Yun-Bo Duan

Nonlinear stochastic models of neurons activities

Abstract In this paper we propose a new nonlinear evolution model of neuronal activities to obtain the average number density, which is used to describe neurocommunication among populations of neurons. The average number density is a function of the amplitude, phase and time. The number density of the diffusion process of neurocommunication is given for the active states of two populations of coupled oscillators under perturbation by both periodic stimulation and random noise. It is emphasized that the oscillatory coupling strengths and initial conditions within and between two populations of neurons are very important for investigating the mechanism of the transmission process. Particularly, the model presented in this paper can be used to describe the evolution process of the amplitudes in activities of multiple interactive populations of neurons.

Correlation problems and a correlation-free torsion-rotation Hamiltonian for a molecule with an internal rotor

To develop a correlation-free reduced form of torsion-rotation Hamiltonian that is suitable for analyzing observed spectra for methanol and its isotopic species, the origin of various classes of correlation problems often encountered in fitting the molecular constants to experimental data are analyzed for a molecule with an internal rotation. It is shown that the correlation problems can be completely eliminated by considering either the data set or the reduction of the Hamiltonian together with practical considerations, where an appropriate definition of order of magnitude plays an important role. For a molecule with C3v(M) symmetry such as methanol and its isotopic species, it is found that some terms which are included in the traditional or a reduced Hamiltonian given so far should not be used simultaneously. For example, the traditional terms k5Pa2(1−cos 3γ) and k6Pa{Pγ,1−cos 3γ} should not be used simultaneously as adjustable ones and one of three traditional terms k6Pa{Pγ,1−cos 3γ}, k7{Pγ2,1−cos 3γ}...

The calculation of molecular parameters for a molecule with an internal rotor

A derivation for the formulas to calculate centrifugal distortion constants, based on a recent formulation [Duan and Takagi, Phys. Lett. A (1995)] of centrifugal distortion effects for a molecule containing a threefold symmetric internal rotor, is presented. Some constants which are independent of the barrier derivatives, especially the constants representing interactions between torsion and rotation, are given in terms of molecular structural parameters and force constants. These calculated constants are helpful in the reduction of the Hamiltonian and in the analysis of observed transitions. The derived formulas are applied to numerical calculations of the centrifugal distortion constants of methanol. It is shown that most of the calculated constants are in good agreement with those obtained from the fitting to experimental data.

Observation and analysis of high-J o1−e1 inter-state transitions in CH2DOH

We report the observation and assignments of several series of transitions in CH2DOH, including a new and intense series of Q-branch c-type transitions between the e1 and o1 torsional substates through high values of the rotational quantum number J. Other transitions assigned are c-type R-branch and P-branch transitions between these two substates and a-type lines within the e1 and o1 substates. The assignments were facilitated by initial analysis of the strong Q-branch series, as recorded by the fast scan submillimeter spectroscopy technique (FASSST). The assigned lines of CH2DOH include the first inter-state transitions in the sub-millimeter-wave region and the first to possess high J-values. The completeness of the data generated by FASSST and the success of a simple power series analysis suggest that many parts of the spectrum of CH2DOH may be far more tractable than previously believed. The data should be useful in the development of a full Hamiltonian and in the assignment of astronomical emission f...

Molecular parameters for 12C and 13C-methanol isotopomers with O-16, 17, and 18

Torsion–rotational parameters have been determined for 12C and 13C-methanol isotopomers CH3OH with O-16, 17, and 18 using a recent formulation [Duan and Takagi, Phys. Lett. A 207, 203 (1995)] of the centrifugal distortion effects from potential parameters for a molecule containing a threefold symmetric internal rotor. The calculated parameters, especially the constants representing interactions between torsion and rotation, are used to interpret the relationships among the terms in reduced Hamiltonian and in the analysis of the observed torsion–rotational spectrum. Molecular parameters are calculated from potential energy surfaces for methanol to check the quality of these surfaces. The calculated parameters are compared with parameters obtained from global fits to large experimental data sets. The good agreement between the calculated centrifugal distortion terms and those derived from fits to spectra demonstrates that the derived formulas provide a useful tool for understanding the physical origins and ...

