J Predictions for Defective Pipe Elbows via the Reference Stress Method

In R6, the J-based failure assessment diagram (FAD) method is used in the fracture assessment, and is underpinned by the reference stress J scheme. Therefore, an assessment using the R6 FAD method is equivalent to a J prediction using the reference stress method. In this paper, the effect of global and local limit load solutions for defective elbows on the reference stress and hence the J predictions is investigated using published three dimensional elastic-plastic finite element (FE) J results, in order to create guidance for users to follow when performing structural integrity assessments of defective elbows using the R6 procedure. The results show that using the global limit load solutions recommended in this paper can lead to good and reasonably conservative J predictions. However, the availability of global limit load solutions is very limited. The results also show that using the local limit load evaluated from the local limit load model recommended in this paper can lead to conservative J predictions for most of the cases considered.

Applications of, and Extensions to, Selected Exact Solutions in General Relativity

<p>In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.</p>

Applications of, and Extensions to, Selected Exact Solutions in General Relativity

<p>In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing down any arbitrary polarisation in this form. In addition to this we have extended this algorithm to an arbitrary number of dimensions, and have written down an explicit solution for a circularly polarized Rosen wave. In the second part a particular, ultra-local limit along an arbitrary timelike geodesic in any spacetime is constructed, in close analogy with the well-known lightlike Penrose limit. This limit results in a Bianchi type I spacetime. The properties of these spacetimes are examined in the context of this limit, including the Einstein equations, stress-energy conservation and Raychaudhuri equation. Furthermore the conditions for the Bianchi type I spacetime to be diagonal are explicitly set forward, and the effect of the limit on the matter content of a spacetime are examined.</p>

On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws

We deal with the numerical investigation of the local limit of nonlocal conservation laws. Previous numerical experiments seem to suggest that the solutions of the nonlocal problems converge to the entropy admissible solution of the conservation law in the singular local limit. However, recent analytical results state that (i) in general convergence does not hold because one can exhibit counterexamples; (ii)~convergence can be recovered provided viscosity is added to both the local and the nonlocal equations. Motivated by these analytical results, we investigate the role of numerical viscosity in the numerical study of the local limit of nonlocal conservation laws. In particular, we show that Lax-Friedrichs type schemes may provide the wrong intuition and erroneously suggest that the solutions of the nonlocal problems converge to the entropy admissible solution of the conservation law in cases where this is ruled out by analytical results. We also test Godunov type schemes, less affected by numerical viscosity, and show that in some cases they provide an intuition more in accordance with the analytical results.

Local limit theorems for generalized scheme of allocation of particles into ordered cells

A generalized scheme of allocation of n particles into ordered cells (components). Some statements containing sufficient conditions for the weak convergence of the number of components with given cardinality and of the total number of components to the negative binomial distribution as n → ∞ are presented as hypotheses. Examples supporting the validity of these statements in particular cases are considered. For some examples we prove local limit theorems for the total number of components which partially generalize known results on the convergence of this distribution to the normal law.

Non-uniformly parabolic equations and applications to the random conductance model

We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $$\mathbb Z^d$$ Z d . In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.