Conditions for Mixed Mode Oscillations and Deterministic Chaos in Nonlinear Chemical Systems

An approach has been proposed for finding the conditions for the existence of mixed-mode oscillations and deterministic chaos in a kinetic scheme after reduction to a simple system of equations. Analysis of the position and stability of the steady states of this system suggested simple conditions for the existence of mixed-mode oscillations and deterministic chaos. The boundaries for monostability, bistability, and oscillations were also found. The results obtained were completely confirmed by numerical modelling.     

分子转动和激光脉冲对多光子激发控制的影响(英文)

用解析代数方法研究了分子转动和激光脉冲对双原子分子多光子激发控制的影响并推导得到不同转动通道下的分子振动激发几率的解析表达式.为了考察转动能级和考虑分子转动后与激光场夹角的变化对分子多光子振动激发和振动激发控制的影响,我们计算并比较了分子纯振动和加入分子转动两种情况,并分别给出了分子与极化激光场在不同取向角下三光子选择激发的图像.研究发现分子的转动能级对多光子非共振激发有修正作用,但是分子转动会降低多光子激发的选择性,而选择合适的激光脉冲形状有利于目标多光子激发控制的实现.文中还进一步讨论了激光脉冲初相位对分子多光子激发控制的影响,发现脉冲初相位对多光子激发过程有明显的调制作用.     

A new approach to polarimetric measurements based on birefringent crystals and diode lasers

A new polarimetric instrument and measurement method is described based on the use of diode lasers as radiation source (532, 650 and 1064 nm) and birefringent prisms, such as Glan-Laser and Wollaston, as analyzers. The laser radiation is passed through a dichroic polarizer film for further orientation of its polarization plane at 45° in relation to the polarization plane of the analyzer. The polarized beam, oriented in that way, passes the sample cell, impinges the prism surface, and the intensities of the two emerged beams are detected by two twin silicon detectors. Ideally, in the absence of any optically active substances, the crystals produces two orthogonally polarized refracted beams of equal intensity. In the presence of an optically active substance, the arctangent of the square root of the beam intensities ratio is equal to the new polarization angle (β) of the laser beam. The rotation angle imposed for any optically active substance present in the sample cell is then given by: α = (45 – β)°. Because the rotation is obtained by the ratio of the intensities of two beams, it is independent of the laser intensity, which can vary up to ±15% with no significant effect on the accuracy of the polarimetric measurement. The instrument has been evaluated for measurement of optically active substances such as sucrose and fructose. The instrument employs low cost components, is capable of attaining a repeatability of ±0.003° and can measure the rotation angle, over a ±45° range, in less than 2 s. Because it does not present any moving parts it can be easily adapted for in/on-line process monitoring of optically active substances.     

Temperature-induced route to chaos in the H2O2-HSO3(-)-S2O3(2-) flow reaction system

Low-frequency, high-amplitude pH-oscillations observed experimentally in the H2O2-HSO3(-)-S2O3(-) flow reaction system at 21.0 degrees C undergo period-doubling cascades to chemical chaos upon decreasing the temperature to 19.0 degrees C in small steps. Period-4 oscillations are observed at 20.0 degrees C and can be calculated on the basis of a simple model. A reverse transition from chaos to high-frequency limit cycle oscillations is also observable in the reaction system upon decreasing further the temperature step by step to 15.0 degrees C. Period-2 oscillations are measured at 18.0 degrees C. Such a temperature-change-induced transition between periodic and chaotic oscillatory states can be understood by taking into account the different effects of temperature on the rates of composite reactions in the oscillatory system. Small differences in the activation energies of the composite reactions are responsible for the observed transitions. Temperature-change-induced period doubling is suggested as a simple tool for determining whether an experimentally observed random behavior in chemical systems is of deterministic origin or due to experimental noise.     

Chemical chaos in novel iodate-driven oscillator-thiophenol-iodate-H2SO4 system

Chaotic oscillations in redox potential have been observed in thiophenol-KIO₃-H₂SO₄ system in batch reactors. These occur in a concentration and temperature range. Bifurcation from a stable regime to a chaotic regime occurs in a straight way in the entire concentration and temperature range. Oscillations were also studied in continuously stirred tank reactors. These oscillations are deterministic chaos. It is tentatively suggested that chaos in the system is due to a time delay caused by a large number of intermediates.     