Quantum dynamics of methanol: Hamiltonian, representation and intensity considerations

Abstract Employing a body-fixed axis system and Jacobi coordinates, a model for the vibration–torsion–rotation Hamiltonian of the CH 3 OH molecule with large-amplitude internal motions has been derived. This Hamiltonian is expressed in terms of Jacobi coordinates and is partitioned in the form H A + H B + H int , where H A and H B are the rovibrational Hamiltonians of methyl group CH 3 and asymmetric rotor OH, and H int represents their interactions. The resulting Hamiltonian is used to carry out a pure quantum mechanical calculation for this kind of molecule or to construct the potential surface using observed data. The detailed discussion of the Hamiltonian is presented for the model with a rigid methyl group and a rigid OH, which describes five lower frequency vibrational modes and pure rotation in the molecule. We discuss the advantages of body-fixed Jacobi form of the Hamiltonian and solution strategies for practical programming. The properties of labels of the energy states, potential function and dipole moments are investigated according to the molecular symmetry group G 6 of methanol. Finally, the developed formulation is used to calculate the energy levels of CO-stretching–torsion–rotation for lower rotational excitation ( J ⩽5). Comparison of the calculated results with experimental ones is presented.

On the physical interpretation of torsion–rotational parameters for CH3OD isotopomers

Abstract Using the formulation (Phys. Lett. A 207 (1995) 203) of the centrifugal distortion effects in terms of the potential parameters for a molecule that contains a threefold symmetric internal rotor, molecular parameters have been determined for the 12 C and 13 C isotopomers of CH 3 OD with O-16, 17 and 18. The calculated parameters, especially the constants that represent interactions between torsion and rotation, are used to interpret the relationships among the terms in the reduced Hamiltonian and in the analysis of the observed torsion–rotational spectrum. Molecular parameters are calculated from several potential energy functions for methanol isotopomers to check the quality of these potentials. The dependence of torsion–rotational parameters on the mass of atom and the geometric parameters are addressed by comparisons of calculated values for various isotopomers of CH 3 OD. The parameters are compared with the parameters that were obtained from several global fits to experimental spectrum data. The good agreement between the calculated torsion–rotational parameters and those derived from the global fits demonstrates that the derived formulae provide a useful tool for understanding the physical origins of the Hamiltonian parameters and the dependence of torsion–rotational parameters on fundamental molecular parameters.

An Exploration of Dynamics of the Moving Mechanism of the Growth Cone

A stochastic, nonlinear dynamic model is proposed to explain the growth cone at the tip of a cell process, such as a growing axon or dendrite of a neuron. The model explains the outward motion of the tip as an extension of the cytoskeleton, using the actin-myosin system as a molecular motor. The kinetic energy is supplied by heat from ATP hydrolysis in the form of random motion of water molecules embedding the actin-myosin. The mechanical structure is provided by the F-actin macromolecules forming a spiral filament. The myosin heads form a stochastic distribution of small spheres. They are attached by elastic springs to the spiral rods of the myosin filaments. Under thermal agitation the system sustains oscillation, which is directed by the interaction between the myosin heads and the actin filament. As the energy of oscillation is dissipated, the actin filament is moved toward the center of the growth cone. The joint probability density of movement of the actin filament is obtained by solving a non-stationary version of the FPK equation. By incorporating a probability distribution of actin filaments provided by the geometry of the tip, the directed motion of the tip is explained.

Spectroscopic determination of fundamental molecular parameters for methanol and its isotopomers

Abstract An approach is presented, in which such fundamental molecular parameters as geometric structural parameters and potential ones are used to analyze observed spectra of a molecule with an internal rotor. As an example, geometric structural parameters, harmonic vibrational force constants, barrier heights to the internal rotation, and barrier derivatives with respect to molecular internal coordinates are determined by fitting them to observed torsion–rotational spectra for methanol and its isotopomers. By using these determined parameters, all the unreduced torsion–rotational molecular constants up to fourth order are calculated numerically.

Analysis of torsion-rotational transitions in the first three torsional states of CH3OD

Abstract In the framework of systematic analysis and fitting of transition frequencies of methanol isotopomers with a reduced torsion-rotational Hamiltonian that is obtained from the one-large-amplitude internal rotation model, 1126 Fourier transform far-infrared (FIR) transitions involving the second excited torsional level ( v t =2) have been added to the data set of Duan and McCoy [J. Mol. Spectros. 199 (2000) 302] to achieve a global fit of the observed high resolution microwave (MW), millimeter wave (MMW) and Fourier transform FIR spectra for CH 3 OD. The CH 3 OD data set contains 460 MW and MMW transitions and 3474 Fourier transform FIR transitions with v t ⩽2 and J ⩽21. The MW and MMW transitions have been fit with a root-mean-square (rms) deviation of 0.12 MHz, whereas FIR transitions have a rms deviation of 0.00026 cm −1 . These deviations are approximately equal to the experimental uncertainties, indicating that the MW, MMW and FIR spectral transitions have been fit to an accuracy approaching the experimental uncertainties and the reduced torsion-rotational Hamiltonian model is capable of accurately describing CH 3 OD energy levels up through the second excited torsional level. The success of the fit demonstrates that the increased general asymmetry in CH 3 OD can be taken care adequately by the reduced Hamiltonian model.