Control and coupling of spiral waves in excitable media

We report the complex dynamics of spiral waves observed in the ferroin-catalyzed BZ reaction. The reaction is run in an open unstirred reactor (CFUR) with the catalyst immobilized on a polysulfone membrane. The catalyst-loaded membrane is placed between two well stirred compartments which are fed with solutions of sulfuric acid/malonic acid/bromide and sulfuric acid/bromate, respectively. An electrical field perpendicular to the membrane can be applied via Pt-ring electrodes or, alternatively, via transparent electrodes made of ITO-coated glass. In the field-free case relatively simple target and spiral patterns are observed in the membrane. If an alternating electrical field is applied the spiral core drifts through the membrane. The actual trajectory of the spiral tip depends on the amplitude and frequency of the applied electrical field. If the perturbation parameters are chosen properly the wave fronts break up and new spiral cores emerge under the influence of the alternating field. Complex spatio-temporal patterns may be induced which are reminiscent of "spiral-chaos". After switching off the perturbation the system returns to its previous, "simple" behaviour. Our experimental observations are confirmed by model calculations based on the Barkley model of spiral waves. The technique of using modulated excitability to control the dynamics of spiral waves is further extended to the coupling of two spirals in two CFURs. We present numerical simulations based on two identical excitable reaction-diffusion (RD) systems which are mutually coupled. The coupling is based on the observation of an arbitrarily chosen point inside each of the RD systems: If a chemical wave passes the point of optical observation in system 1 an electric field is applied to system 2 and vice versa. Thus, a local observation made in one system is transformed in a global perturbation of the second CFUR. We report the observation of CFUR states where the two spiral waves are spatially and temporally coupled to each other.     

Stark and field-born resonances of an open square well in a static external electric field

The resonance positions, widths (inverse lifetimes), and wave functions of a square-potential well in the presence of a static electric field are calculated by using the outgoing boundary conditions. Our study concentrates on the field-born states that, unlike the well-known Stark resonances, are not associated with the field-free bound states. The effect of a lower cutoff of the static field on the field-born resonance phenomena is studied. The feasibility of experiments, where the isolated long-lived and overlapping short-lived field-born resonances can be explored, is discussed.     

Intrinsic reaction coordinate of perturbed potential energy surfaces: Construction of perturbed energy profiles

This contribution analyzes the changes in the intrinsic reaction coordinate (IRC ) and in the potential energy profiles (PEP ) caused by application of a uniform electric field evaluated using standard ab initio MO methods. Two typical organic processes have been studied, namely, the Friedel–Crafts and the Walden inversion reactions, which are modeled by suitable simple systems. The results for the Walden inversion reaction show that the IRC for the field-free and that for perturbed processes are almost coincident; in this case, using the field-free IRC to compute the perturbed energy profile is a very good approximation. On the contrary, for the Friedel–Crafts model reaction, the two IRC s differ slightly, so the energy profiles using the perturbed and the unperturbed IRC s are somewhat different. © 1993 John Wiley & Sons, Inc.     

The permanent electric dipole moment of calcium monodeuteride

The sub-Doppler laser induced fluorescence spectra of numerous branch features in the B 2Sigma+ -X 2Sigma+(0,0) band of calcium monodeuteride were recorded field-free and in the presence of a static electric field of up to 7 kV/cm. The field-free spectra were analyzed to produce an improved set of fine structure parameters for the B 2Sigma+(v=0) state. The observed electric field induced splittings and shifts were analyzed to produce permanent electric dipole moments of 2.57(3) and 2.51(3) D for B 2Sigma+(v=0) and X 2Sigma+(v=0) states, respectively. The permanent electric dipole moment for the X 2Sigma+(v=0) state of CaH is estimated to be 2.53(3) D.     

Quantum observable homotopy tracking control

This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.     

