Coarse-Graining and Renormalization of Atomistic Binding Relations and Universal Macroscopic Cohesive Behavior

We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large---but finite---number of interatomic planes and find that the macroscopic cohesive law adopts a universal asymptotic form. The universal form of the macroscopic cohesive law is an attractive fixed point of a suitably-defined renormalization-group transformation.Comment: 15 pages, 6 figures, submitted to the Journal of the Mechanics and Physics of Solid

Isostaticity and the solidification of semiflexible polymer melts

Using molecular dynamics simulations of a tangent-soft-sphere bead-spring polymer model, we examine the degree to which semiflexible polymer melts solidify at isostaticity. Flexible and stiff chains crystallize when they are isostatic as defined by appropriate degree-of-freedom-counting arguments. Semiflexible chains also solidify when isostatic if a generalized isostaticity criterion that accounts for the slow freezing out of configurational freedom as chain stiffness increases is employed. The dependence of the average coordination number at solidification $Z(T_s)$ on chains' characteristic ratio $C_\infty$ has the same functional form [$Z \simeq a - b\ln(C_\infty)$] as the dependence of the average coordination number at jamming $Z(\phi_J)$ on $C_\infty$ in athermal systems, suggesting that jamming-related phenomena play a significant role in thermal polymer solidification

Introducing the VRT gas turbine combustor

An innovative annular combustor configuration is being developed for aircraft and other gas turbine engines. This design has the potential of permitting higher turbine inlet temperatures by reducing the pattern factor and providing a major reduction in NO(x) emission. The design concept is based on a Variable Residence Time (VRT) technique which allows large fuel particles adequate time to completely burn in the circumferentially mixed primary zone. High durability of the combustor is achieved by dual function use of the incoming air. The feasibility of the concept was demonstrated by water analogue tests and 3-D computer modeling. The computer model predicted a 50 percent reduction in pattern factor when compared to a state of the art conventional combustor. The VRT combustor uses only half the number of fuel nozzles of the conventional configuration. The results of the chemical kinetics model require further investigation, as the NO(x) predictions did not correlate with the available experimental and analytical data base

SLE_k: correlation functions in the coefficient problem

We apply the method of correlation functions to the coefficient problem in stochastic geometry. In particular, we give a proof for some universal patterns conjectured by M. Zinsmeister for the second moments of the Taylor coefficients for special values of kappa in the whole-plane Schramm-Loewner evolution (SLE_kappa). We propose to use multi-point correlation functions for the study of higher moments in coefficient problem. Generalizations related to the Levy-type processes are also considered. The exact multifractal spectrum of considered version of the whole-plane SLE_kappa is discussed

Third type of domain wall in soft magnetic nanostrips

Magnetic domain walls (DWs) in nanostructures are low-dimensional objects that separate regions with uniform magnetisation. Since they can have different shapes and widths, DWs are an exciting playground for fundamental research, and became in the past years the subject of intense works, mainly focused on controlling, manipulating, and moving their internal magnetic configuration. In nanostrips with in-plane magnetisation, two DWs have been identified: in thin and narrow strips, transverse walls are energetically favored, while in thicker and wider strips vortex walls have lower energy. The associated phase diagram is now well established and often used to predict the low-energy magnetic configuration in a given magnetic nanostructure. However, besides the transverse and vortex walls, we find numerically that another type of wall exists in permalloy nanostrips. This third type of DW is characterised by a three-dimensional, flux closure micromagnetic structure with an unusual length and three internal degrees of freedom. Magnetic imaging on lithographically-patterned permalloy nanostrips confirms these predictions and shows that these DWs can be moved with an external magnetic field of about 1mT. An extended phase diagram describing the regions of stability of all known types of DWs in permalloy nanostrips is provided.Comment: 19 pages, 7 figure

The average connectivity matrix of a graph

For a graph $G$ and for two distinct vertices $u$ and $v$, let $\kappa(u,v)$ be the maximum number of vertex-disjoint paths joining $u$ and $v$ in $G$. The average connectivity matrix of an $n$-vertex connected graph $G$, written $A_{\bar{\kappa}}(G)$, is an $n\times n$ matrix whose $(u,v)$-entry is $\kappa(u,v)/{n \choose 2}$ and let $\rho(A_{\bar{\kappa}}(G))$ be the spectral radius of $A_{\bar{\kappa}}(G)$. In this paper, we investigate some spectral properties of the matrix. In particular, we prove that for any $n$-vertex connected graph $G$, we have $\rho(A_{\bar{\kappa}}(G)) \le \frac{4\alpha'(G)}n$, which implies a result of Kim and O \cite{KO} stating that for any connected graph $G$, we have $\bar{\kappa}(G) \le 2 \alpha'(G)$, where $\bar{\kappa}(G)=\sum_{u,v \in V(G)}\frac{\kappa(u,v)}{{n\choose 2}}$ and $\alpha'(G)$ is the maximum size of a matching in $G$; equality holds only when $G$ is a complete graph with an odd number of vertices. Also, for bipartite graphs, we improve the bound, namely $\rho(A_{\bar{\kappa}}(G)) \le \frac{(n-\alpha'(G))(4\alpha'(G) - 2)}{n(n-1)}$, and equality in the bound holds only when $G$ is a complete balanced bipartite graph