最小二乘有限元法求解非定常应力的Navier-Stokes方程

为精确求解非定常层流问题,发展一种非定常速度-应力-压力的方法.采用牛顿法对非线性对流项进行线性化处理和预处理共轭梯度法,实现了非定常应力形式Navier-Stokes方程的求解.方腔层流流动比较发现,非定常应力形式比涡量形式与试验结果更加吻合,精度更高.该方法有效地解决亚格子应力项的问题,实现基于最小二乘有限元法的湍流求解.比较方腔湍流流动的试验与仿真结果,证明本文的方法具有可行性,为湍流大涡模拟计算打下基础.     

Long-distance behaviour of fermion propagators in the chiral Schwinger model

The chiral Schwinger model's fermionic sector is studied by comparing the fermion propagator of the original Jackiw-Rajaraman formulation with a propagator in the gauge invariant formulation. The main difference consists in the existence of fermionic single particle states in the original formulation, while there are no such states in the gauge invariant formulation. It is suggested that this difference is caused by renormalization, which changes the Hilbert space.     

MC-Smooth: A mass-conserving,smooth vorticity–velocity formulation for multi-dimensional flows

A novel vorticity–velocity formulation of the Navier–Stokes equations – the Mass-Conserving, Smooth (MC-Smooth) vorticity–velocity formulation – is developed in this work. The governing equations of the MC-Smooth formulation include a new second-order Poisson-like elliptic velocity equation, along with the vorticity transport equation, the energy conservation equation, and N_spec species mass balance equations. In this study, the MC-Smooth formulation is compared to two pre-existing vorticity–velocity formulations by applying each formulation to confined and unconfined axisymmetric laminar diffusion flame problems. For both applications, very good to excellent agreement for the simulation results of the three formulations has been obtained. The MC-Smooth formulation requires the least CPU time and can overcome the limitations of the other two pre-existing vorticity–velocity formulations by ensuring mass conservation and solution smoothness over a broader range of flow conditions. In addition to these benefits, other important features of the MC-Smooth formulation include: (1) it does not require the use of a staggered grid, and (2) it does not require excessive grid refinement to ensure mass conservation. The MC-Smooth formulation is a computationally attractive approach that can effectively extend the applicability of the vorticity–velocity formulation.     

Frequency-domain acoustic pressure formulation for rotating source in uniform subsonic inflow with arbitrary direction

This paper presents a frequency-domain formulation for predicting noise radiated from the rotating thickness and loading sources in uniform subsonic inflow with arbitrary direction. The proposed frequency-domain formulation is an extension of the recently published frequency-domain formulation for the stationary medium. It avoids the singular integral and numerical interpolation problems encountered in the time-domain numerical method. Three test cases, i.e., noise radiation from the rotating monopole and dipole point sources and the Isom thickness noise of a transonic rotor in the subsonic uniform flow, have been carried out to validate the proposed formulation. Both the acoustic pressure spectrum and directivity pattern computed with the present frequency-domain method are in good agreement with those obtained from the time-domain method, thus validating the correctness of the present formulation. Furthermore, the numerical results indicate that the frequency-domain formulation is suitable for tonal noise prediction, while it is inefficient for broadband noise prediction.     

Formulation of the Shannon theorem for a discrete noisy channel

In this paper, the Shannon theorem is formulated for a discrete noisy channel in terms used in the Shannon formulation. Proof of the theorem is based on the theory of optimal signals reception, in which the signal intensity with respect to noise has a significant meaning. Although the formulation contains the notions of the channel capacity and the message-source entropy, it substantially differs from the Shannon formulation. The obtained formulation allows us to explain some cases where the information transmission conditions do not satisfy the Shannon theorem.     

Generalized Foldy-Lax formulation

We present a method for numerical wave propagation in a heterogeneous medium. The medium is defined in terms of an extended scatterer or target which is surrounded by many small scatterers. By extending the classic Foldy-Lax formulation we developed an efficient algorithm for numerical wave propagation in two dimension. In the method that we set forth multiple scattering among the point scatterers and the extended target is fully taken into account via a boundary integral formulation coupled with the Foldy-Lax formulation. This formulation forms the basis for our numerical procedure.     

