关于Hirota-Satsuma系统初值问题的局部和整体适定性

本文利用ＫＤＶ方程所对应的线性方程解所具有的光滑效应及压缩映像原理,得到了Ｈｉｒｏｔａ－Ｓａｔｓｕｍａ系统初值问题的局部和整体适定性结果．     

Overlapping B3Π0u ← X1Σ g/+ and 1Π1u ← X1Σ g/+ non-radiative characteristic of Br2 vapour in the wavelength region 505–541 nm

The vibronic vapour phase photoacoustic spectrum of Br₂ in the wavelength region 505–541 nm (19796–18480 cm⁻¹) has been recorded using microphone as well as pump-probe method. Discrete vibronic bands superimposed on a monotonically increasing continuum background towards the dissociation limit results from the overlapping B ³Π _0u ^/+ ← X ¹Σ _g ^/+ and ¹Π_1u ← X ¹Σ _g ^/+ electronic transitions. Vibronic bands originating from υ″=0 have been used to estimate the relative rate of non-radiative relaxation as a function of the excited state B ³Π_0u vibrational quantum number υ′. A comparison with the optical absorption spectroscopy of Br₂ leads to the identification of three broad spectral regions between 505 and 541 nm (19796 and 18480 cm⁻¹) on the basis of different non-radiative relaxation processes.     

The sea-wave elevation and multistability in a non-autonomous nonlinear Itô’s stochastic differential equation for the rolling angle of a ship

Prediction of the rolling behavior of ships in irregular sea remains one of the most difficult problems in ship engineering. The present work facilitates solution of this problem by derivation of a model which is meaningful from the subject-specific point of view and can efficiently be analyzed with the path-integration method. The model is a single Itô’s stochastic differential equation for the rolling angle of a ship located at a fixed spatial point. The equation appears to be of the third order and nonlinear. It takes into account the elevation of stochastic traveling sea waves. The stochasticity of the elevation is allowed for by stationary stochastic velocity of the waves. The works also notes the picture for the multistability of the derived model. Improvement of capabilities of the methods for multistable nonlinear systems is included in directions for future research.     

Characterization of thermally sensitive interactions in aqueous mixtures of hydrophobically modified hydroxyethylcellulose and cyclodextrins

Effects of beta-cyclodextrin (beta-CD) or hydroxypropyl-beta-cyclodextrin (HP-beta-CD) addition and temperature on thermodynamic, rheological, and structural features of semidilute solutions of hydroxyethylcellulose (HEC) and its hydrophobically modified analogue (HM-HEC) are reported. Differential scanning calorimetric (DSC) measurements revealed a thermally induced crystal melting transition of beta-CD at high concentrations in solutions of HEC and HM-HEC. No transition with HP-beta-CD was observed in aqueous solution. Viscosity results indicated that at a cosolute concentration of 2 mm, the beta-CD units are threaded onto hydrophobic tails of HM-HEC (C16 groups) to form columnar structures. This arrangement is more effective in the encapsulation of the hydrophobic chains than the monomer hydrophobic deactivation accomplished by the HP-beta-CD units. At cosolute concentrations above 8 mm, no further decoupling of the hydrophobic interactions occurs for any of the cosolutes. Small-angle neutron scattering (SANS) experiments on HM-HEC/beta-CD mixtures suggest that the large-scale association structures in HM-HEC/D(2)O solutions are reduced upon addition of beta-CD, and an interesting temperature effect is observed at 2 mm beta-CD addition. At high beta-CD concentrations and low temperatures, the formation of large beta-CD clusters or crystallites generates cross-links in the HEC and HM-HEC networks, resulting in a viscosity enhancement of several orders of magnitude. This strong temperature effect is not reflected in the structural features probed by SANS.     

On numerical density approximations of solutions of SDEs with unbounded coefficients

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in application oriented fields. In this paper we provide a rigorous analysis of the method that covers systems of equations with unbounded coefficients. Working in a natural space for densities, L ¹, we obtain stability, consistency, and new convergence results for the method, new well-posedness and semigroup generation results for the related Fokker-Planck-Kolmogorov equation, and a new and rigorous connection to the corresponding probability density functions for both the approximate and the exact problems. To prove the results we combine semigroup and PDE arguments in a new way that should be of independent interest.     

