The diagrammatic structure of deep inelastic scattering in asymptotically free theories

We investigate the structure of the leading diagrams in QCD. The diagrams of a simple scalar gluon model form the basis of a generalisation to the more complicated vector gluon theory. It is found that a certain set of a generalised ladder diagrams gives the standard QCD result for the non-singlet structure function in the limit x → 1. A simple brems-strahlung model is presented which forms a useful link between QCD field theory and more intuitive parton formulations. The value of a diagrammatic treatment is that it provides an accessible approach to the discussion of other processes such as the Drell-Yan mechanism for heavy muon pair production.     

Two-dimensional analysis of natural frequencies and mode shapes of a wide beam: Application to the determination of mechanical characteristics of viscoelastic materials

The theory of plane elastodynamics is used to provide a simple method for calculating the natural frequencies and the normal mode shapes of a wide rectangular beam. The boundary conditions at both ends are prescribed in a mean-value sense. It is shown that the elementary (vibrating string) beam theory turns out to be an approximation of the theoretical model; the results obtained agree with those given by the Love theory. The method enables one to predict all frequency branches in terms of the width-to-length ratio, by comparatively simple calculations, in contrast to the situation when sufficiently elaborate one-dimensional theories are used. A second application is the determination of the complex Young's modulus and Poisson's ratio for viscoelastic materials.     

A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics

In structural dynamics, a predictive model is constructed by developing a mathematical-mechanical model of a designed system in order to predict the response of the real system which is the manufactured system realized from the designed system. The mathematical-mechanical modelling process of the designed system introduces two fundamental types of uncertainties: the data uncertainties and the model uncertainties. Uncertainties have to be taken into account for improving the predictability of the model. Model uncertainties cannot be modelled by using the usual parametric probabilistic approach. Recently, a general non-parametric probabilistic approach of model uncertainties for dynamical systems has been proposed using the random matrix theory. This paper gives a comprehensive overview of this approach in developing its foundations in simple terms and in illustrating all the concepts and the tools introduced in the general theory, by using a simple example. This paper deals with (1) notions of designed systems, real systems, mean models as predictive models, errors and uncertainties; (2) the definition of a simple example in linear elastodynamics; (3) a comprehensive overview of the non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics; (4) a summary of the random matrix ensembles which are necessary for the non-parametric modelling of random uncertainties; (5) the estimation of the dispersion parameters of the non-parametric probabilistic model using experimental data; (6) the method to solve the stochastic equation of the dynamical system with non-parametric probabilistic model of random uncertainties; (7) a numerical simulation and the validation for the simple example.     

A model with superconducting solution in quantum field theory

By considering a theory based on a simple model the mathematical possibilities are analysed when the same energy operator may have in quantum theory two (approximatively) orthogonal ground states and eigenfunction systems. The consequences for the elementary particle physics are discussed.

     

量子场论方法在电子与分子碰撞中的应用

这是一种利用量子场论所进行的探究性的研究方法,在文章中,我们设 计了一种新的较为简单的电子-原子碰撞模型,将量子场论方法与光学势方法中的可加性规 则结合起来.利用这种模型,我们计算了e-H,e-He和e-Li的微分碰撞截面,获得了较满意的 结果.     

A QCD model for e+e− annihilation

A QCD model for e⁺e^? annihilation is presented, and its consequences are compared with experimental data. The model involves production of a shower of partons described by a simple approximation to QCD perturbation theory, and decay of colour singlet clusters of produced partons into hadrons through a simple phase space process. The model reproduces most known theoretical features of QCD, and, with certain choices of parameters, appears to correspond well with experimental results.     

A study of non-thermalized luminescence spectra: the case of Cu2O

The emission spectra of a non-thermalized distribution of excitons in Cu₂O have been studied experimentally and theoretically. The emission spectra were found to exhibit interesting dependence on both the excitation frequencies and on the sample temperatures. These experimental results are explained quantitatively by a simple model calculation of the exciton distribution in Cu₂O under continuous excitation. Using this model the exciton non-radiative lifetime was deduced from the emission spectra. In addition, the present theory accounts for the lineshape of the resonant Raman peaks in Cu₂O more satisfactorily than the existing theory.     

Large N phases of chiral QCD2

A matrix model is constructed which describes a chiral version of the large NU (N) gauge theory on a two-dimensional sphere of area A. This theory has three separate phases. The large area phase describes the associated chiral string theory. An exact expression for the free energy in the large area phase is used to derive a remarkably simple formula for the number of topologically inequivalent covering maps of a sphere with fixed branch points and degree n.     

一种近似矢量衍射模型在衍射微光学元件分析中的应用

标量衍射理论形式简洁，有很高实用性，但是在衍射微光学元件分析中显得模型粗糙，准确度下降。严格矢量衍射理论由于计算复杂，非常耗费时间和资源，因此也不是一种很有效的设计工具。 我们在本文中运用了一种简单的近似矢量衍射模型分析了几种典型衍射微光学元件衍射性能，此衍射模型采用了标量衍射理论和近似近场模型的结合。 TE和TM两种偏振模式均运用此近似矢量衍射模型进行了分析，我们发现此衍射模型可以得到比标量衍射理论更准确的结果，而与严格电磁场理论相比，它占用很少的计算时间。     

Relativistic Calogero-Moser model as gauged WZW theory

Integrable deformation of the Calogero-Moser system is examined in the framework of the topological G/G Wess-Zumino-Witten model. It is shown that in the Hamiltonian approach the gauged WZW theory has a Hilbert space, which contains the one of the Ruijsenaars model. The latter can be described with the help of Verlinde algebra. Moreover, the evolution operator in the quantum mechanical problem has an interpretation in terms of the path integral in G/G theory with inserted Wilson line. We compute a partition function of the model using techniques from Chem-Simons theory, in particular, some surgeries of simple threefolds.     