Instantaneous Formulation for Transitions Between Two Instantaneous Bound States and Its Gauge Invariance

We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.     

Nonlinear Axisymmetric Deformation Model for Structures of Revolution

An axisymmetric formulation for modeling three-dimensional deformation of structures of revolution is presented. The axisymmetric deformation model is described using the cylindrical coordinate system. Large displacement effects and material nonlinearities and anisotropy are accommodated by the formulation. Mathematical derivation of the formulation is given, and an example is presented to demonstrate the capabilities and efficiency of the technique compared to the full three-dimensional model.     

Geometric phase in the causal quantum theories

The projective-geometric formulation of geometric phase for any ensemble in the causal quantum theories is given. This formulation generalizes the standard formulation of geometric phase to any causal ensemble including the cases of a single causal trajectory, the experimental geometric phase and the classical geometric phase.     

Analysis of Suzuki, Shanker, and Kumar formulations under strong compressions

A critical analysis of the Suzuki, Shanker, and Kumar formulations is presented by studying different classes of materials under high pressure. A similar trend for all the materials studied in the present work, demonstrates that Suzuki formulation is not capable to yield compression behaviour of solids. The Shanker formulation improves the results obtained by the Suzuki formulation in small compression range (0.9<V/V₀<1). For further compressions Shanker formulation also fails. On the other hand, the Kumar formulation is found to work well for the entire range of pressure. The reasons for the failure of Suzuki and Shanker formulations are discussed.     

A moving medium formulation for prediction of propeller noise at incidence

This paper presents a time domain formulation for the sound field radiated by moving bodies in a uniform steady flow with arbitrary orientation. The aim is to provide a formulation for prediction of noise from body so that effects of crossflow on a propeller can be modeled in the time domain. An established theory of noise generation by a moving source is combined with the moving medium Green's function for derivation of the formulation. A formula with Doppler factor is developed because it is more easily interpreted and is more helpful in examining the physic of systems. Based on the technique presented, the source of asymmetry of the sound field can be explained in terms of physics of a moving source. It is shown that the derived formulation can be interpreted as an extension of formulation 1 and 1A of Farassat based on the Ffowcs Williams and Hawkings (FW–H) equation for moving medium problems. Computational results for a stationary monopole and dipole point source in moving medium, a rotating point force in crossflow, a model of helicopter blade at incidence and a propeller case with subsonic tips at incidence verify the formulation.     

Diffeomorphism invariance in the Hamiltonian formulation of General Relativity

It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity.     

A Unified Algebraic Approach to Quantum Theory

Conventional approaches to quantum mechanics are essentially dualistic. This is reflected in the fact that their mathematical formulation is based on two distinct mathematical structures: the algebra of dynamical variables (observables) and the vector space of state vectors. In contrast, coherent interpretations of quantum mechanics highlight the fact that quantum phenomena must be considered as undivided wholes. Here, we discuss a purely algebraic formulation of quantum mechanics. This formulation does not require the specification of a space of state vectors; rather, the required vector spaces can be identified as substructures in the algebra of dynamical variables (suitably extended for bosonic systems). This formulation of quantum mechanics captures the undivided wholeness characteristic of quantum phenomena, and provides insight into their characteristic nonseparability and nonlocality. The interpretation of the algebraic formulation in terms of quantum process is discussed.     

Equivalence Between Two Different Field-Dependent BRST Formulations

Finite field-dependent BRST (FFBRST) transformations were constructed by integrating infinitesimal BRST transformation in a closed form. Such a generalized transformations have been extended in various branch of physics and found many applications. Recently BRST transformation has also been generalized with same goal and motivation in slightly different manner. In this work we have shown that the later formulation is conceptually equivalent to the earlier formulation. We justify our claim by producing the same result of later formulation using earlier FFBRST formulation.     

