Derivation of variational principles for rigid-plastic solids obeying non-associated flow laws—I: Further development of the nonlinear method of adding the adjoint operator,prescribed jumps

In this paper several variational functionals have been derived for a perfectly plastic solid obeying non-associated flow rule. The nonlinear method of adding the adjoint operator has been applied. Making use of the method a basic variational functional is obtained, from which others, with a reduced number of independent fields, are derived. In the first part of the paper discontinuities of stress and velocity fields are prescribed. Also further results concerning the method of adding the adjoint operator are presented.     

Hochfeld-13C-kernresonanz an acrylnitril/vinylchlorid-copolymeren

Copolymers of acrylonitrile and vinylchloride (molar ratio ACN : VC = 44.5 : 55.5) were synthesized by continuous emulsion polymerization. Their sequence distribution was studied by ¹³C-NMR-spectra at 90.52 MHz. Three different methylene carbon regions were attributed to diads of the type ? VC? VC? ,? VC? ACN? and ? ACN? ACN? . The experimentally determined diad distribution was in good agreement with the calculated diad distribution, using reactivity ratios of r_ACN = 3.6 and r_VC = 0.05.     

Equation of motion approach to the Hubbard model in infinite dimensions

We consider the Hubbard model on the Bethe lattice with infinite Coordination number and construct (i) a systematic series of self-consistent approximations to the one-particle Green's function, G⁽ⁿ⁾(), n = 2,3,... and (ii) conduct an exact diagonalization study of the Hubbard star and the star of the stars. We present analytic and numerical results for the Mott-Hubbard transition at half filling. We find consistently (i) a critical U_c 2.5 and (ii) that the gap opens like (U-U_c)^3/2.     

Thermodynamic analysis of the δ ferrite in the systems Fe-Cr-N and Fe-Cr-Mn-N

The solubility of nitrogen in ferritic iron-chromium alloys with mass contents of between 6.08 to 23.94 % chromium was measured in the temperature range 1523 to 1773 K. Combining the results with published data for the nitrogen solubility in iron-chromium, improved parameters describing the chromium-nitrogen interaction were derived. The Gibbs free excess energy can be described by . Calculations of the nitrogen solubility using this equation and calculations using parameters published by the Swedish Institute of Metals Research differ the more the higher the temperature. A repeated analysis of measurements of the nitrogen solubility in ferritic Fe-Cr-Mn alloys using the Gibbs free excess energy derived in this investigation for the chromium-nitrogen interaction leads to the manganese-nitrogen interaction energy .     

Stability and passivity preserving Petrov–Galerkin approximation of linear infinite-dimensional systems

This contribution presents two approximation methods for linear infinite-dimensional systems that ensure the preservation of stability and passivity. The first approach allows one to approximate internal source free infinite-dimensional systems such that the resulting approximation is a port-controlled Hamiltonian system with dissipation. The second method deals with the class of systems that are not required to have conjugated outputs but only a dissipative system operator. It yields approximations with a dissipative system matrix for which bounds of their stability margin are provided. Both approaches are based on a state space formulation of the infinite-dimensional system. This makes it possible to use the Petrov–Galerkin approximation whose free parameters are partly used for achieving the structure preservation. Since still free parameters remain, further application specific objectives, such as, e.g., moment matching, can be achieved. Both approaches are applied to the approximation of an Euler–Bernoulli beam.     

A Comparison of Static Analysis and Evolutionary Testing for the Verification of Timing Constraints

This paper contrasts two methods to verify timing constraints of real-time applications. The method of static analysis predicts the worst-case and best-case execution times of a task's code by analyzing execution paths and simulating processor characteristics without ever executing the program or requiring the program's input. Evolutionary testing is an iterative testing procedure, which approximates the extreme execution times within several generations. By executing the test object dynamically and measuring the execution times the inputs are guided yielding gradually tighter predictions of the extreme execution times. We examined both approaches on a number of real world examples. The results show that static analysis and evolutionary testing are complementary methods, which together provide upper and lower bounds for both worst-case and best-case execution times.     

GCD of Random Linear Combinations

We show that for arbitrary positive integers with probability the gcd of two linear combinations of these integers with rather small random integer coefficients coincides with This naturally leads to a probabilistic algorithm for computing the gcd of several integers, with probability via just one gcd of two numbers with about the same size as the initial data (namely the above linear combinations). This algorithm can be repeated to achieve any desired confidence level.     

Complex logarithmic views for small details in large contexts

Commonly known detail in context techniques for the two-dimensional Euclidean space enlarge details and shrink their context using mapping functions that introduce geometrical compression. This makes it difficult or even impossible to recognize shapes for large differences in magnification factors. In this paper we propose to use the complex logarithm and the complex root functions to show very small details even in very large contexts. These mappings are conformal, which means they only locally rotate and scale, thus keeping shapes intact and recognizable. They allow showing details that are orders of magnitude smaller than their surroundings in combination with their context in one seamless visualization. We address the utilization of this universal technique for the interaction with complex two-dimensional data considering the exploration of large graphs and other examples     

A generic and scalable pipeline for GPU tetrahedral grid rendering

Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics hardware architectures, large and deformable grids, as well as different rendering options. At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local barycentric coordinates. Then, sampling requires minimum GPU memory and texture access operations, and it maps efficiently onto a feed-forward pipeline of multiple stages performing computation and geometry construction. We propose to spawn rendered elements from one single vertex. This makes the method amenable to upcoming Direct3D 10 graphics hardware which allows to create geometry on the GPU. By only modifying the algorithm slightly it can be used to render per-pixel iso-surfaces and to perform tetrahedral cell projection. As our method neither requires any pre-processing nor an intermediate grid representation it can efficiently deal with dynamic and large 3D meshes.