Optical Stark spectroscopy of the 2(0)(6) Ã1A'-X̃1A' band of chloro-methylene, HCCl

The laser induced fluorescence spectra of the 2(0)(6)A?(1)A(')-X?(1)A(') band of a rotationally cold (<20 K) molecular beam sample of chloro-methylene, HCCl, has been recorded, field-free and in the presence of a static electric field. The field-free spectrum has been analyzed to produce an improved set of spectroscopic parameters for the A?(1)A(') (060) vibronic state. The magnitude of the a-component of the permanent electric dipole moment, μ(a), for the X?(1)A(') (000) vibronic state has been determined to be 0.501(1) D from the analysis of the observed electric field induced shifts. Comparisons with theoretical predictions and flouro-methylene, HCF, are presented.     

Space-time contours to treat intense field-dressed molecular states. II. Applications

This second article in the two back-to-back articles presents a numerical application to support and strengthen two theoretical findings extensively discussed in the previous article (article I). In I, we found that introducing the space-time contours enables to distinguish between N, the number of nuclear Schrodinger equations to be solved, and L, the number of field-free states that become populated by the external field (in the ordinary, perturbative approaches this distinction is not apparent). In the numerical study we show, employing the electronic transition probability matrix P(s,t) [which closely is related to the transformation matrix omega(s,t)--see Eqs. (21) and (25) in I], that the N=L case is rare and in most cases we have N相似文献   

Space-time contours to treat intense field-dressed molecular states. I. Theory

A molecular system exposed to an intense external field is considered. The strength of the field is measured by the number L of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced space-time contours [R. Baer, et al., J. Chem. Phys. 119, 6998 (2003)], to form N coupled Schrodinger equations where N相似文献   

Coherent control of wavepacket dynamics by locally designed external field

A new coherent control theory for manipulating quantum mechanical dynamics is proposed. The control field is designed locally (in time domain) so as to realize monotonous increase of the overlap between currently evolving wavefunction and the time-dependent target state, which will eventually reach to a desired quantum state under field-free condition. The present theory is applied to one-dimensional harmonic oscillator and Morse potential systems.     

A molecular orbital study of the effect of an external electric field on methanol

We report the results of INDO-MO calculations to investigate the influence of an external electric field on methanol. We predict that during a field-ionisation experiment, ionisation will occur from a quite different molecular geometry than the field-free olie.     

Stacked-ring electrostatic ion guide

In 1969 Bahr, Gerlich, and Teloy introduced an rf device that consisted of a stack of ring electrodes, with charge sign alternation between neighboring rings, to store or transport ions. Here we propose to operate such a device with electrostatic potentials rather than rf potentials: ions that move axially along the center of the guide are thereby subjected to an oscillating electrical potential similar to the sinusoidal rf potential in familiar rf-only multipole ion guides. The oscillating potential of the stacked-ring static ion guide focuses ions by exerting a field gradient force on the ions so as to push ions toward the central axis where the field is weakest. The stacked-ring ion guide produces an effectively static “pseudopotential” that is much steeper at the edge (potential varies as e ^r) compared to a quadrupole or octupole guide (for which the potential varies as r ² or r ⁶, where r is radial position) and that is much flatter near the center of the guide (for potentially higher ion flux). Advantages of the new ion guide include static rather than rf potential, low electrical noise, a large field-free region near the central axis of the guide, and simple mechanical construction. A disadvantage of the stacked-ring ion guide is that high ion axial kinetic energy is required; ions with axial kinetic energy that is too low may be trapped in the shallow pseudopotential well between adjacent ring electrodes.     

A microfluidic device for performing pressure-driven separations

Microchannels in microfluidic devices are frequently chemically modified to introduce specific functional elements or operational modalities. In this work, we describe a miniaturized hydraulic pump created by coating selective channels in a glass microfluidic manifold with a polyelectrolyte multilayer (PEM) that alters the surface charge of the substrate. Pressure-driven flow is generated due to a mismatch in the electroosmotic flow (EOF) rates induced upon the application of an electric field to a tee channel junction that has one arm coated with a positively charged PEM and the other arm left uncoated in its native state. In this design, the channels that generate the hydraulic pressure are interconnected via the third arm of the tee to a field-free analysis channel for performing pressure-driven separations. We have also shown that modifications in the cross-sectional area of the channels in the pumping unit can enhance the hydrodynamic flow through the separation section of the manifold. The integrated device has been demonstrated by separating Coumarin dyes in the field-free analysis channel using open-channel liquid chromatography under pressure-driven flow conditions.     