Microemulsion electrokinetic chromatography in suppressed electroosmotic flow environment. Separation of fat-soluble vitamins

Microemulsion electrokinetic chromatography (MEEKC) was carried out in a pH 2.5 phosphate buffer to effectively suppress the electroosmotic flow (EOF). With 66.6% (w/w) 25 mM phosphate buffer pH 2.5, 20.0% (w/w) 2-propanol, 6.6% (w/w) 1-butanol, 6.0% (w/w) sodium lauryl sulphate (SDS), and 0.8% (w/w) n-octane as the separation medium, the fat-soluble vitamins A palmitate, E acetate, and D3 were baseline separated within 11 min. With strongly suppressed EOF, the polarity of the separation voltage was reversed (positive electrode at the outlet); the n-octane micro droplets surrounded by negatively charged SDS molecules migrated towards the detector. The aqueous part of the microemulsion was modified with 20% (w/w) 2-propanol to improve partition between the n-octane phase and the surrounding aqueous medium. The fat-soluble vitamins were separated in order of decreasing hydrophobicity with a high migration time stability (repeatable within 0.1% RSD). Excellent accuracy and precision were obtained when the system was applied for the determination of vitamin E acetate in commercial vitamin tablets; quantitative data corresponded to 97.0% of label claim, intra-day results varied within 1.72% RSD (n=6), and inter-day results varied within 3.22% RSD (n=5).     

Response statistics of van der Pol oscillators excited by white noise

The joint probability density function of the state space vector of a white noise exoited van der Pol oscillator satisfics a Fokker-Planck-Kolmogorov (FPK) equation. The paper describes a numerical procedure for solving the transient FPK equation based on the path integral solution (PIS) technique. It is shown that by combining the PIS with a cubic B-spline interpolation method, numerical solution algorithms can be implemented giving solutions of the FPK equation that can be made accurate down to very low probability levels. The method is illustrated by application to two specific examples of a van der Pol oscillator.     

Nonlinear vibrations of a rotating shaft with broadband random variations of internal damping

A simple Jeffcott rotor is considered with broadband temporal random variations of internal damping which are described using the theory of Markov processes. Transverse response of the rotor with stiffening nonlinearity either in external damping or in restoring force is studied by stochastic averaging method. This method reduces the problems to stochastic differential equations (SDEs) for which analytical solutions are obtained for the Fokker–Planck–Kolmogorov (FPK) equations for stationary probability density functions (PDFs) of the squared whirl radius of the shaft. These PDFs do exist beyond the dynamic instability threshold and they correspond to forward whirl of the rotor. At rotation speeds just slightly above the instability threshold, the response PDF has integrable singularity at zero which corresponds to intermittency in the response.     

Use of Cartesian Rotation Vectors in Brownian Dynamics Algorithms: Theory and Simulation Results

Summary: We have shown that the components of Cartesian rotation vectors can be used successfully as generalized coordinates describing angular orientation in Brownian dynamics simulations of non‐spherical nanoparticles. For this particular choice of generalized coordinates, we rigorously derived the conformation‐space diffusion equations from kinetic theory for both free nanoparticles and nanoparticles interconnected by springs or holonomic constraints into polymer chains. The equivalent stochastic differential equations were used as a foundation for the Brownian dynamics algorithms. These new algorithms contain singularities only for points in the conformation‐space where both the probability density and its first coordinate derivative equal zero (weak singularities). In addition, the coordinate values after a single Brownian dynamics time step are throughout the conformation‐space equal to the old coordinate values plus the respective increments. For some parts of the conformation‐space these features represent a major improvement compared to the situation when Eulerian angles describe rotational dynamics. The presented simulation results of the equilibrium probability density for free nanoparticles are in perfect agreement with the results from kinetic theory.

Simulation of p^(eq)(Φ) for free nanoparticles.     

Stochastic synchronization of rotating parametric pendulums

In this paper synchronization of two pendulums mounted on a mutual elastic single degree-of-freedom base is examined. The response of the pendulums is considered when their base is externally excited by a random phase sinusoidal force, thus leading to stochastic parametric excitation of the pendulums. The target is for the pendulums to establish and preserve rotary response since this study is motivated by a recently proposed ocean wave energy extraction concept where the heaving motion of waves excites a pendulum’s hinge point. Since the wave bobbing motion is random the system’s excitation is modelled as a narrow-band stochastic process. Mounting two pendulums on the same elastic base creates a coupling between them through their interaction with the base, providing a path for energy exchange between them. The dynamic response of the pendulums is numerically investigated with respect to establishment of rotations as well as identification of synchronization with the pendulums characteristics spanning along non-identical parameters.