Implicit Regularization and Renormalization of QCD

We apply the Implicit Regularization (IR) technique in a non-abelian gauge theory. We show that IR preserves gauge symmetry as encoded in relations between the renormalization constants required by the Slavnov–Taylor identities at the one-loop level of QCD. Moreover, we show that the technique handles divergencies in massive and massless QFT on equal footing.     

An efficient upwind/relaxation algorithm for the Euler and Navier–Stokes equations

An efficient Euler and full Navier–Stokes solver based on a flux splitting scheme is presented. The original Van Leer flux vector splitting form is extended to arbitrary body-fitted co-ordinates in the physical domain so that it can be used with a finite volume scheme. The block matrix is inverted by Gauss–Seidel iteration. It is verified that the often used reflection boundary condition will produce incorrect flux crossing the wall and cause too large numerical dissipation if flux vector splitting is used. To remove such errors, an appropriate treatment of wall boundary conditions is suggested. Inviscid and viscous steady transonic internal flows are analysed, including the case of shock-induced boundary layer separation.     

Symbolic topological sorting with OBDDs

We present a symbolic OBDD algorithm for topological sorting which requires O(log²|V|) OBDD operations. Then we analyze its true runtime for the directed grid graph and show an upper bound of O(log⁴|V|loglog|V|). This is the first true runtime analysis of a symbolic OBDD algorithm for a fundamental graph problem, and it demonstrates that one can hope that the algorithm behaves well for sufficiently structured inputs.     

An implicit high-order spectral difference approach for large eddy simulation

The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgrid-scale stress tensor is modelled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower–upper symmetric Gauss–Seidel (LU-SGS) algorithm. In order to study the sensitivity of the method, first, the implicit solver is used to compute the two-dimensional (2D) laminar flow around a NACA0012 airfoil at Re = 5 × 10⁵ with zero angle of attack. Afterwards, the accuracy and the reliability of the solver are tested by solving the 2D “turbulent” flow around a square cylinder at Re = 10⁴ and Re =  2.2 × 10⁴. The results show a good agreement with the experimental data and the reference solutions.     

Implicit runge-kutta methods for differential inclusions

This paper is concerned with the application of implicit Runge-Kutta methods suitable for stiff initial value problems to initial value problems for differential inclusions with upper semicontinuous right-hand sides satisfying a uniform one-sided Lipschitz condition and a growth condition. The problems could stem from differential equations with state discontinuous right-hand sides. It is shown that there exist methods with higher order of convergence on intervals where the solution is smooth enough. Globally we get at least the order one.     

Systematic dynamic modelling of mechanical systems containing kinematic loops

In this tutorial paper a systematic procedure is presented to obtain the dynamic models of mechanical systems containing kinematic loops, with a main emphasis on efficiency and with particular regard to robotic systems. The procedure retains a minimal set of generalized coordinates for the corresponding open loop structure, obtained by removing some additional constraints closing loops in the original structure, while adopting an efficient Newton-Euler formulation of the equations of motion. Two methods for including the loop closure equations are then discussed: the Lagrange multipliers method and the method based on an explicit solution of the constraint equations. In the first case the dynamic model is given in the form of an implicit Differential Algebraic Equations (DAE) system, while in the second case an Ordinary Differential Equations (ODE) system could be obtained.     

Controllability results for the Moore–Gibson–Thompson equation arising in nonlinear acoustics

We show that the Moore–Gibson–Thomson equation

$\tau {?}_{ttt}y+\alpha {?}_{tt}y?c^2\mathrm{\Delta }y?b\mathrm{\Delta }{?}_{t}y=k{?}_{tt}(y^2)+{\chi }_{\omega (t)}u,$

is controlled by a force that is supported on an moving subset $\omega (t)$ of the domain, satisfying a geometrical condition. Using the concept of approximately outer invertible map, a generalized implicit function theorem and assuming that $\gamma :=\alpha ?\frac{\tau c^2}{b}>0$, the local null controllability in the nonlinear case is established. Moreover, the analysis of the critical value $\gamma =0$ for the linear equation is included.     

关于“解一维热传导方程的高精度的隐式差分格式”一文的评注

本文指出了文[1]中存在的几个问题。     

A note on the classification of anisotropy of bodies defined by implicit constitutive relations

In this note we consider the definition of anisotropy with regard to the response of bodies described by implicit constitutive relations. The class of response relations under considerations in this work is implicit relations between the history of the stress, the history of the density, and the history of the deformation gradient. It is shown that the work of Noll [4] defining the anisotropy of bodies in terms of symmetry groups for Simple Materials can be very easily extended to define the anisotropy in terms of symmetry groups for materials whose response is described by relations between the histories of the stresses and the deformation gradient. While symmetry groups are defined, the more arduous task of developing representation theorems for bodies defined through implicit response relations is an important open task.     

A modified implicit Monte Carlo method for time-dependent radiative transfer with adaptive material coupling

In this paper we develop a robust implicit Monte Carlo (IMC) algorithm based on more accurately updating the linearized equilibrium radiation energy density. The method does not introduce oscillations in the solution and has the same limit as Δt→∞$\mathrm{\Delta }t\to \infty$ as the standard Fleck and Cummings IMC method. Moreover, the approach we introduce can be trivially added to current implementations of IMC by changing the definition of the Fleck factor. Using this new method we develop an adaptive scheme that uses either standard IMC or the modified method basing the adaptation on a zero-dimensional problem solved in each cell. Numerical results demonstrate that the new method can avoid the nonphysical overheating that occurs in standard IMC when the time step is large. The method also leads to decreased noise in the material temperature at the cost of a potential increase in the radiation temperature noise.