Molecular dynamics simulation of processing using AFM pin tool

A three-dimensional molecular dynamics (MD) model is utilized to investigate the effect of tool geometry on the deformation process of the workpiece and the nature of deformation process at the atomic-scale. Results show that different states exist between the atomic force microscope (AFM) pin tool and the workpiece surface, i.e. the non-wear state, the ploughing state, the state in which ploughing is dominant and the state in which cutting plays a key role. A relationship between the deformation process of the workpiece and the potential energy variation is presented. The potential energy variation of atoms in different deformed regions in the workpiece such as plastically deformed region, elastically deformed region and the mixed deformation region is different. The features of variations of potential energy are discussed.     

Primal cutting plane algorithms revisited

Dual fractional cutting plane algorithms, in which cutting planes are used to iteratively tighten a linear relaxation of an integer program, are well-known and form the basis of the highly successful branch-and-cut method. It is rather less well-known that various primal cutting plane algorithms were developed in the 1960s, for example by Young. In a primal algorithm, the main role of the cutting planes is to enable a feasible solution to the original problem to be improved. Research on these algorithms has been almost non-existent.  In this paper we argue for a re-examination of these primal methods. We describe a new primal algorithm for pure 0-1 problems based on strong valid inequalities and give some encouraging computational results. Possible extensions to the case of general mixed-integer programs are also discussed.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

The push-out region of an immersed manifold

We consider immersions: and construct a subspace of which corresponds to a set of embedded manifolds which are either parallel to f, tubes around f or, in general, partial tubes around f. This space is invariant under the action of the normal holonomy group, We investigate the case where is non-trivial and obtain some results on the number of connected components of . Received 24 March 2000.     

Nielsen realization for 3-manifolds containing two-sided projective planes

For compact irreducible sufficiently large 3-manifolds containing 2-sided projective planes, we consider the following Realization Problem: Given a finite subgroup of the outer automorphism group of the fundamental group, is there a finite group of homeomorphisms, which induces this subgroup? Received: 16 November 1999; in final form: 18 January 2001 / Published online: 8 November 2002     

Rank-perfect and" weakly rank-perfect graphs

An edge e of a perfect graph G is critical if G−e is imperfect. We would like to decide whether G−e is still “almost perfect” or already “very imperfect”. Via relaxations of the stable set polytope of a graph, we define two superclasses of perfect graphs: rank-perfect and weakly rank-perfect graphs. Membership in those two classes indicates how far an imperfect graph is away from being perfect. We study the cases, when a critical edge is removed from the line graph of a bipartite graph or from the complement of such a graph.     

Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001