Dynamics near Unstable,Interfacial Fluids

We study three examples of unstable interfacial fluid motions: vortex sheets with surface tension, Hele-Shaw flows with surface tension, and vortex patches. In all three cases, the nonlinear dynamics of a large class of smooth perturbations is proven to be characterized by the corresponding fastest linear growing mode(s) up to the time scale of , where is the magnitude of the initial perturbation. In all three cases, the analysis is based on an unified analytical framework that includes precise bounds on the growth of the linearized operator, given by an explicit solution formula, as well as a special sharp nonlinear energy growth estimate. Our main contribution is establishing this nonlinear energy growth estimate for each interface problem in certain high energy norms. Y. G. was supported in part by NSF grants DMS-0305161, INT-9815432 and a Salomon award of Brown University. D. S. was supported in part by NSF grant DMS-0510121.     

Near Wall Dynamics of Premixed Flames

Highly-resolved numerical simulations employing detailed reaction kinetics and molecular transport have been applied to flame-wall interaction (FWI) of laminar premixed flames. A multiple plane-jet flame (2D) has been considered, which is operated with premixed methane/air mixtures at atmospheric conditions and with different equivalence ratios. Free flame (FF) and side-wall quenching (SWQ) conditions have been accomplished by defining one lateral boundary as either a symmetry plane for FF or a cold wall with fixed temperature for SWQ. An equidistant grid with a resolution of 20 µm is used to resolve the FWI zone. The GRI-3.0 mechanism is used for computing chemical reaction rates. The flame is tangentially compressed when approaching the cold wall, and elongated in the FF case, causing an inversion of the sign of the tangential strain rate Ka_s and a considerable decrease of the total stretch rate Ka_tot for the SWQ flame. The flame consumption speed S_L decreases with decreasing normal stretch due to curvature Ka_c while approaching the cold wall, but it increases with decreasing Ka_c for the FF case, leading to an inversion of the Markstein number Ma_tot based on Ka_tot from positive in FF to negative in the SWQ case. The results reveal a strong correlation of flame dynamics during transitions from FWI to freely propagating flames, which may bring a new perspective for modeling FWI phenomena by means of flame dynamics. To do this, the quenching effect of the wall may be reproduced by an inversion of the Markstein number from positive to negative in the FWI zone and applying the general linear Markstein correlation, leading to a decrease of the flame consumption speed. In addition, the quenching distance evaluated from S_L has been found to be almost equal to the unstretched laminar flame thickness, which compares quantitatively well with measured data from literature.     

Domain-Wall Dynamics After Photoexcitations Near neutral-Ionic Phase Transitions

Real-time dynamics of domain walls between the neutral and ionic phases just after photoexcitations is studied by fully solving the time-dependent Schrödinger equation for a one-dimensional extended Peierls-Hubbard (PH) model, not by relying on the adiabatic approximation. The unrestricted Hartree-Fock (HF) approximation is used for electrons, and the lattice displacements are treated classically. Three characteristic time scales are observed: rapid oscillation of ionicity owing to the local charge transfer; slow oscillation of lattice displacements; and even slower and collective motion of domain walls. Steady growth of a metastable domain is achieved after complicated competition of micro domains. The relevance to recently measured, time-resolved photoreflectance spectra in TTF-CA is discussed.     

Oscillating Decay of an Unstable System

We study the medium-time behavior of the survival probability in the frame of the N-level Friedrichs model. The time evolution of an arbitrary unstable initial state is determined. We show that the survival probability may oscillate significantly during the so-called exponential era. This result explains qualitatively the experimental observations of the NaI decay. The Gamow states for N-level Friedrichs model are constructed. The time evolution in terms of the complex spectral representation including the Gamow states is discussed.     

重离子碰撞中阈能附近超子产生机制

在量子分子动力学输运模型LQMD(Lanzhou quantum molecular dynamics transport model)框架下,研究了不同重离子反应系统中同位旋和核介质效应对超子产生以及动能谱的影响.基于手征有效场理论,引入了动量和密度相关的排斥超子-核子光学势,并且考虑了该势对超子产生截面阈能的修正....     

带圆锥透镜的非稳贝塞尔光学谐振腔

研究了由圆锥透镜和凸面镜组成的非稳贝塞尔光学谐振腔. 利用几何光学原理,讨论了非稳贝塞尔谐振腔中光线传输的ABCD矩阵和腔内光线实现自再现的条件.从波动光学角度出发,利用惠更斯 菲涅尔衍射积分方程导出了谐振腔两镜面处光场的迭代方程,并通过数值模拟得到了凸面镜曲率半径不同时零阶贝塞尔光束在输出镜面上的光强分布.     

带圆锥透镜的非稳贝塞尔光学谐振腔

研究了由圆锥透镜和凸面镜组成的非稳贝塞尔光学谐振腔. 利用几何光学原理,讨论了非稳贝塞尔谐振腔中光线传输的ABCD矩阵和腔内光线实现自再现的条件.从波动光学角度出发,利用惠更斯-菲涅尔衍射积分方程导出了谐振腔两镜面处光场的迭代方程,并通过数值模拟得到了凸面镜曲率半径不同时零阶贝塞尔光束在输出镜面上的光强分布.     