The influence of channelling on the sputtering yield of polycrystalline copper

Abstract A simple model is proposed to test the applicability of Sigmund's theory to polycrystalline copper targets. A fixed amount of fortuitous chan = nelling is allowed in the target and the sputtering coefficient is calculated by using a combination of single crystal sputtering theory and Sigmund's for= mula. The results indicate that the effect of channelling is to shift the sputtering maximum to higher energy values than predicted by the amorphous target theory. Furthermore, the form of the sputtering yield-energy curves deviate significantly from the Sigmund sputtering curve.     

Plane wave topography on crystals with step-like impurity distributions

In this paper a qualitative and quantitative study is presented of the contrast formation in the plane wave topography of quartz plates with step-like impurity atoms distributions which are connected with different lattice parameters. Contrast distributions are calculated by means of a simple local application of the dynamical theory of the X-ray diffraction from the perfect crystal and using a simple mathematical model of the lattice deformation according to the isotropic theory of elasticity. A surprisingly good agreement between calculations and experimental results can be stated.The authors thank Dr. V. Holý for helpful discussions.     

Phenomenological model of nonequilibrium solidification

The maximum entropy production principle is used as a foundation for the nonequilibrium solidification theory. Based on this principle, a new simple model of dendrite solidification is proposed. The model predicts the explicit dependency of a dendrite’s rate and tip size on supercooling. The obtained results are devoid of the contradictions of the previous models and show quantitative agreement with the recent experimental data for the SCN dendrite.     

Quantum dynamical semigroups and dissipative collisions of heavy-ions

The theory of quantum dynamical semigroups is briefly reviewed including the scattering theory and WKB approximation. This formalism is illustrated by a simple model of dissipative heavy-ion collision.     

Density of states for the lowest landau level of a three-dimensional disordered system

A Quantum Monte Carlo investigation of a one-dimensional two band model with strong correlations in one band is presented. This two band model can be considered as a one-dimensional realization of the highT _c cuprates. In particular, the densities in the two bands, the formation of magnetic moments and the spin-spin correlations are studied as a function of particle number. The Quantum Monte Carlo results are compared with a simple mean field theory describing antiferromagnetic correlations, a variational Gutzwiller type calculation and a mapping to an effective one band model.     

Thermodynamic properties of the gadolinium gallium garnet, Gd3Ga5O12, between 0.05 and 25 K

The specific heat, the entropy, the thermal conductivity and the diffusivity of Gd₃Ga₅O₁₂ have been measured in the presence of an applied magnetic field. Calculations have been performed in order to explain simultaneously all these results within the framework of a simple molecular field theory. The agreement is good above 5 K and at low temperatures the deviations may be explained by the limitations of the simple model.     

Electron correlations in alloys of simple and transition metals

The effect of dynamical electron-electron correlations on the electronic structure of the paramagnetic disordered binary alloy of the transition and simple metals is studied for the Anderson model extended to arbitrary concentration of the transition metal impurities. We use the terminal-point approximation for the many-body quantities, which allows us to solve the random part of the problem within the single-site approximation. The many-body part of the problem is treated within the selfconsistent T-matrix approximation, valid for low, but finite concentration of particles ( ? 0.3/atom/spin). For low concentration of the transition metal impurities we obtain results identical with those for the Anderson model. The theory is illustrated numerically for a simple bandstructure model.     

Auto-model based computer simulation of Plateau-Rayleigh instability of mixtures of immiscible liquids

The classic theory to derive the characteristic Rayleigh wavelength, i.e., the distance between neighbouring droplets into which an originally cylindrical liquid body disintegrates, as a consequence of Rayleigh instability, is analysed in terms of the phenomenon of self-organization due to the mechanism of ‘fastest forming instability’. The paper aims at simulating this self-organization with Monte Carlo dynamics while accounting spatial interactions in lattices of Markov Random Fields that enable also modelling of Plateau-Rayleigh instability of instable mixtures of dispersed immiscible liquids. The Hammersley and Clifford theorem, concerning the general form of energy function, belonging to Markov Random Fields, is introduced for detailed classification of a simple model used for computer simulation. The relevant Auto-model, with Kawasaki dynamics, is chosen to investigate the liquid jet and the instability of the liquid’s cylindrical film. The computer-simulated outputs show encouraging agreement with the classic analytical predictions on main features of the Rayleigh instability. The model is also used as a foundation stone for developing a simple analytical approach for the estimation of Rayleigh wavelength of jets and cylindrical films, composed of instable mixtures of immiscible liquids. Qualitatively, the theory agrees with both computer simulation and experiment.