Period Doubling and Chaos of Spontaneous Oscillatory Phenomena on Iron

 A new self-oscillating system introducing spontaneous oscillatory phenomena on iron in a sulfuric acid solution of hydrogen peroxide is discussed. This phenomenon can be explained by a continuous oscillation between the active and passive state of iron. Unlike other published systems that only show one-peak oscillations, the potential of iron shows highly complex dynamics: depending on the concentration of hydrogen peroxide and sulfuric acid, a period doubling and non-periodic oscillations in a self-oscillating system were observed for the first time. The reactions were analyzed by methods based on chaos theory and could finally be identified as an example of deterministic chaos.     

Period Doubling and Chaos of Spontaneous Oscillatory Phenomena on Iron

Summary.  A new self-oscillating system introducing spontaneous oscillatory phenomena on iron in a sulfuric acid solution of hydrogen peroxide is discussed. This phenomenon can be explained by a continuous oscillation between the active and passive state of iron. Unlike other published systems that only show one-peak oscillations, the potential of iron shows highly complex dynamics: depending on the concentration of hydrogen peroxide and sulfuric acid, a period doubling and non-periodic oscillations in a self-oscillating system were observed for the first time. The reactions were analyzed by methods based on chaos theory and could finally be identified as an example of deterministic chaos. Received April 24, 2001. Accepted May 7, 2001     

Optical phase grating diffraction in a quasistatic electric field biased nematic liquid crystal film

Abstract

It is known that an optical phase grating can be obtained when two mutually coherent laser beams overlap in a nematic liquid crystal. This is mainly due to director reorientation which contributes to a large optical non-linearity. It has been suggested by Herman and Serinko that a phase grating could be obtained in nematic liquid crystals if a D.C. field is used to bias it near the critical orientational Freedericksz transition. A homeotropic MBBA film biased by an electric field at 1 kHz has been studied. Two weak Ar⁺ laser beams were incident normally to the film with a small intersection angle (?0·4?). Using the picture of a director reorientation mechanism and a degenerate four wave mixing scheme, we have obtained the dependence of the diffraction beam intensity on that of the incident beam and the strength of the biased electric field. The theoretical prediction and experimental results both show that the phase grating diffraction can be dramatically enhanced by the coupling of the electric field to the optical field in the Freedericksz transition region. This is due to the critical behaviour of the sample at that transition. The prominently improved signal-to-noise ratio is discussed.     

Twist viscosities and flow alignment of biaxial nematic liquid crystal phases of a soft ellipsoid-string fluid studied by molecular dynamics simulation

We have calculated the twist viscosity and the alignment angle between the director and the stream lines in shear flow of a liquid crystal model system, which forms biaxial nematic liquid crystals, as functions of the density, from the Green-Kubo relations by equilibrium molecular dynamics simulation and by a nonequilibrium molecular dynamics algorithm, where a torque conjugate to the director angular velocity is applied to rotate the director. The model system consists of a soft ellipsoid-string fluid where the ellipsoids interact according a repulsive version of the Gay-Berne potential. Four different length-to-width-to-breadth ratios have been studied. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the uniaxial nematic phase there is one twist viscosity and one alignment angle. In the biaxial nematic phase there are three twist viscosities and three alignment angles corresponding to the rotation around the various directors and the different alignments of the directors relative to the stream lines, respectively. It is found that the smallest twist viscosity arises by rotation around the director formed by the long axes, the second smallest one arises by rotation around the director formed by the normals of the broadsides, and the largest one by rotation around the remaining director. The first twist viscosity is rather independent of the density whereas the last two ones increase strongly with density. One finds that there is one stable director alignment relative to the streamlines, namely where the director formed by the long axes is almost parallel to the stream lines and where the director formed by the normals of the broadsides is almost parallel to the shear plane. The relative magnitudes of the components of the twist viscosities span a fairly wide interval so this model should be useful for parameterisation experimental data.     

Effect of the Gouy phase on the coherent phase control of chemical reactions

We show how the spatial phase of a focused laser beam may be used as a tool for controlling the branching ratio of a chemical reaction. Guoy discovered [Acad. Sci., Paris, C. R. 110, 1250 (1890)] that when an electromagnetic wave passes through a focus its phase increases by pi. In a coherent control scheme involving the absorption of n photons of frequency omega(m) and m photons of frequency omega(n), the overall phase shift produced by the Gouy phase is (n-m)pi. At any given point in space, this phase shift is identical for all reaction products. Nevertheless, if the yields for different reaction channels have different intensity dependencies, the Gouy phase produces a net phase lag between the products that varies with the axial coordinate of the laser focus. We obtain here analytical and numerical values of this phase as the laser focus is scanned across the diameter of the molecular beam, taking into account the Rayleigh range and astigmatism of the laser beam and saturation of the transition. We also show that the modulation depth of the interference pattern may be increased by optimizing the relative intensities of the two fields.     