界面附近光剥离过程中的量子经典对应

研究了氢负离子在弹性墙附近的光剥离过程，导出了剥离截面的解析公式。此截面为光滑背景项与一正弦振荡项之和，后者与离子与弹性墙的距离有关。分析了光剥离电离的经典动力学及其量子对应。在本模型中，半经典光剥离截面与量子结果一致。     

The Kirchhoff gauge

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge, the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.     

椭圆旋转对称群

提出椭圆旋转对称群,它是一个单参数阿贝尔群.辅助参数η确定群轨道的形状,SO(2)旋转群对应η=1时的情况.     

Unstable fields and the recollapse of an open universe

The effects of classically unstable fields upon the evolution of an open universe are considered. It is shown that such fields can cause an open universe to cease expanding and recollapse to a final singularity, even if the total mass density is less than the critical density at the present time.     

Calculation of the Spatio-Temporal Dynamics of Q-switched Yb^3＋：YAG Laser with an Unstable Cavity and a Super-Gaussian Mirror

A numerical simulation used to compute the spatio-temporal dynamics of pulse formation of diode-pumped Q- switched Yb： YA G laser is carried out. The model takes the laser amplification and gain saturation, the properties of the laser cavity, and the diffractive effects of the laser disc into account. The numerical calculation is performed for a confocal positive-branch unstable resonator with a super Gaussian coupling mirror. The simulation results show that the laser pulse starts from a Gaussian intensity distribution and becomes rapidly non-Gaussian. The corresponding beam quality M^2 factor is seen to vary approximately from 1.5 at the beginning of the formation of pulse to more than 10 in the tail of the pulse, with a value of 11.6 at the peak of the pulse.     

In Vitro Monitoring of Live Cardiomyocytes Dynamics by a Scanning Near Field Optical Microscope Setup

We describe an original scanning near field optical microscope setup developed to examine rhythmically beating cardiac myocytes fully immersed in culture media. Scans could be halted at any point to record localized contraction profiles. Contractions could be detected with high sub nanometric vertical sensitivity and changed shape dramatically within adjacent sub micron-sized areas. We believe that the spatial dependency of contractions arises because of system’s ability to resolve the dynamic behavior of individual sub membrane actin bundles. Our results, combining imaging and real time recording in localized areas, reveal a new, non-invasive method for studying sub micron morphological activity in live biological samples.This paper was originally presented at the 5th International Conference on NEAR FIELD OPTICS and RELATED TECHNLOGIES (NFO-5), which was held on December 6–10, 1998 at Coganoi Bay Hotel, Shirahama, Japan, in cooperation with the Japan Society of Applied Physics and Mombusho Grant-in Aid for Scientific Research on Priority Areas “Near-Field Nano-optics” Projects, sponsored by Japan Society for the Promotion of Science.     

Acoustic Manifestations of a Gas Inclusion Near an Interface

The study continues previous investigations based on the use of specific (bispherical) coordinates in describing the behavior of bubbles in the presence of bounding surfaces. Explicit dependences of the first oscillation modes and the scattered field on bubble size, distance to the boundary, and physical parameters of contacting media are obtained. It is shown that, as the distance to the boundary decreases, dipole oscillations acquire resonance nature and become comparable in amplitude with radial oscillations. This effect is of applied value for modern ultrasonic cleaning techniques, because it leads to a considerable increase in bubble-generated microstreaming.     

Near fields scattered by an underwater finite cylindrical baffle

In this work,acoustic vector characteristics of near fields scattered by an underwater finite cylindrical baffle are investigated theoretically and experimentally.The analytic expressions for the scattered pressure and particle velocity are derived using the elastic thin shell theory.Calculations are presented for the scattered near fields of the pressure,the particle velocity and the intensity.It is found that the pressure and the particle velocity fields near the surface of the cylindrical baffle are characterized by complex interference structure,particle velocity directions and the source bearings are not consistent.The phase difference between the pressure and the particle velocity is not zero and the intensity vector does not reflect the sound bearings.It can be noted that the distortions of the fields will make the original vector signal processing method based on the free space assumption be no longer applicable in the presence of the cylindrical baffle.These results can serve as a basis of the application for the acoustic vector sensor on board.     

A Kirchhoff solution to plasmon hybridization

Using Ohm’s law, a solution to plasmon hybridization via Kirchoff’s equations results in a simple and intuitive picture of a metal nanoparticle dimer as a capacitively coupled circuit. Calculated absorption spectra and surface charge densities show that dimers of different metallic composition support different super- and sub-radiant plasmons compared to homodimers. Strong screening of Coulomb interactions between nanoparticles of different metallic background prohibits the excitation of anti-bonding plasmons, while changes to the free electron conductivity upon a collective response result in coupled plasmon lifetimes which shift as a function of interparticle distance. Smaller separations then result in the longest lived plasmons.     

Loschmidt Echo and Fidelity Decay Near an Exceptional Point

Non‐Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non‐Hermitian dynamical quantum phase transitions, and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here, a rather counterintuitive phenomenon in certain non‐Hermitian systems near an EP is disclosed, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non‐perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single‐particle hopping dynamics on a tight‐binding lattice under an imaginary gauge field.     

Poincaré Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.