Monte-Carlo studies of trigger self-oscillations in a bimolecular heterogeneous catalytic reaction

Dynamics of processes on metal surfaces and conditions for rate oscillations taking into account reconstruction of the catalyst are investigated using the Monte-Carlo method for a catalytic reaction following the Langmuir-Hinshelwood mechanism. Different regions of the oscillations were found, particularly the region where the oscillations are governed by the formation of a steady compact cluster which controls the frequency and amplitude of oscillations.     

Solution behavior of random copolymers of styrene with sodium-2-acrylamido-2-methylpropane sulfonate

The nonaqueous solution behavior of random copolymers of styrene (ST) with sodium-2-acrylamido-2-methylpropane sulfonate (Na-AMPS) [poly(ST-Na-AMPS)] has been investigated using the transient electric birefringence (TEB) technique. The copolymers with varying high sulfonate contents (about 30–70 mol%), bridging the gap between conventional ionomers and classical polyelectrolytes, were dissolved in the solvent methylformamide (MFA) with a high permittivity ? of ca. 190. The solutions showed a negative birefringence at electric field strength E of the order of kV/cm. A typical Kerr effect was observed at low polymer concentrations C of ca. 10^?3g/mL and electric field strengths of the order of kV/cm. However, the detailed, TEB studies demonstrated different behavior at two concentration regimes in dilute solution. At a low concentration regime (e.g., C ≤ 1 × 10^?3g/mL for the copolymer with a 66.7 mol % sulfonate content) where the reduced viscosity exhibited a pronounced polyelectrolyte effect, the birefringence signal pattern showed a maximum before reaching a steady value. Additionally, during the rise at an applied electric field strength beyond a threshold value, it was observed that the nonexponential field-free decay was slower than the single exponential field-induced rise. The observed anomalous behavior was similar to those of a polyelectrolyte [sodium poly (styrene sulfonate)] in aqueous solution and might be attributed to the perturbation of the molecular shape by the applied electric field. At the higher concentration regime (e.g., C ≥ 4 × 10^?3g/mL for the same copolymer with a 66.7 mol % sulfonate content) where the polyelectrolyte effects started to diminish as indicated by the viscosity study, the birefringence shape showed no variation with an increased electric field strength and the field-free decay turned out to be faster than the single exponential rise. The dissociation of ionic aggregates was tentatively interpreted to be responsible for this observation. It seems that by simply varying the polymer concentration, poly (ST-Na-AMPS) could behave either as a polyelectrolyte or as an ionomer in a single polar organic solvent.     

The Effect of an Electric Field on Reaction Fronts in Autocatalytic Systems

The effects of applying a constant electric field E to an ionic autocatalytic reaction with a general power p (p≥1) are discussed through a consideration of the equations for the corresponding travelling waves. It is shown that, when the ratio of diffusion coefficients D of autocatalyst and substrate is less than some value D₀ (which depends on p), the effect of a negative electric field is to increase the wave speed of the reaction front over its field-free value. This is in contrast to previous results for cubic autocatalysis (p=2) [J.H. Merkin and H. Ševčíková. J. Math. Chem. 25 (1999) 111.] for D>D₀, where the effect is to decrease the wave speed. This feature, seen in the numerical solutions of the travelling wave equations, is confirmed by an expansion for small E and in an asymptotic analysis for p large     

