Femtosecond electron pulse compression by using the time focusing technique in ultrafast electron diffraction

We present a new model of an electron gun for generating subrelativistic femtosecond (fs) electron pulses. The basic idea is to utilize a dc acceleration stage combined with a time focusing region, the time focusing electrode generates an electron energy chirp for bunching at the target. Without considering the space charge effects, simulations of the electron gun were carried out under the conditions of different dc voltages and various slopes of the voltage added on the time focusing electrode. Tracing and simulating large numbers of photoelectrons through Monte-Carlo and finite difference methods, the electron pulses with 1 ps can be compressed to 55 fs, which will allow significant advances in the field of ultrafast diagnosis.     

基于α-肉桂酰环乙烯酮二硫缩酮的一类新型D-A有机发光材料的理论

用密度泛函理论B3LYP方法对四种新型D-π-A分子(PKD,NKD,TKD和CKD)进行基态几何构型全优化,计算分子的电离势IP和电子亲和势EA等相关能量。用含时密度泛函(TDDFT)方法计算吸收光谱,用单组态相互作用方法(CIS)优化四种化合物分子的S₁激发态结构,分析其能量与发射光谱的关系。根据化合物组成的不同恰当地选择泛函计算分子的发射光谱,并与实验结果对照表明,计算结果比较可靠。     

Superposition rules, lie theorem, and partial differential equations

A rigorous geometric proof of the Lie theorem on nonlinear superposition rules for solutions of nonautonomous ordinary differential equations is given filling in all the gaps present in the existing literature. The proof is based on an alternative but equivalent definition of a superposition rule: it is considered as a foliation with some suitable properties. The problem of uniqueness of the superposition function is solved, the key point being the codimension of the foliation constructed from the given Lie algebra of vector fields. Finally, as a more convincing argument supporting the use of this alternative definition of superposition rule, it is shown that this definition allows an immediate generalization of the Lie theorem for the case of systems of partial differential equations.     

Collision site effect on the radiation dynamics of cytosine induced by proton

By combing the time-dependent density functional calculations for electrons with molecular dynamics simulations for ions (TDDFT-MD) nonadiabatically in real time, we investigate the microscopic mechanism of collisions between cytosine and low-energy protons with incident energy ranging from 150 eV to 1000 eV. To explore the effects of the collision site and the proton incident energy on irradiation processes of cytosine, two collision sites are specially considered, which are N and O both acting as the proton receptors when forming hydrogen bonds with guanine. Not only the energy loss and the scattering angle of the projectile but also the electronic and ionic degrees of freedom of the target are identified. It is found that the energy loss of proton increases linearly with the increase of the incident energy in both situations, which are 14.2% and 21.1% of the incident energy respectively. However, the scattering angles show different behaviors in these two situations when the incident kinetic energy increases. When proton collides with O, the scattering angle of proton is larger and the energy lost is more, while proton captures less electrons from O. The calculated fragment mass distribution shows the high counts of the fragment mass of 1, implying the production of H⁺ fragment ion from cytosine even for proton with the incident energy lower than keV. Furthermore, the calculated results show that N on cytosine is easier to be combined with low-energy protons to form NH bonds than O.     

具有剩余寿命且排队空间有限的M/G/1排队模型非负解的存在唯一性

研究了以剩余寿命作为增补变量,排队空间有限的M/G/1排队模型,利用泛函分析中线性算子半群的积分半群理论讨论了该模型的瞬态解的存在唯一性问题。     

An Exact Solution for an M(t)/M(t)/1 Queue with Time-Dependent Arrivals and Service

We consider an M/M/1 queue with a time dependent arrival rate (t) and service rate (t). For a special form of the traffic intensity, we obtain an exact, explicit expression for the probability p _n (t) that there are n customers at time t. If the service rate is constant (=), this corresponds to (t)=(t)/=(b–at)^–2. We also discuss the heavy traffic diffusion approximation to this model. We evaluate our results numerically.     

Robust tracking for MIMO nonlinear time-dependent mismatched uncertain systems: non-adaptive versus adaptive control

This paper considers the problem of robust output-tracking controlfor multi-input multi-output (MIMO) nonlinear systems in thepresence of mismatched time-dependent uncertainties. It firstgeneralizes the stable combined-variable perturbation method(SCVPM) which was proposed by Li et al. (1996) to derive a newrobust controller and its adaptive version for MIMO systemsto track a desired trajectory. It is shown that both controllersnot only stabilize the closed-loop systems but also guaranteethat the tracking errors remain in an O() neighbourhood of theorgin, where is a small design parameter of the controller.Moreover, the adaptive robust controller is only based on thenominal system, and no a priori data on the uncertainties areneeded. Therefore, it is more feasibly implemented than thenon-adaptive controller.     

A weak formulation of boundary integral equations for time dependent parabolic problems

A weak formulation for ‘direct’ boundary methods for time dependent parabolic problems, deduced from distribution theory, is presented. The present approach seems particularly valuable when dealing with problems with non-integrable singularities and solutions with an exponential growth. Numerical examples are also reported for plane diffusion.