Application of discontinuity layout optimization to plane plasticity problems

A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described. The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems. Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology. Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (e. g. Tresca or Mohr Coulomb in plane strain). Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward. The procedure, coined 'discontinuity layout optimization' (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (e. g. slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss. Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here. The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems. Close agreement with the exact analytical solutions is obtained

Two-dimensional Chiral Anomaly in Differential Regularization

The two-dimensional chiral anomaly is calculated using differential regularization. It is shown that the anomaly emerges naturally in the vector and axial Ward identities on the same footing as the four-dimensional case. The vector gauge symmetry can be achieved by an appropriate choice of the mass scales without introducing the seagull term. We have analyzed the reason why such a universal result can be obtained in differential regularization.Comment: 9 pages, RevTex, no figures, a mistake in the massive case pointed out by the referee is correcte

Two-Loop Finiteness of Chern-Simons Field Theory in Background Field Method

We perform two-loop calculation of Chern-Simons in background field method using the hybrid regularization of higher-covariant derivative and dimensional regularization. It is explicitly shown that Chern-Simons field theory is finite at the two-loop level. This finiteness plays an important role in the relation of Chern-Simons theory with two-dimensional conformal field theory and the description of link invariant.Comment: RevTex, 13 pages. The proof of the existence of the large topological mass limit has been proved. Some typewritten mistakes have been correcte

Bianchi type I space and the stability of inflationary Friedmann-Robertson-Walker space

Stability analysis of the Bianchi type I universe in pure gravity theory is studied in details. We first derive the non-redundant field equation of the system by introducing the generalized Bianchi type I metric. This non-redundant equation reduces to the Friedmann equation in the isotropic limit. It is shown further that any unstable mode of the isotropic perturbation with respect to a de Sitter background is also unstable with respect to anisotropic perturbations. Implications to the choice of physical theories are discussed in details in this paper.Comment: 5 pages, some comment adde

On the Low-Energy Effective Action of N=2 Supersymmetric Yang-Mills Theory

We investigate the perturbative part of Seiberg's low-energy effective action of N=2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on $U(1)_R$ anomaly and non-perturbative $\beta$-function arguments.Comment: 27 pages, RevTex, no figure

Simulation of the stochastic wave loads using a physical modeling approach

In analyzing stochastic dynamic systems, analysis of the system uncertainty due to randomness in the loads plays a crucial role. Typically time series of the stochastic loads are simulated using traditional random phase method. This approach combined with fast Fourier transform algorithm makes an efficient way of simulating realizations of the stochastic load processes. However it requires many random variables, i.e. in the order of magnitude of 1000, to be included in the load model. Unfortunately having too many random variables in the problem makes considerable difficulties in analyzing system reliability or its uncertainty. Moreover applicability of the probability density evolution method on engineering problems faces critical difficulties when the system embeds too many random variables. Hence it is useful to devise a method which can make realization of the stochastic load processes with low, say less than 20, number of random variables. In this article we introduce an approach, so-called "physical modeling of stochastic processes", and show its applicability for simulation of the wave surface elevation.</jats:p

A Remark on Lorentz Violation at Finite Temperature

We investigate the radiatively induced Chern-Simons-like term in four-dimensional field theory at finite temperature. The Chern-Simons-like term is temperature dependent and breaks the Lorentz and CPT symmetries. We find that this term remains undetermined although it can be found unambiguously in different regularization schemes at finite temperature.Comment: To appear in JHEP, 8 pages, 1 eps figure, minor changes and references adde