A hybrid method of modal synthesis using vibration tests

The assembly of structures along continuous boundaries presents great difficulty in the context of modal synthesis. In order to solve such problems, a method is proposed in which a hybrid model is defined reflecting the dynamic behavior of a structure loaded along a boundary. It is based on Weinstein's method and corresponds to a generalization of the impedance matrix method. Generalized boundary co-ordinates are defined from branch modes obtained by introducing mass loading along the boundary. Thus, the hybrid model can be derived from testing as a result of two independent modal identifications. The method permits high precision prediction of the influence of strong structural modifications. Thus, in the case of rectangular plates, it has been possible to find the modes of a cantilever plate and of a plate with stiffeners from the free modes.     

A self-consistent method for treating point impurities with arbitrary range potentials

We propose a generalized Green's function technique for treating impurities whose potential has an arbitrary short, intermediate, or long-range nature. The approach exploits the recursion method, and can be formulated in a self-consistent way for point impurities.     

Stabilization of cell-centered compressible Lagrangian methods using subzonal entropy

This work deals with the stabilization of early stages of Lagrangian calculations of compressible gas dynamics in the context of cell-centered discretization. We describe a totally conservative algorithm based on an entropy analysis of the distortion of a Lagrangian mesh. It prevents the tangling of the mesh, while remaining consistent and conservative in mass, momentum, and total energy. The method described can be applied to any cell-centered Lagrangian scheme. In this article, we detail the extension to the cell-centered Glace scheme published in Carré et al. (2009) [G. Carré, S. Del Pino, B. Després, E. Labourasse, A cell-centered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension, J. Comput. Phys. 228 (2009) 5160–5183]. Numerical tests are proposed to assess the accuracy and robustness.     

一类非线性非完整系统的Routh方程：从Chetaev条件到Euler条件

对于一类其非线性约束方程可展开为关于广义速度的MacLaurin级数的非完整系统,可以在 完全理想的情况下用Lagrange未定乘数法和d'Alembert原理建立其Routh方程.由此可以得到 结论：Chetaev条件只有在线性非完整系统中才成立并且等价于Vacco条件.引入“Euler条件 ”,可以统一Chetaev条件和Vacco条件,统一d'Alembert原理和Hamilton原理,并解决所有 现存于非线性非完整系统中的问题. 关键词： 非线性非完整系统 Routh方程 Chetaev条件 Vacco条件 Euler条件     

Numerical data and experimental proof of the unified theory of electron emission (Christov)

In order to check the unified theory of electron emission (Christov), the temperature dependence of the electron emission from the (013), (001) and (112) single crystal faces of tungsten is measured between 300 °K and 1500 °K at relatively low fields yielding low current densities (10^?1 to 10^?7 A/cm²). Experiments are performed in a field electron microscope using a probe hole technique with an electron multiplier. The experimental results are in a fairly good agreement with Christov's theory. Tables of numerical data of Christov's formulae are presented. Using these tables, typical results of the theory are described.     

An eikonal perturbation theory having applications in hadron dynamics,I: Genesis

We develop a Lagrangian field-theoretic laboratory where one can rigorously investigate ideas and problems in high-energy hadronic interactions. In this paper (the first of a series) the general field-theoretic framework is outlined in the oversimplified model of a scalar-scalar Yukawa interaction. Functional methods are used to cast all Green's functions in an “operator eikonal” form. The eikonal approximations (EA's) in Lagrangian relativistic quantum mechanics are reviewed and discussed. We then derive an exact eikonal equation in quantum field theory. The perturbation theoretic solution of this equation leads to a new kind of eikonal perturbation theory (EPT) which generalizes simultaneously the EA's as well as the ordinary perturbation theory (OPT). Some salient features of Green's functions in the EPT are as follows: (i) the lowest-order EPT amplitudes correspond to a kind of semiclassical approximation; (ii) the lowest-order four-point amplitudes contain the high-energy part of the full radiatively corrected crossed ladder series, without vacuum polarization effects; (iii) for spin-one gluons, the latter amplitude develops diffractive behavior in the direct channel and, for spin-one and spin-zero gluons, Regge behavior in the crossed channel; (iv) for vanishing gluon mass, this amplitude develops poles, in the direct channel, corresponding to a positronium-like bound-state spectrum. Properties (i)–(iv) are generalized to EPT from EA's and are absent in OPT. Unlike in the case of EA's we also have that (v) the EPT is a quantum field theory, which properly includes selfinteraction effects; (vi) the EPT is an iterative perturbation theoretic scheme, which shares with OPT the properties of renormalizability.     

Instanton contributions in reggeon quantum mechanics

The full semiclassical approximation to reggeon field theory without transverse dimensions is derived. By using Polyakov's method in Lagrangian form and paying due attention to the quantum terms of the potential it is shown that instanton contributions are able to explain the tunnel-like energy gap for α(0) ? 1 > > λ.     

