Covering continuous demand in the plane

Continuous demand is generated in a convex polygon. A facility located in the area covers demand within a given radius. The objective is to find the locations for p facilities that cover the maximum demand in the area. A procedure that calculates the total area covered by a set of facilities is developed. A multi start heuristic approach for solving this problem is proposed by applying a gradient search from a randomly generated set of p locations for the facilities. Computational experiments for covering a square area illustrate the effectiveness of the proposed algorithm.     

Vehicle routing and scheduling with time-varying data: A case study

A heuristic algorithm is described for vehicle routing and scheduling problems to minimise the total travel time, where the time required for a vehicle to travel along any road in the network varies according to the time of travel. The variation is caused by congestion that is typically greatest during morning and evening rush hours. The algorithm is used to schedule a fleet of delivery vehicles operating in the South West of the United Kingdom for a sample of days. The results demonstrate how conventional methods that do not take time-varying speeds into account when planning, except for an overall contingency allowance, may still lead to some routes taking too long. The results are analysed to show that in the case study using the proposed approach can lead to savings in CO₂ emissions of about 7%.     

Modelling credit risk of portfolio of consumer loans

One of the issues that the Basel Accord highlighted was that, though techniques for estimating the probability of default and hence the credit risk of loans to individual consumers are well established, there were no models for the credit risk of portfolios of such loans. Motivated by the reduced form models for credit risk in corporate lending, we seek to exploit the obvious parallels between behavioural scores and the ratings ascribed to corporate bonds to build consumer-lending equivalents. We incorporate both consumer-specific ratings and macroeconomic factors in the framework of Cox Proportional Hazard models. Our results show that default intensities of consumers are significantly influenced by macro factors. Such models then can be used as the basis for simulation approaches to estimate the credit risk of portfolios of consumer loans.     

Cosmic ray studies with the L3-cosmics program at CERN

The L3 detector at the CERN electron-positron collider had a muon spectrometer which was employed during the last years of LEP operation for cosmic ray studies. The results of this program include a precise muon spectrum and charge ratio between 20 GeV and 3 TeV, a limit on TeV primary antiprotons from a study of the Moon’s shadow, the (possible) observation of a are signal from a fixed position in the northern hemisphere through muons, a solar anisotropy of 200 GeV protons, and other results. Negative limits on muons associated with known H.E. gamma sources or gamma bursts, the search for anomalous H.E. interaction or decay events such as reported from the Kolar Gold Fields, and a search for muons correlated with a solar are are also noted.     

Computing the Loewner Driving Process of Random Curves in the Half Plane

We simulate several models of random curves in the half plane and numerically compute the stochastic driving processes that produce the curves through the Loewner equation. Our models include models whose scaling limit is the Schramm-Loewner evolution (SLE) and models for which it is not. We study several tests of whether the driving process is Brownian motion, as it is for SLE. We find that testing only the normality of the process at a fixed time is not effective at determining if the random curves are an SLE. Tests that involve the independence of the increments of Brownian motion are much more effective. We also study the zipper algorithm for numerically computing the driving function of a simple curve. We give an implementation of this algorithm which runs in a time O(N ^1.35) rather than the usual O(N ²), where N is the number of points on the curve.     

Superconducting state parameters of binary metallic glasses

Ashcroft’s empty core (EMC) model potential is used to study the superconducting state parameters (SSPs) viz. electron-phonon coupling strength λ, Coulomb pseudopotential μ*, transition temperature T _C , isotope effect exponent αand effective interaction strength N _O V of some binary metallic glasses based on the superconducting (S), conditional superconducting (S’) and non-superconducting (NS) elements of the periodic table. Five local field correction functions proposed by Hartree (H), Taylor (T), Ichimaru-Utsumi (IU), Farid et al. (F) and Sarkar et al. (S) are used for the first time with EMC potential in the present investigation to study the screening influence on the aforesaid properties. The T _C obtained from the H-local field correction function are in excellent agreement with available theoretical or experimental data. In the present computation, the use of the pseudo-alloy-atom model (PAA) was proposed and found successful. Present work results are in qualitative agreement with such earlier reported experimental values which confirm the superconducting phase in all metallic glasses. A strong dependency of the SSPs of the metallic glasses on the valence ‘Z’ is identified.      

Dimer Coverings on the Sierpinski Gasket

We present the number of dimer coverings N _d (n) on the Sierpinski gasket SG _d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N _d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as , is calculated to be ln (2)/3 exactly for SG ₂. The numbers of dimers on the generalized Sierpinski gasket SG _d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG ₃ is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG _d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. This paper is written during the Lung-Chi Chen visit to PIMS, University of British Columbia. The author thanks the institute for the hospitality.     

Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

Revisiting non-degenerate parametric down-conversion

The quantum dynamics of a two-mode non-resonant parametric down-conversion process is studied by recasting the time evolution equations for the basic operators in an equivalent spin equation form with simpler exact solutions for a pump field with harmonic time dependence. Expectation values of suitable operators for studying important features such as squeezing and quantum revivals are presented in simple forms.      

Pair production of charged Higgs bosons in the left–right twin Higgs model at the ILC and LHC

The left–right twin Higgs (LRTH) model predicts the existence of a pair of charged Higgs bosons φ^±. In this paper, we study the production of the charged Higgs boson pair φ^± at the international linear collider (ILC) and the CERN large hadron collider (LHC). The numerical results show that the production rates are at the level of several tens fb at the ILC, and the process e⁺e^-→φ⁺φ^- can produce adequately distinct multi-jet final states. We also discuss the charged Higgs boson pair production via the process qq̄→φ⁺φ^- at the LHC and estimate in this case the production rates. We find that, as long as the charged Higgs bosons are not too heavy, they can be abundantly produced at the LHC. The possible signatures of these new particles might be detected at the ILC and LHC experiments. PACS 12.60.Fr; 14.80.Mz; 14.65.Ha; 12.15.Lk