Applications of charge stripping/charge exchange spectra of organic ions

The application of a new technique which involves the combination of charge stripping and charge exchange processes has been investigated. Ions are charge-stripped in the second field-free region of a triple-sector mass spectrometer (BEE geometry), and then subjected to a charge exchange reaction in the third field-free region. The resulting charge stripping/charge exchange (CS/CE) spectrum is free from interference, which is otherwise common in charge stripping spectra. Comparisons between charge stripping and CS/CE spectra are made in cases where both kinds of spectra are obtainable. In order to assess the applicability of this new technique to studies of isomeric ion structures, species for which charge stripping spectra have previously been unobtainable have been chosen. CS/CE spectra of [C₆H₆]⁺˙, [C₆H₅]⁺, [C₈H₁₀]⁺˙ and [C₇H₇O]⁺ ions from a variety of precursors are recorded: in most cases, sufficient differences are observed to permit distinction between isomeric structures (or mixtures of structures). Previous studies which have shown that stable doubly charged molecular ions of ethane cannot be formed by the charge stripping technique are confirmed from its CS/CE spectrum.     

Classical Dynamics of H<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> in an Intense Laser Field by Using the Symplectic Method

The classical dynamics of 1D H₂⁺ in an intense field are discussed. The initial conditions are chosen at random in the field-free case, and then the Hamiltonian canonical equations of H₂⁺ system in the intense laser field are solved numerically by mean of the symplectic method under these initial conditions. The probabilities of survival, dissociation, ionization, and Coulomb explosion of H₂⁺ system in the intense laser field are obtained for different laser intensity based on the classical theory.     

Modeling the influence of a laser pulse on the potential energy surface in optimal molecular control theory

Understanding and modeling the interaction between light and matter is essential to the theory of optical molecular control. While the effect of the electric field on a molecule's electronic structure is often not included in control theory, it can be modeled in an optimal control algorithm by a set or toolkit of potential energy surfaces indexed by discrete values of the electric field strength where the surfaces are generated by Born-Oppenheimer electronic structure calculations that directly include the electric field. Using a new optimal control algorithm with a trigonometric mapping to limit the maximum field strength explicitly, we apply the surface-toolkit method to control the hydrogen fluoride molecule. Potential energy surfaces in the presence and absence of the electric field are created with two-electron reduced-density-matrix techniques. The population dynamics show that adjusting for changes in the electronic structure of the molecule beyond the static dipole approximation can be significant for designing a field that drives a realistic quantum system to its target observable.     

Imaging ultrafast dynamics of molecules with laser-induced electron diffraction

We introduce a laser-induced electron diffraction method (LIED) for imaging ultrafast dynamics of small molecules with femtosecond mid-infrared lasers. When molecules are placed in an intense laser field, both low- and high-energy photoelectrons are generated. According to quantitative rescattering (QRS) theory, high-energy electrons are produced by a rescattering process where electrons born at the early phase of the laser pulse are driven back to rescatter with the parent ion. From the high-energy electron momentum spectra, field-free elastic electron-ion scattering differential cross sections (DCS), or diffraction images, can be extracted. With mid-infrared lasers as the driving pulses, it is further shown that the DCS can be used to extract atomic positions in a molecule with sub-angstrom spatial resolution, in close analogy to the standard electron diffraction method. Since infrared lasers with pulse duration of a few to several tens of femtoseconds are already available, LIED can be used for imaging dynamics of molecules with sub-angstrom spatial and a few-femtosecond temporal resolution. The first experiment with LIED has shown that the bond length of oxygen molecules shortens by 0.1 ? in five femtoseconds after single ionization. The principle behind LIED and its future outlook as a tool for dynamic imaging of molecules are presented.     

Efficient vector potential method for calculating electronic and nuclear response of infinite periodic systems to finite electric fields

The response of periodic systems to external electric fields is a challenging theoretical problem. The authors show how the vector potential approach yields a numerically efficient treatment of the combined electronic and nuclear response to a finite static field. Their method is based on a self-consistent reformulation of the charge flow term in the single particle Hamiltonian. Careful numerical implementation yields a treatment whose computational needs are only marginally larger than those of a conventional field-free calculation. To prove the method exemplary polymer calculations are done for a model Hamiltonian. The latter contains all essential elements of an ab initio Kohn-Sham or Hartree-Fock Hamiltonian but allows for extensive testing. The extension to three-dimensional systems is described.