Variational inequalities for ferroelectric constitutive modeling

This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of free energy as well as switching and saturation conditions in form of inequalities. Thermodynamically consistent models naturally lead to variational formulations. We propose to use the concept of variational inequalities. We aim at combining the different phenomenological conditions into one variational inequality. In our formulation we use one Lagrange multiplier for each condition (the onset of domain switching and saturation), each satisfying Karush-Kuhn-Tucker conditions. An update for reversible and remanent quantities is then computed within one, in general nonlinear, iteration.

Localized Linear Systems in Sequential Implicit Simulation of Two-Phase Flow and Transport

Summary Implicit-reservoir-simulation models offer improved robustness compared with semi-implicit or explicit alternatives. The implicit treatment gives rise to a large nonlinear algebraic system of equations that must be solved at each timestep. Newton-like iterative methods are often used to solve these nonlinear systems. At each nonlinear iteration, large and sparse linear systems must be solved to obtain the Newton update vector. It is observed that these computed Newton updates are often sparse, even though the sum of the Newton updates over a converged iteration may not be. Sparsity in the Newton update suggests the presence of a spatially localized propagation of corrections along the nonlinear iteration sequence. Substantial computational savings may be realized by restricting the linear-solution process to obtain only the nonzero update elements. This requires an a priori identification of the set of nonzero update elements. To preserve the convergence behavior of the original Newton-like process, it is necessary to avoid missing any nonzero element in the identification procedure. This ensures that the localized and full linear computations result in the same solution. As a first step toward the development of such a localization method for general fully implicit simulation, the focus is on sequential implicit methods for general two-phase flow. Theoretically conservative, a priori estimates of the anticipated Newton-update sparsity pattern are derived. The key to the derivation of these estimates is in forming and solving simplified forms of infinite-dimensional Newton iteration for the semidiscrete residual equations. Upon projection onto the discrete mesh, the analytical estimates produce a conservative indication on the update's sparsity pattern. The algorithm is applied to several large-scale computational examples, and more than a 10-fold reduction in simulation time is attained. The results of the localized and full simulations are identical, as is the nonlinear convergence behavior.

General exact solutions for the full gluon propagator in QCD with the mass gap

We have explicitly shown that Quantum Chromodynamics is a color gauge invariant theory with non-zero mass gap, which has been defined as the value of the regularized full gluon self-energy at a finite scale point. The mass gap itself is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found: (i) The nonlinear iteration solution at which the gluons remain massless is explicitly present. (ii) Existence of the solution with an effective gluon mass is also demonstrated.

Position Accuracy Analysis on Disc Storing Mechanism for Benthic Drill

The positional accuracy of disc storing mechanism for benthic drill is the guarantee of long hole coring in deep sea. Aiming the lack of positional accuracy analysis on disc storing mechanism, the mathematic model of the positional accuracy for disc storing mechanism is presented by using complex vector and matrix analyzing method. The analytical formula of crank rotation positional accuracy is acquired through rotation positional analysis of crank in disc storing mechanism driven by hydraulic cylinder. Adopting numerical nonlinear iteration solution method of Newton-Simpson, the variation rule of rotation positional error for disc storing mechanism to cylinder length is acquired, which supports an important theory, leading to tolerance design for dimensional parameters of disc storing mechanism.