An Explicit Formula for the Matrix Logarithm

We present an explicit polynomial formula for evaluating the principal logarithm of all matrices lying on the line segment $\{I(1-t)+At:t\in [0,1]\}$ joining the identity matrix $I$ (at $t=0$) to any real matrix $A$ (at $t=1$) having no eigenvalues on the closed negative real axis. This extends to the matrix logarithm the well known Putzer's method for evaluating the matrix exponential.Comment: 6 page

A geometrical non-linear model for cable systems analysis

Cable structures are commonly studied with simplified analytical equations. The evaluation of the accuracy of these equations, in terms of equilibrium geometry configuration and stress distribution was performed for standard cables examples. A three-dimensional finite element analysis (hereafter FEA) procedure based on geometry-dependent stiffness coefficients was developed. The FEA follows a classical procedure in finite element programs, which uses an iterative algorithm, in terms of displacements. The theory is based on a total Lagrange formulation using Green-Lagrange strain. Pure Newton-Raphson procedure was employed to solve the non-linear equations. The results show that the rigid character of the catenary’s analytical equation, introduce errors when compared with the FEA

K\"all\'en-Lehmann representation of noncommutative quantum electrodynamics

Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some attention to the quantization of NC field theory on lower dimensions and look closely at the issue of dynamical mass generation to the gauge field. This work encompasses the quantization of the two-dimensional massive quantum electrodynamics and three-dimensional topologically massive quantum electrodynamics. We begin by addressing the problem on a general dimensionality making use of the perturbative Seiberg-Witten map to, thus, construct a general action, to only then specify the problem to two and three dimensions. The quantization takes place through the K\"all\'en-Lehmann spectral representation and Yang-Feldman-K\"all\'en formulation, where we calculate the respective spectral density function to the gauge field. Furthermore, regarding the photon two-point function, we discuss how its infrared behavior is related to the term generated by quantum corrections in two dimensions, and, moreover, in three dimensions, we study the issue of nontrivial {\theta}-dependent corrections to the dynamical mass generation

Visco-elastic regularization and strain softening

In this paper it is intended to verify the capacity of regularization of the numerical solution of an elasto-plastic problem with linear strain softening. The finite element method with a displacement approach is used. Drucker-Prager yield criteria is considered. The radial return method is used for the integration of the elasto-plastic constitutive relations. An elastovisco- plastic scheme is used to regularize the numerical solution. Two constitutive laws have been developed and implemented in a FE-program, the first represent the radial return method applied to Drucker-Prager yield criteria and the second is a time integration procedure for the Maxwell visco-elastic model. Attention is paid to finite deformations. An associative plastic flow is considered in the Drucker-Prager elasto-plastic model. The algorithms are tested in two problems with softening. Figures showing the capability of the algorithms to regularize the solution are presented