Influence of Succinimide Dispersants on Film Formation, Friction and Antiwear Properties of Zinc Dialkyl Dithiophosphate

ZDDP (zinc dialkyldithiophosphate) is arguably the most successful antiwear additive ever employed in crankcase engine lubricants. It was originally used as an antioxidant and shortly afterwards recognized for its antiwear and extreme pressure properties. Unfortunately, another critical additive polyisobutylsuccinimide-polyamine (PIBSA-PAM), which is used as a dispersant in engine oils, is known to be antagonistic to ZDDP in terms of film formation, friction and wear. The mechanisms of this antagonism have been widely studied, but they are still not well understood. Furthermore, in order to protect engine exhaust catalysts from sulphated ash, phosphorus and sulphur (SAPS) and extend drain intervals of engine lubricants, a progressive reduction in ZDDP quantity but a growth in the use of PIBSA-PAM is required. The aim of this study is to explore the mechanisms and practical effects of the antagonism between ZDDP and PIBSA-PAM. Of particular interest is the impact on performance of the ratio of ZDDP to PIBSA-PAM, as measured by P:N ratio. Since ZDDP is a very effective antiwear additive, it produces only very low or "mild" rates of wear. To study this requires a new way to measure mild wear behaviour of formulated oils. Several techniques have been applied in this study to investigate the film formation, friction and wear properties of ZDDP- and/or PIBSA-PAM-containing oils. These include a new mild wear testing method, which is tested and developed using a range of different types of additives. It is found that the ratio of P:N plays a strong role in determining tribofilm formation and friction of ZDDP/PIBSA-PAM blends. However it plays a much weaker role in determining wear behaviour. It is found that some PIBSA-PAMs have considerable friction-reducing properties in their own right. The results suggest that PIBSA-PAM may interfere with the behaviour of ZDDP in several ways: by forming a ZDDP/ PIBSA-PAM complex at the metal surfaces to reduce the local activity of ZDDP; by PIBSA-PAM partially removing the ZDDP film; possibly also by PIBSA-PAM blocking ZDDP from metal surfaces. The newly-developed wear testing method can be used conveniently and effectively to study mild wear properties not just of ZDDP but of a wide range of other additives

Average-case Approximation Ratio of Scheduling without Payments

Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and approximation schemes of Theoretical Computer Science. For instance, the approximation ratio, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs. In this paper, we take the average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design -- the scheduling problem [Nisan and Ronen 1999]. One version of this problem which includes a verification component is studied by [Koutsoupias 2014]. It was shown that the problem has a tight approximation ratio bound of (n+1)/2 for the single-task setting, where n is the number of machines. We show, however, when the costs of the machines to executing the task follow any independent and identical distribution, the average-case approximation ratio of the mechanism given in [Koutsoupias 2014] is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio, and indicates that the optimal mechanism for the problem actually works well on average, although in the worst-case the expected cost of the mechanism is Theta(n) times that of the optimal cost

Laplacian coefficients of unicyclic graphs with the number of leaves and girth

Let $G$ be a graph of order $n$ and let $\mathcal{L}(G,\lambda)=\sum_{k=0}^n (-1)^{k}c_{k}(G)\lambda^{n-k}$ be the characteristic polynomial of its Laplacian matrix. Motivated by Ili\'{c} and Ili\'{c}'s conjecture [A. Ili\'{c}, M. Ili\'{c}, Laplacian coefficients of trees with given number of leaves or vertices of degree two, Linear Algebra and its Applications 431(2009)2195-2202.] on all extremal graphs which minimize all the Laplacian coefficients in the set $\mathcal{U}_{n,l}$ of all $n$-vertex unicyclic graphs with the number of leaves $l$, we investigate properties of the minimal elements in the partial set $(\mathcal{U}_{n,l}^g, \preceq)$ of the Laplacian coefficients, where $\mathcal{U}_{n,l}^g$ denote the set of $n$-vertex unicyclic graphs with the number of leaves $l$ and girth $g$. These results are used to disprove their conjecture. Moreover, the graphs with minimum Laplacian-like energy in $\mathcal{U}_{n,l}^g$ are also studied.Comment: 19 page, 4figure

Effective potential calculation of the MSSM lightest CP-even Higgs boson mass

I summarize results of two-loop effective potential calculations of the lightest CP-even Higgs boson mass in the minimal supersymmetric standard model.Comment: 4 pages, 1 figur