considered energy range at large total angular momentum &lt;i&gt;J&lt;/i&gt; = 40, 50, 60 and 70. The gap between CS and CC probability get more pronounced with increasing of &lt;i&gt;J&lt;/i&gt;, which reveals that Coriolis coupling effects become more and more important with &lt;i&gt;J&lt;/i&gt; increasing for the title reaction&lt;i&gt;.&lt;/i&gt; Moreover, the exact quantum-wave calculations show that the thermal rate constant between 300 K and 1000 K for the title reaction shows a similar temperature independent behavior to that for the H + CH reaction, but the value of the rate constant for the H + SiH reaction is an order of magnitude larger than that for the H + CH reaction.

Structure of a Quasi-parallel Shock Front

The aim of this study is to compare observations of the magnetic field structure of observed quasi-parallel collisionless shock fronts with the results obtained analytically. A two-fluid analytic model of the shock front structure was derived under the assumptions that the shock is stationary and planar. The ion and electron kinetic pressures were assumed to be scalar, and polytropic state equations were used. The results of this analytical approach show that the shock magnetic field has an oscillatory structure. Venus Express (VEX) observations of the Venusian bow shock have been used to validate these theoretical findings. The Venusian bow shock and corresponding foreshock are significantly smaller than those of Earth. Thus, observations of the underlying structure of the quasi-parallel shock at Venus are not masked by the presence of high-amplitude waves and nonlinear structures originating in the foreshock. It is shown that the structure of the shock front, as observed by VEX, has a very strong similarity to the structure obtained analytically.

UV Absorption Spectroscopy of the Conformer-Dependent Reactivity of the Four Carbon Criegee Intermediate of Methyl Vinyl Ketone Oxide: An Ab initio Quantum Dynamics Study.

An extended theoretical analysis of the photodissociation dynamics of the four-carbon Criegee intermediate (CH2═CH(CH3)COO) or methyl vinyl ketone oxide, which has four conformers, following excitation to the B state, is presented. Our analysis relies on multireference electronic wave functions combined with a wavepacket propagation treatment for the two coupled B1A' and C1A' electronic states and two nuclear degrees of freedom. For each conformer, the 2D model depends on potential energy surfaces (PESs) along the O-O and C-O-O bending modes for the two lowest excited states, B1A' and C1A', and is sufficiently accurate to reproduce the experimental B1A' ← X1A' absorption spectrum with unprecedented accuracy. It is found that the roles of each conformer are essential in producing a cumulative spectrum, which is close to the recent experimental spectrum. The anti-trans and anti-cis conformers make contributions at the longer and shorter wavelengths of the cumulative spectrum, respectively, while the syn-cis and syn-trans conformers have contributions in the middle wavelength range of the cumulative spectrum of MVK-oxide. The existence of a deep well for each conformer on the PESs of the (diabatic) B state causes a considerable amount of the wavepacket to be reflected by the B state wells, which can explain the oscillatory structures appearing in the long wavelength range of 360-480 nm of the spectrum. The weakly avoided crossings between the B-state and C-state PESs of each conformer appearing within the range of 2.80-3.08 eV excitation energy cause considerable disturbance in the vibronic fine structure of the bands. The results give novel insight into the complex interactions governing this intriguing process.

Approximate Solution of a Class of Highly Oscillatory Integral Equations Using an Exponential Fitting Collocation Method

This paper deals with the numerical solution of a class of highly oscillatory Volterra integral equations by collocation methods based on the exponential fitting technique. By reviewing the oscillatory structures of solutions of these problems, we construct an exponential fitting collocation method which is best tuned to capture the qualitative behaviour of the solution of these equations. We also investigate the convergence properties of the proposed collocation solution based on the interpolation remainder. Some numerical examples are provided which illustrate the efficiency and accuracy of the proposed method and confirm its superiority over the polynomial collocation methods.

Study of damped oscillating structures from charged and neutral K-meson electromagnetic form factors data

The damped oscillating structures were recently revealed in the proton “effective” form factor data. For the time being they can neither be confirmed nor disproved by investigations of the individual proton form factors data because the data have not yet achieved the required level of precision. On the other hand, conjectures that the oscillating structures are direct manifestations of the quark-gluon structure of the proton indicate that they should not be specific only to the proton and neutron. This opens a possibility to find these structures also in the data of other hadrons by the same procedure as for the proton. In this paper the oscillatory structures are investigated in the electromagnetic form factor data of the charged and neutral K-mesons. If the charged and neutral K-meson data are described by the three parametric formula by means of which the oscillating structures have been revealed for the proton (although with a large value of chi ^2/ndf) then oscillating structures appear. On the other hand, if the physically well founded Unitary and Analytic model of the K-meson electromagnetic structure is used for the description of the charged K-meson data, no damped oscillating structures are visible. However, in the case of the neutral K-meson data one cannot make a definite conclusion, and more precise data are needed. These results indicate that also the damped oscillating structures obtained from the “effective” proton form factor data are likely an artefact of the three parametric formula, which cannot describe the data with sufficient precision.