The energy and the linear momentum of space-times in general relativity

We extend our previous proof of the positive mass conjecture to allow a more general asymptotic condition proposed by York. Hence we are able to prove that for an isolated physical system, the energy momentum four vector is a future timelike vector unless the system is trivial. Furthermore, we allow singularities of the type of black holes.Supported in part by an NSF grant     

Absence of simulation evidence for critical depletion in slit pores

Recent Monte Carlo simulation studies of a Lennard-Jones fluid confined to a mesoscopic slit pore have reported evidence of "critical depletion" in the pore local number density near the liquid-vapor critical point. In this Brief Report we demonstrate that the observed depletion effect is in fact a simulation artifact arising from small systematic errors associated with the use of long range corrections for the potential truncation. Owing to the large near-critical compressibility, these errors lead to significant changes in the pore local number density. We suggest ways of avoiding similar problems in future studies of confined fluids.     

New results for molecular formation under pairwise potential minimization

We establish new lower bounds on the distance between two points of a minimum energy configuration of N points in ℝ³ interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, which improves previously known lower bounds. Moreover, we prove that the optimal configuration cannot be two-dimensional, and establish an upper bound for the distance to the nearest neighbour of every particle, which depends on the position of this particle. On the boundary of the optimal configuration polytope, this is unity while in the interior, this bound depends on the potential function. In the Lennard-Jones case, we get the value . Also, denoting by V _N the global minimum in an N point minimum energy configuration, we prove in Lennard-Jones clusters for all N≥2, while asymptotically holds (as opposed to in the planar case, confirming non-planarity for large N).     

Refined asymptotics for constant scalar curvature metrics with isolated singularities

We consider the asymptotic behaviour of positive solutions u of the conformal scalar curvature equation, , in the neighbourhood of isolated singularities in the standard Euclidean ball. Although asymptotic radial symmetry for such solutions was proved some time ago, [2], we present a much simpler and more geometric derivation of this fact. We also discuss a refinement, showing that any such solution is asymptotic to one of the deformed radial singular solutions. Finally we give some applications of these refined asymptotics, first to computing the global Pohožaev invariants of solutions on the sphere with isolated singularities, and then to the regularity of the moduli space of all such solutions. Oblatum 26-II-1997 & 6-II-1998 / Published online: 12 November 1998     

Local search based heuristics for global optimization: Atomic clusters and beyond

Finding good solutions to large scale, hard, global optimization problems, is a demanding task with many relevant applications. It is well known that, in order to tackle a difficult problem, an algorithm has to incorporate all of the available information on the problem domain. However, as we will show in this paper, some general purpose methods and the ideas on which they are built can provide guidance towards the efficient solution of difficult instances. Most of this paper will be devoted to heuristic techniques applied to the problem of finding a minimum energy configuration of a cluster of atoms in R³${\mathbb{R}}^3$. This is a very relevant problem with a large set of applications which has triggered considerable research efforts in the last decade. We will show how some relatively simple ideas can be used to generate fairly efficient methods which have been employed to discover many new cluster structures. In this paper we will introduce some of the main algorithmic ideas which have proven to be particularly successful in the field of global optimization applied to atomic cluster conformation problems. We will mainly discuss Basin Hopping methods, as well as their population–based variant, and some specific technique based on “direct moves”. These methods, although designed for the specific problem, have a much wider applicability. In fact, one of the aims of this paper is also that of suggesting that similar ideas can be employed in order to design innovative methods even for totally different global optimization problems, like, e.g., circle packing and space trajectory planning.     

ChemInform Abstract: Structure Prediction of Binary Pernitride MN2 Compounds (M: Ca,Sr, Ba,La, and Ti)

Based on ab initio calculations at various pressures meta(stable) modifications of CaN₂, LaN₂, and TiN₂ are predicted.     

Defect topologies in a nematic liquid crystal near a patchy colloid

Using isothermal-isobaric Monte Carlo simulations we investigate defect topologies due to a spherical colloidal particle immersed in a nematic liquid crystal. Defects arise because of the competition between the preferential orientation at the colloid's surface and the far-field director ?n(0). Considering a chemically homogeneous colloid as a special case we observe the well-known surface and saturn ring defect topologies for weak and strong perpendicular anchoring, respectively; for homogeneous, strong parallel anchoring we find a boojum defect topology that has been seen experimentally [see P. Poulin and D. A. Weitz, Phys. Rev. E 57, 626 (1998)] but not in computer simulations. We also consider a heterogeneous, patchy colloid where the liquid-crystal molecules anchor either preferentially planar or perpendicular at the surface of the colloid. For a patchy colloid we observe a boojum ring defect topology in agreement with recent experimental studies [see M. Conradi, M. Ravnik, M. Bele, M. Zorko, S. Z?umer, and I. Mus?evic?, Soft Matter 5, 3905 (2009)]. We also observe two other novel defect topologies that have not been reported thus far neither experimentally nor theoretically.     

Investigation of an enhanced resolution triple quadrupole mass spectrometer for high-throughput liquid chromatography/tandem mass spectrometry assays

Triple quadrupole mass spectrometers, when operated in multiple reaction monitoring (MRM) mode, offer a unique combination of sensitivity, specificity, and dynamic range. Consequently, the triple quadrupole is the workhorse for high-throughput quantitation within the pharmaceutical industry. However, in the past, the unit mass resolution of quadrupole instruments has been a limitation when interference from matrix or metabolites cannot be eliminated. With recent advances in instrument design, triple quadrupole instruments now afford mass resolution of less than 0.1 Dalton (Da) full width at half maximum (FWHM). This paper describes the evaluation of an enhanced resolution triple quadrupole mass spectrometer for high-throughput bioanalysis with emphasis on comparison of selectivity, sensitivity, dynamic range, precision, accuracy, and stability under both unit mass (1 Da FWHM) and enhanced (相似文献