Field-induced alignment of the nematic director: studies of nuclear magnetic resonance spectral oscillations in the limit of fast director rotation

Time-resolved NMR spectroscopy is a powerful method to investigate field-induced rotation of the director in a nematic liquid crystal. The method requires that the director does not rotate significantly during the acquisition of the free induction decay and hence the NMR spectrum. We have extended the method to systems where this is not the case and the observed NMR spectra are now found to contain novel oscillatory features. To understand these oscillations, we have developed a model combining both director and spin dynamics. In addition to increasing the information content of the time-resolved NMR spectra, it also proves possible to determine the field-induced relaxation time from a single spectrum.     

Anomalous Lehmann Rotation of Achiral Nematic Liquid Crystal Droplets Trapped under Linearly Polarized Optical Tweezers

Continuous rotation of a cholesteric droplet under the heat gradient was observed by Lehmann in 1900. This phenomenon, the so-called Lehmann effect, consists of unidirectional rotation around the heat flux axis. We investigate this gradient heat effect using infrared laser optical tweezers. By applying single trap linearly polarized optical tweezers onto a radial achiral nematic liquid crystal droplet, trapping of the droplet was performed. However, under a linearly polarized optical trap, instead of stable trapping of the droplet with slightly deformed molecular directors along with a radial hedgehog defect, anomalous continuous rotation of the droplet was observed. Under low power laser trapping, the droplet appeared to rotate clockwise. By continuously increasing the laser power, a stable trap was observed, followed by reverse directional rotation in a higher intensity laser trap. Optical levitation of the droplet in the laser beam caused the heat gradient, and a breaking of the symmetry of the achiral nematic droplet. These two effects together led to the rotation of the droplet under linearly polarized laser trapping, with the sense of rotation depending on laser power.     

Volumetric intensity dependence on the formation of molecular and atomic ions within a high intensity laser focus

The mechanism of atomic and molecular ionization in intense, ultra-short laser fields is a subject which continues to receive considerable attention. An inherent difficulty with techniques involving the tight focus of a laser beam is the continuous distribution of intensities contained within the focus, which can vary over several orders of magnitude. The present study adopts time of flight mass spectrometry coupled with a high intensity (8 x 10(15) Wcm(-2)), ultra-short (20 fs) pulse laser in order to investigate the ionization and dissociation of the aromatic molecule benzene-d1 (C(6)H(5)D) as a function of intensity within a focused laser beam, by scanning the laser focus in the direction of propagation, while detecting ions produced only in a "thin" slice (400 and 800 microm) of the focus. The resultant TOF mass spectra varies significantly, highlighting the dependence on the range of specific intensities accessed and their volumetric weightings on the ionization/dissociation pathways accessed.     

Analysis of complex oscillatory dynamics of a pH oscillator

Reaction systems that display pronounced periodic and aperiodic variations in the pH value of the reaction medium are known as pH oscillators. A member of this family of reactions studied here, the Cu(II)-catalyzed oxidation of thiosulfate by hydrogen peroxide in acidic solution, is known to display a rich variety of oscillatory dynamics. We focus on experimental time series showing complex aperiodic dynamics that simultaneously possesses the characteristics of period-doubled large-amplitude oscillations and irregular small-amplitude oscillations reminiscent of mixed-mode dynamics. An analysis based on the reconstruction of the attractor from the measured time series by two different methods and subsequent calculation of the maximal Lyapunov exponent reveals that this interesting dynamical regime is a manifestation of deterministic chaos. The text was submitted by the authors in English.     

Orientational Behaviour of the Nematic Director upon Macroscopic Rotation at the Magic Angle

The ¹⁹F N.M.R. spectrum of 1,2,2,2-tetrachloro-l,l-difluoroethane has been studied in the nematic liquid crystal ZLI1167 (Merck) upon rotation at the magic angle. The director of the liquid crystal is oriented perpendicular to the spinning axis when the angle between the rotation axis and the magnetic field is less than the magic angle and parallel when this angle is more than the magic angle. It is shown that exactly at the magic angle the spectrum corresponds to a frequency modulated powder pattern. This powder pattern leads to an understanding of the orientational behaviour of the director when a nematic is spun at the magic angle.     