Computer simulation of the phenomenological transport coefficient in the lattice gas and Fick's First Law

A direct steady state computer simulation method for calculating the Onsager phenomenological transport coefficient from the gradient of the chemical potential in the one component lattice gas is presented. It is shown that the results are in good agreement with the Einsteinian method. A recent alternative formulation for Fick's First Law that had been proposed to replace the standard Fick's First Law formulation is also analysed using the same model. It is shown that the alternative formulation gives poor agreement with the simulation data whereas the standard Fick's First Law gives excellent agreement. Accordingly, the alternative formulation does not appear to have merit as a new definition of the diffusion coefficient. It is shown that the alternative formulation is a rough approximation for the dependence of the interstitial solute diffusion coefficient on solute concentration in an interstitial solid solution if information about the activity coefficient and solute diffusion coefficient at very dilute concentrations is available. However, in this role, this is not an entirely new idea.     

Hybrid magnetic field formulation based on the losses separation method for modified dynamic inverse Jiles-Atherton model

Dynamic formulation based on the losses separation method in conducting media for the inverse Jiles-Atherton model is proposed. This formulation is based on the concept of the Hybrid Magnetic Field model (HMF). The HMF consists of the modification of the effective field by introducing two counter-fields associated, respectively, with the eddy current and excess losses. Such a formulation is characterized by seven parameters with five parameters issued from the quasi-static Jiles-Atherton model. Thus, two new parameters related to these fields are added to that defined in the quasi-static model. The identification of these new parameters is based on the measurements of the volumetric energy density. To validate this formulation, measurements are carried out on grain non-oriented Fe-Si 3% electrical sheets.     

5 kVA高温超导变压器双饼线圈不同有限元模型对比分析

本文基于5 kVA 高温超导变压器的高压绕组双饼线圈, 运用有限元软件, 完成了均质化建模. 相比于全模型, 采用均质化模型不仅不影响计算精度, 而且大大减少了计算时间, 同时能够快速有效地计算出双饼线圈的磁场分布、 电流密度分布以及线圈交流损耗. 为了验证双饼线圈有限元计算模型的正确性, 本文进行了 H 方程全模型、H 方程均质化模型、T-A 方程全模型及T-A 方程均质化模型下的对比仿真分析. 仿真结果的一致性表明了双饼线圈有限元计算模型的正确性. 本文为后续基于T-A 方程下高温超导变压器均质化模型的研究提供了参考.     

Formation for Bass-Relief Microprofiles Based on an Analytic Formulation

A method of fast design and fabrication for bass-relief micro-profiles is developed by using an analytic formulation to determine the exposure distribution. Based on an equivalent exposure threshold model, the formulation is simplified for the case of bass-relief profile corresponding to the smaller exposure dose. The mask function for a microlens array is designed without iteration involved by the analytic formulation. The experiment is performed to validate the method, and the fabrication result is obtained with the profile error less than 30nm （rms）.     

Imaginary-time formulation of steady-state nonequilibrium: application to strongly correlated transport

We extend the imaginary-time formulation of the equilibrium quantum many-body theory to steady-state nonequilibrium with an application to strongly correlated transport. By introducing the Matsubara voltage, we maintain the finite chemical potential shifts in the Fermi-Dirac function, in agreement with the Keldysh formulation. The formulation is applied to strongly correlated transport in the Kondo regime using the quantum Monte Carlo method.     

Multiloop calculations of effective action for local composite operators

Effective action for local composite operators is described for both the standard loop expansion formulation and an improved two-particle irreducible formulation. Rules for calculating multiloop contributions to the effective action are given in both formulations and are exemplified in the Gross-Neveu model in the large-N limit. Calculation of the exact effective action in the Gross-Neveu model is considerably simplified in the improved formulation. Results obtained from the conventional auxiliary field method, like dynamical symmetry breaking, non-classical solitions, etc., can all be obtained in the present formulation by dealing with the composite operators directly without introducing auxiliary fields. The present method can be applied to models in which the auxiliary field method is difficult to implement.