Computer-assisted Modelling and Analysis of Linear Programming Problems: Towards a Unified Framework

A framework for model formulation and analysis to support operationsand management of large-scale linear programs is developed fromthe combined capabilities of CAMPS and ANALYZE. Both the systemsare reviewed briefly and the interface which integrates thetwo systems is then described. The model formulation, matrixgeneration, and model management capability of CAMPS and thecomplementary model and solution analysis capability of ANALYZEare presented within a unified framework. Relevant generic functionsare highlighted, and an example is presented in detail to illustratethe level of integration achieved in the current prototype system.Some new results on discourse models and model management supportare given in a framework designed to move toward an ‘intelligent’system for linear programming modelling and analysis.     

Two-texture zeros and near-maximal atmospheric neutrino mixing angle

We study the implications of a large value of the effective Majorana neutrino mass for a class of two-texture zero neutrino mass matrices in the flavour basis. We find that these textures predict near-maximal atmospheric neutrino mixing angle in the limit of large effective Majorana neutrino mass. We present the symmetry realization of these textures using the discrete cyclic group Z₃. It is found that the texture zeros realized in this work remain stable under the renormalization group running of the effective neutrino mass matrix at one-loop level.     

Electroweak symmetry breaking beyond the Standard Model

In this paper, two key issues related to electroweak symmetry breaking are addressed. First, how fine-tuned different models are that trigger this phenomenon? Second, even if a light Higgs boson exists, does it have to be necessarily elementary? After a brief introduction, the fine-tuning aspects of the MSSM, NMSSM, generalized NMSSM and GMSB scenarios shall be reviewed, then the little Higgs, composite Higgs and the Higgsless models shall be compared. Finally, a broad overview will be given on where we stand at the end of 2011.     

Review of dark matter direct detection experiments

Matter, as we know it, makes up less than 5% of the Universe. Various astrophysical observations have confirmed that one quarter of the Universe and most of the matter content in the Universe is made up of dark matter. The nature of dark matter is yet to be discovered and is one of the biggest questions in physics. Particle physics combined with astrophysical measurements of the abundance gives rise to a dark matter candidate called weakly interacting massive particle (WIMP). The low density of WIMPs in the galaxies and the extremely weak nature of the interaction with ordinary matter make detection of the WIMP an extraordinarily challenging task, with abundant fakes from various radioactive and cosmogenic backgrounds with much stronger electromagnetic interaction. The extremely weak nature of the WIMP interaction dictates detectors that have extremely low naturally occurring radioactive background, a large active volume (mass) of sensitive detector material to maximize statistics, a highly efficient detector-based rejection mechanism for the dominant electromagnetic background and sophisticated analysis techniques to reject any residual background. This paper reviews currently available major technologies being pursued by various collaborations, with special emphasis on the cryogenic Ge detector technology used by the Cryogenic Dark Matter Search Collaboration (CDMS).     

The use of linear programming duality in mixed integer programming

This paper is about the primal-dual relationship in a mixedinteger programming problem (MIP) in which integer variablesare binary. It shows how the primal-dual relationship of a linearprogramming problem (LP) can be used to advantage in MIPs. Thecentral idea is to look conceptually at the nature of all possibleLPs that arise from all possible settings for the discrete variablesin order to deduce general properties of the solution set. Afterdeveloping the relevant theory, we show the usefulness of thisaproach by applying it to three totally different problems.New results are derived for the method of least median of squaresin robust regression, the problem of rectilinear obnoxious-facilitylocation, and the problem of finding a fixed-size rectanglecontaining the minimum weight of points.     

Phase-locked solutions and their stability in the presence of propagation delays

We investigate phase-locked solutions of a continuum field of nonlocally coupled identical phase oscillators with distance-dependent propagation delays. Equilibrium relations for both synchronous and travelling wave solutions in the parameter space characterizing the nonlocality and time delay are delineated. For the synchronous states a comprehensive stability diagram is presented that provides a heuristic synchronization condition as well as an analytic relation for the marginal stability curve. The relation yields simple stability expressions in the limiting cases of local and global coupling of phase oscillators.     

The Hoyle state in nuclear lattice effective field theory

We review the calculation of the Hoyle state of ¹²C in nuclear lattice effective field theory (NLEFT) and its anthropic implications in the nucleosynthesis of ¹²C and ¹⁶O in red giant stars. We also analyse the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the α nuclei ¹⁶O, ²⁰Ne, ²⁴Mg, and ²⁸Si by Euclidean time projection. Finally, we discuss recent NLEFT results for the spectrum, electromagnetic properties, and α-cluster structure of ¹⁶O.     

Fragmentation and momentum correlations in heavy-ion collisions

The role of momentum correlations in the production of light and medium mass fragments is studied by imposing momentum cut in the clusterization of the phase space. Our detailed investigation shows that momentum cut has a major role to play in the emission of fragments. A comparison with the experimental data is also presented. The calculations showed better agreement with the experimental data when momentum cut is imposed.