Effect of molecular rotation on enantioseparation

Recently, several laser schemes have been proposed to separate racemic mixtures of enantiomers by splitting a molecular beam into subbeams consisting of molecules of definite chirality [Y. Li, C. Bruder, and C. P. Sun, Phys. Rev. Lett. 99, 130403 (2007); X. Li and M. Shapiro, J. Chem. Phys. 132, 194315 (2010)]. These ideas rely on laser-induced effective gauge potentials in an adiabatic basis which lead to a chirality dependent force on the center-of-mass. However, the effect of molecular rotation has been neglected in these studies. Accounting for the full molecular quantum state we find that the potentials from the adiabatic dressed state approach cannot be recovered once the molecular orientation dynamics is included, even in the rotational ground state. This affects substantially the ability to perform enantioseparation in the above mentioned setups.     

Modelling of the simple shear flow of a flow-aligning nematic

The shear flow induced deformations of a nematic liquid crystal layer have been modelled numerically for the case of flow-aligning nematics. The director deviation from the plane of shear, which was predicted earlier for special surface orientation angles, has been confirmed. This deformation takes a form of director rotation about the axis perpendicular to the layer plane. As a result, transverse flow of the nematic arises. The rotation angle is close to pi at sufficiently strong shear stress, and the director is oriented at the usual flow alignment angle in a significant part of the layer. The director coming out of the shear plane should not be treated as a separate effect taking place during the flow, but rather as a way in which the usual flow-aligned structure is achieved.     

纳秒强激光电离苯产生高价碳离子的波长效应

The photoionization of seeded benzene beam by 25 ns laser pulse at wavelengths of 266,355 and 1064 nm has been studied by the time-of-flight mass spectrometry. The observed mass spectra at 266 nm and 355 nm at intensities of 1010-1011 W/cm2 indicate a multiphoton ionization and dissociation（MPID）process,in which C+,C2Hx+,C3Hx+,C4Hx+ and C6H6+ are main products. While at 1064 nm laser of similar intensities,the domain ion is C4+ which is produced from Coulomb explosion. The longer wavelength facilities the energy absorption rate during inverse bremsstrahlung,which leads to the resulting wavelength dependence of the multicharged atomic ions.     

Improvements in ion signal reproducibility obtained using a homogeneous laser beam for on-line laser desorption/ionization of single particles

A major factor limiting on-line single particle mass spectrometry techniques from becoming more quantitative is the large shot-to-shot variability in ion intensities observed in the laser desorption/ionization (LDI) mass spectra.1,2 In previous work, lab-generated particles showed fluctuations of up to 152% in the absolute ion intensities in averaged spectra of 200-300 'identical' particles.2 Most of these fluctuations were attributed to inhomogeneities in the laser beam profile, leading to significant differences in the power each particle encountered depending on the position in the LDI laser beam where it underwent analysis. The goal of the work presented herein is to determine whether a fiber optic actually reduces the observed variability in single particle LDI mass spectral data. Initial results are presented for individual single component organic particles composed of 2,4-dihydroxybenzoic acid (2,4-DHB) analyzed using a low-power flat-top laser beam profile created by sending an ultraviolet (266 nm) DI laser through a fiber optic. Relative standard deviations of the total ion intensities for peaks in individual spectra are reduced to 31%. Single particle spectra, compared with and without laser homogenization at the same nominal laser fluence, show a marked enhancement. Specifically, the ion signal patterns of the 2,4-DHB particle spectra obtained using a homogenous LDI beam look identical to one another (i.e. only one particle type was produced with a commonly used neural network grouping algorithm), whereas without beam homogenization 25 different particle types (based on ion intensity patterns) were obtained. Future publications will explore more particle types and matrices but the initial results described herein are quite encouraging.     

Energy distributions in multiple photon absorption experiments

Photofragmentation experiments on molecules and clusters often involve multiple photon absorption. The distributions of the absorbed number of photons are frequently approximated by Poisson distributions. For realistic laser beam profiles, this approximation fails seriously due to the spatial variation of the mean number of absorbed photons across the laser beam. We calculate the distribution of absorbed energy for various laser and molecular-beam parameters. For a Gaussian laser beam, the spatially averaged distributions have a power-law behavior for low energy with a cutoff at an energy which is proportional to fluence. The power varies between -1 for an almost parallel laser beam and -5/2 for a divergent beam (on the scale of the molecular beam). We show that the experimental abundance spectra of fullerenes and small carbon clusters can be used to reconstruct the distribution of internal energy in the excited C60 molecule prior to fragmentation and find good agreement with the calculated curves.