Weak type heterodimensional cycle bifurcation with orbit-flip

In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence conditio...     

A life cycle framework for the investigation of environmentally benign nanoparticles and products

While significant advances in our understanding of the behavior of engineered nanoparticles in the environment continue, there remains a need to engage the nanoparticle research community directly in the development and evaluation of environmentally benign nanoparticles to ensure that nanomaterial‐based industries emerge as tools for sustainability rather than environmental liabilities. Current research efforts aimed at understanding the environmental implications of nanotechnology emphasize existing groups of nanoparticles and products already in commercial distribution. While this is clearly necessary, this approach fails to identify and address the many tradeoffs associated with product performance and environmental quality. We believe this to be a critical gap in the ongoing exploration of nanostructured materials and their properties and applications. We posit that a number of issues are not being holistically addressed, including resource availability and allocation, manufacturing energy requirements and embodied energy, material efficiency, environmental properties of nanomaterials and nanoproducts, and waste generation. An interdisciplinary approach to research, based on the life cycle paradigm and devoted to the identification, investigation, synthesis, testing, and analysis of groups of new, more environmentally conscious nanoparticles is needed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radioactive waste partitioning and transmutation within advanced fuel cycles: Achievements and challenges

If nuclear power becomes a sustainable source of energy, a safe, robust, and acceptable solution must be pursued for existing and projected inventories of high-activity, long-lived radioactive waste. Remarkable progress in the field of geological disposal has been made in the last two decades. Some countries have reached important milestones, and geological disposal (of spent fuel) is expected to start in 2020 in Finland and in 2022 in Sweden. In fact, the licensing of the geological repositories in both countries is now entering into its final phase. In France, disposal of intermediate-level waste (ILW) and vitrified high-level waste (HLW) is expected to start around 2025, according to the roadmap defined by an Act of Parliament in 2006. In this context, transmutation of part of the waste through use of advanced fuel cycles, probably feasible in the coming decades, can reduce the burden on the geological repository. This article presents the physical principle of transmutation and reviews several strategies of partitioning and transmutation (P&T). Many recent studies have demonstrated that the impact of P&T on geological disposal concepts is not overwhelmingly high. However, by reducing waste heat production, a more efficient utilization of repository space is likely. Moreover, even if radionuclide release from the waste to the environment and related calculated doses to the population are only partially reduced by P&T, it is important to point out that a clear reduction of the actinide inventory in the HLW definitely reduces risks arising from less probable evolutions of a repository (i.e., an increase of actinide mobility in certain geochemical situations and radiological impact by human intrusion).     

On Toughness and Hamiltonicity of 2K2‐Free Graphs

The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields components. Determining toughness is an NP‐hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K₂‐free graphs, that is, graphs that do not contain two vertex‐disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K₂‐free graphs.     

Biembedding a Steiner Triple System With a Hamilton Cycle Decomposition of a Complete Graph

We construct a face two‐colourable, blue and green say, embedding of the complete graph in a nonorientable surface in which there are blue faces each of which have a hamilton cycle as their facial walk and green faces each of which have a triangle as their facial walk; equivalently a biembedding of a Steiner triple system of order n with a hamilton cycle decomposition of , for all and . Using a variant of this construction, we establish the minimum genus of nonorientable embeddings of the graph , for where and .     

Orientable Hamilton Cycle Embeddings of Complete Tripartite Graphs II: Voltage Graph Constructions and Applications

In an earlier article the authors constructed a hamilton cycle embedding of in a nonorientable surface for all and then used these embeddings to determine the genus of some large families of graphs. In this two‐part series, we extend those results to orientable surfaces for all . In part II, a voltage graph construction is presented for building embeddings of the complete tripartite graph on an orientable surface such that the boundary of every face is a hamilton cycle. This construction works for all such that p is prime, completing the proof started by part I (which covers the case ) that there exists an orientable hamilton cycle embedding of for all , . These embeddings are then used to determine the genus of several families of graphs, notably for and, in some cases, for .     

Averaging on slow and fast cycles of a three time scale system

Pontryagin–Rodygin?s Theorem for slow and fast systems describes the slow drift during the rolling up of the trajectories around the cycles of the fast dynamics. This drift is approximated by the averaging on the cycles. The calculation of this average is generally a difficult task since it requires the knowledge of the closed orbits and their periods. We present two paradigms of three time scale systems where we can overcome this limitation. It is the case of systems the fast dynamics of which have cycles with relaxation presenting or not a canard phenomenon. We can not apply Pontryagin–Rodygin?s Theorem to these systems because their fast equation is itself singularly perturbed. We also investigate the extension of the results to unbounded time intervals. The results are stated classically and proved within the framework of nonstandard analysis.     

Limit cycle bifurcations by perturbing a class of integrable systems with a polycycle

In this paper, we deal with the problem of limit cycle bifurcation near a 2-polycycle or 3-polycycle for a class of integrable systems by using the first order Melnikov function. We first get the formal expansion of the Melnikov function corresponding to the heteroclinic loop and then give some computational formulas for the first coefficients of the expansion. Based on the coefficients, we obtain a lower bound for the maximal number of limit cycles near the polycycle. As an application of our main results, we consider quadratic integrable polynomial systems, obtaining at least two limit cycles.