Three small cubic graphs with interesting hamiltonian properties

We present here three graphs, which are the smallest known ones of their kind: a cubic three-connected planar nontraceable graph, a cubic three-connected planar graph which is not homogeneously traceable, and a cubic one-Hamiltonian graph which is not Hamiltonian connected.     

Current trends in lead discovery: are we looking for the appropriate properties?

The new drug discovery paradigm is based on high-throughput technologies, both with respect to synthesis and screening. The progression HTS hits lead series candidate drug marketed drug appears to indicate that the probability of reaching launched status is one in a million. This has shifted the focus from good quality candidate drugs to good quality leads. We examined the current trends in lead discovery by comparing MW (molecular weight), LogP (octanol/water partition coefficient, estimated by Kowwin [17]) and LogSw (intrinsic water solubility, estimated by Wskowwin [18]) for the following categories: 62 leads and 75 drugs [11]; compounds in the development phase (I, II, III and launched), as indexed in MDDR; and compounds indexed in medicinal chemistry journals [ref. 20], categorized according to their biological activity. Comparing the distribution of the above properties, the 62 lead structures show the lowest median with respect to MW (smaller) and LogP (less hydrophobic), and the highest median with respect to LogSw (more soluble). By contrast, over 50% of the medicinal chemistry compounds with activities above 1 nanomolar have MW > 425, LogP > 4.25 and LogSw < -4.75, indicating that the reported active compounds are larger, more hydrophobic and less soluble when compared to time-tested quality leads. In the MDDR set, a progressive constraint to reduce MW and LogP, and to increase LogSw, can be observed when examining trends in the developmental sequence: phase I, II, III and launched drugs. These trends indicate that other properties besides binding affinity, e.g., solubility and hydrophobicity, need to be considered when choosing the appropriate leads.     

Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.     

Investigation of advanced strain-path dependent material models for sheet metal forming simulations

Sheet metal forming processes often involve complex loading sequences. To improve the prediction of some undesirable phenomena, such as springback, physical behavior models should be considered. This paper investigates springback behavior predicted by advanced elastoplastic hardening models which combine isotropic and kinematic hardening and take strain-path changes into account. A dislocation-based microstructural hardening model formulated from physical observations and the more classical cyclic model of Chaboche have been considered in this work. Numerical implementation was carried out in the ABAQUS software using a return mapping algorithm with a combined backward Euler and semi-analytical integration scheme of the constitutive equations. The capability of each model to reproduce transient hardening phenomena at abrupt strain-path changes has been shown via simulations of sequential rheological tests. A springback analysis of strip drawing tests was performed in order to emphasize the impact of several influential parameters, namely: process, numerical and behavior parameters. The effect of the two hardening models with respect to the process parameters has been specifically highlighted.