JUMP AND BIFURCATION OF DUFFING OSCILLATOR UNDER NARROW-BAND EXCITATION

The jump and bifurcation of Duffing oscillator with hardening spring subject to narrow-band random excitation are systematically and comprehensively examined. It is shown that, in a certain domain of the space of the oscillator and excitation parameters, there are two types of more probable motions in the stationary response of the Duffing oscillator and jumps may occur. The jump is a transition of the response from one more probable motion to another or vise versa. Outside the domain the stationary response is either nearly Gaussian or like a diffused limit cycle. As the parameters change across the boundary of the domain the qualitative behavior of the stationary response changes and it is a special kind of bifurcation. It is also shown that, for a set of specified parameters, the statistics are unique and they are independent of initial condition. It is pointed out that some previous results and interpretations on this problem are incorrect.

Modeling of Work of Filling Granular Filter with Active Cooling

The solid propellant gas generators having high gas capacity are widely used for fast pressurization of elastic shells of saving devices of different applications. A typical example of such devices are safety system of automobile (airbags). After collision of an automobile with an obstacle the combustion products of gas generator fill the shell during 60 – 100 milliseconds. However the temperature of combustion products even of “low-temperature” fuel compositions of gas generators appears not below 1500К and to reduce of its it is necessary to apply a various types of porous and filling granular filters. There are passive and active granular filters. The passive filter can cool of combustion products as a result of absorption of heat only. The active cooling is evaporation of the granule material and in this case takes a place more intensive cooling of combustion products in the filter. The numerical modeling of cooling process of high- temperature combustion products at their movement in bulk of granular filter of active cooling is investigated. As the material of granules was used the carbonate of magnesium. At its heating takes a place process of gasification and formation of a porous slag shell which sublimates at higher temperature. The physical model of such spherical granule can be presented as the central part consisting of the carbonate magnesium surrounded with the porous slag spherical shell through which gaseous products of gasification of the central part are filtered. The problem of distribution of heat in each granule is Stefan problem when at the given temperature on the surface of sphere there is the front of gasification moving inside of the bulk of material. It is assumed that combustion products are the perfect gas moving in the filter. The upwind difference scheme of the second order of the accuracy with TVD properties was applied to calculation of the movement of gas. The results of calculations at various values of key parameters of the active and passive filters allow to draw a conclusion about enough high efficiency of active cooling filters.

Comparative Analysis for Different Mathematical Models in Electron Optics

The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the BEM （boundary element method） for the field evaluation, and 3rd order aberration expansion for the trajectory analysis. The first version of such computer code ＂OPTICS-3＂ and some results of numerical simulations with this code were presented.

Decomposition Method for Complex 3D Problems in Electron Optics

The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM （Finite Difference Method） and FEM （Finite Element Method） mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM （Boundary Element Method） based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU （Central Processor Unit） desktop computer. New algorithm is iterative one, but exponential convergence for the Schwatlz＇s algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code ＂POISSON-3＂.

空间数据仓库的安全控制

安全在任何数据库访问和数据传输应用里都是一个重要的问题,尤其是在Internet环境下。基于Web的地理空间数据的安全问题和地理空间数据这个整体一样。

Quantitative tracking of trans-synaptic nose-to-brain transport of nanoparticles and its modulation by odor,aging,and Parkinson’s disease

Nanoparticles(NPs)can be transported via the nose-to-brain(N_(2)B)route.Nonetheless,quantitative data on their spatiotemporal dynamics and regulation of the N_(2)B transport are largely lacking.We surveyed metal oxide/hydroxide NPs as magnetic resonance imaging(MRI)contrasts for quantitative N_(2)B tracking.NPs containing divalent transition metals were the only ones capable of N_(2)B transmission.Using T1-weighted(T1W)MRI,we showed that Mn_(3)O_(4)-NPs were readily engulfed by olfactory receptor neurons(ORNs)without disrupting olfactory sensing,we mapped their N_(2)B trajectory.Within neurons,the Mn_(3)O_(4)-NPs were localized to the cytosol,mitochondria,vesicles,moved at mixed fast and slow axonal transport velocities intraand extra-vesicularly through ORNs.The NPs’axonal transport is dependent on neuronal activity and microtubule integrity.The Mn_(3)O_(4)-NPs were trans-synaptically transmitted through at least four synapses across the olfactory tract.Trans-synaptic transmission of the NPs was dependent on N-type Ca^(2+)channels and NMDA receptors but blocked by GABAB receptor activation.A five-parameter Weibull signal increase/decrease model fitted to the T1W MRI data allowed for estimating kinetic parameters of Mn_(3)O_(4)-NP accumulation/elimination.Absolute and relative accumulation rates,but not elimination,correlated negatively with the number of synapses from ORNs,indicating a coupling of the NPs’N_(2)B transport with spontaneous neuronal activity.Accordingly,olfactory stimuli(2,5-dimethylpyrazine and acetophenone)significantly modulated and rerouted the Mn_(3)O_(4)-NP N_(2)B transport odor specifically.Finally,the NPs’trans-synaptic transmission was impaired by aging and the onset of Parkinson’s disease.These data suggest new approaches to diagnostics,functional neuroimaging,controlling N_(2)B drug delivery.

The effect of self-focusing on laser space-debris cleaning

A ground-based laser system for space-debris cleaning will use powerful laser pulses that can self-focus while propagating through the atmosphere.We demonstrate that for the relevant laser parameters,this self-focusing can noticeably decrease the laser intensity on the target.We show that the detrimental effect can be,to a great extent,compensated for by applying the optimal initial beam defocusing.The effect of laser elevation on the system performance is discussed.

A NUMERICAL EXPERIMENT OF CUMULUS DEVELOPMENT

From analyses of observation data it is found that stratification is usually unstable in the moist adiabatic process when cumulus develops vigorously. This shows that water vapour is an important factor for the development of cumulus. Therefore, it can be seen that the condensation of water vapour in cumulus is not only the result of develop-

Dispersive Shallow Water Wave Modelling.Part II:Numerical Simulation on a Globally Flat Space

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.

Dispersive Shallow Water Wave Modelling.Part I:Model Derivation on a Globally Flat Space

In this paperwe reviewthe history and current state-of-the-art in modelling of long nonlinear dispersive waves.For the sake of conciseness of this review we omit the unidirectional models and focus especially on some classical and improved BOUSSINESQ-type and SERRE-GREEN-NAGHDI equations.Finally,we propose also a unified modelling framework which incorporates several well-known and some less known dispersive wave models.The present manuscript is the first part of a series of two papers.The second part will be devoted to the numerical discretization of a practically important model on moving adaptive grids.