约束系统正则形式的对称性质

本文导出场论中用奇异拉氏量描述的系统正则形式的广义Noether第一定理(GNFT),导出无限连续群下变更性系统正则形式的广义Noether恒等式(GNI),讨论了它们在Dirac约束理论中的应用。给出一个新的反倒,说明Dirac猜想失效,指出某些变更性系统也具有Dirac约束,讨论了GNI在色动力学中的应用。 关键词：     

A Further Generalized Lagrangian Density and its Special Cases

By summarizing and extending the Lagrangian densities of general relativity and the Kibble’s gauge theory of gravitation,a further generalized Lagrangian density for a gravitational system is obtained and analyzed in greater detail, which will extend the studying range for the theory of gravitation. Many special cases can be derived from this generalized Lagrangian density, and the general characteristics and some peculiarities of them will be described and discussed.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 4. Theoretical group analysis of exchange Hamiltonian

By analyzing the exchange Hamiltonian, we develop the technique of determining the magnetic structures liable to occur in a crystal. The technique rests on Bertaut's idea that the exchange matrix eigenfunction corresponds to some magnetic structure. A technically simple and efficient method of diagonalizing the exchange matrix is worked out using the devices of space group representation theory. A method is presented to find the magnetic structures with equal exchange energy (exchange multiplets). The occurrence of exchange multiplets results from the additional invariance of the exchange Hamiltonian under rotation of all the spins. The degeneracy within the exchange multiplet may be the reason why some magnetic structures arise not according to one irreducible representation of the space group. The theory is illustrated with reference to an example of the magnetic structure of spinels.     

规范场静态解的稳定性

对有规范条件或约束的非线性理论,研究了其驻点的Hessian形式.指出了规范场的经典解的稳定性由包含拉格朗日乘子贡献的有效拉氏量的二阶变分决定.     

Quantization from Hamilton–Jacobi theory with a random constraint

We propose a method of quantization based on Hamilton–Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization yet with a unique ordering of operators if the Lagrange multiplier that arises in the dynamical system with constraint can only take binary values ±?/2$\pm ?/2$ with equal probability.     

On the structure of generalized monopole solutions in gauge theories

A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. We derive restriction arising from the condition of finite energy. The radial oscillation of the solution is discussed. Using our method we reproduce all the SU(3) solutions known in the literature. Finite energy monopoles possessing magnetic charge in the range g₀?kg₀?(N?1)g₀ are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of our solutions.     

Classical and quantum mechanics of free relativistic membranes

Motivated by the theory of relativistic strings, the theory of a two-dimensional relativistic membrane whose action is proportional to the three-dimensional area it traces out in space-time is investigated both in Lagrangian and Hamiltonian formalisms. The quantum theory is developed using Dirac's method for constrained systems and the question of gauge choices is considered in some detail.     

A green's function analysis of atomic and molecular (e, 2e) reactions

Investigation of Atomic and molecular (e, 2e) spectra will be discussed in terms of a Green's function approach. The energy, intensity and momentum distribution of energy levels observed by electron coincidence ionization spectroscopy, are directly related to the poles, pole strengths and generalized overlap amplitude of the one particle propagator or Green's function. The theoretical calculation of these observable quantities via the Green's function technique will be discussed. In particular, the position and intensity of satellite (or “shakeup”) lines, relative to the main lines, will be analysed in some detail.     

The normalization of the muon-decay current

A normalization condition for the muon decay current in V-A theory with radiative corrections included is obtained by the requirement that the generalized charges corresponding to the constituents of the current should fulfil an appropriate charge algebra. It is shown that the radiative corrections in second order are uniquely fixed by this requirement. The calculation is performed without the use of a cut-off. If the corresponding current algebra is postulated, the currents which, according to Adler, describe scattering of neutrinos on charged leptons, are completely determined. It is pointed out that Adler's Lagrangian for this process must be reduced with a factor $\text{1}\text{2}$ in order to make leptonic spin symmetric the whole interaction Lagrangian for leptonic processes.     

LAGRANGIAN MULTIPLIER AND MASSIVE YANG-MILLS FIELDS YANG-MILLS FIELDS

If we give appropiate constraint to the gauge invariant Lagrangian, the variationprinciple of the action convert to the variational problems with subsidiary condition.The effective Lagrangian which contains Lagrangian multiplier may has the mass termof the mesons. In that case we obtain naturally the massive Yang-Mills fields which wasdiscussed by Nakanishi.     

The relativistic spherical top

The classical theory of the free relativistic spherical top is first developed from a Lagrangian viewpoint. Our method allows the invariant mass to be an arbitrary function of the intrinsic spin. A canonical formalism is established following the approach suggested by Dirac for constrained Hamiltonian systems. There is a second arbitrary function in the theory, in addition to the usual one due to reparametrization invariance. The usual Newton-Wigner variables are supplemented by the Euler angles. The quantum theory of the free top is discussed. The classical theory is generalized to included charged tops with magnetic moments.     

Application of Jacobi’s last multiplier for construction of Hamiltonians of certain biological systems

The relationship between Jacobi’s last multiplier and the Lagrangian of a second-order ordinary differential equation is quite well known. In this article we demonstrate the significance of the last multiplier in Hamiltonian theory by explicitly constructing the Hamiltonians of certain well known first-order systems of differential equations arising in biology.