Thermal entanglement in two-qutrit spin-1 anisotropic Heisenberg model with inhomogeneous magnetic field

The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field (B), a parameter b which controls the inhomogeneity of B, and the bilinear interaction parameters J_{x=Jy≠Jz on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of Jz and lower values of B and b.}     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

Minimizing the probability of lifetime ruin under borrowing constraints

We determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of going bankrupt before she dies, also known as lifetime ruin. We impose two types of borrowing constraints: First, we do not allow the individual to borrow money to invest in the risky asset nor to sell the risky asset short. However, the latter is not a real restriction because in the unconstrained case, the individual does not sell the risky asset short. Second, we allow the individual to borrow money but only at a rate that is higher than the rate earned on the riskless asset.We consider two forms of the consumption function: (1) The individual consumes at a constant (real) dollar rate, and (2) the individual consumes a constant proportion of her wealth. The first is arguably more realistic, but the second is closely connected with Merton’s model of optimal consumption and investment under power utility. We demonstrate that connection in this paper, as well as include a numerical example to illustrate our results.     

A theoretical investigation on Pt3Sn(1 0 2) surface alloy and CO-Pt3Sn(1 0 2) system

The adsorption properties of CO on experimentally verified stepped Pt₃Sn(1 0 2) surface were investigated using quantum mechanical calculations. The two possible terminations of Pt₃Sn(1 0 2) were generated and on these terminations all types of possible adsorption sites were determined. The adsorption energies and geometries of the CO molecule for all those sites were calculated. The most favorable sites for adsorption were determined as the short bridge site on the terrace of pure-Pt row of the mixed-atom-ending termination, atop site at the step-edge of the pure row of pure-Pt-ending termination and atop site at the step-edge of the pure-Pt row of the mixed-atom-ending termination. The results were compared with those for similar sites on the flat Pt₃Sn(1 1 0) surface considering the fact that Pt₃Sn(1 0 2) has terraces with (1 1 0) orientation. The LDOS analysis of bare sites clearly shows that there are significant differences between the electronic properties of Pt atoms at stepped Pt₃Sn(1 0 2) surface and the electronic properties of Pt atoms at flat (1 1 0) surface, which leads to changes in the CO bonding energies of these Pt atoms. Adsorption on Pt₃Sn(1 0 2) surface is in general stronger compared to that on Pt₃Sn(1 1 0) surface. The difference in adsorption strength of similar sites on these two surface terminations is a result of stepped structure of Pt₃Sn(1 0 2). The local density of states (LDOS) of the adsorbent Pt and C of adsorbed CO was utilized. The LDOS of the surface metal atoms with CO-adsorbed atop and of their bare state were compared to see the effect of CO chemisorption on the electron density distribution of the corresponding Pt atom. The downward shift in energy peak in the LDOS curves as well as changes in the electron densities of the corresponding energy levels indicate the orbital mixing between CO molecular orbitals and metal d-states. The present study showed that the adsorption strength of the sites has a direct relation with their LDOS profiles.     

A multiobjective model for locating undesirable facilities

In this paper, we develop a multiobjective model to depict the tradeoffs involved when locating one or more undesirable facilities to service a region. We assume that the region requires a certain capacity of service, and that this capacity can be met by building a combination of different-sized facilities. Examples could include sanitary landfills, incinerators, and power-generating stations. Our objectives are to minimize the total cost of the facilities located, the total opposition to the facilities, and the maximum disutility imposed on any individual. Opposition and disutility are assumed to be nonlinearly decreasing functions of distance, and increasing functions of facility size. We formulate our model as a multiobjective mixed-integer program, and generate the set of efficient solutions using an enumeration algorithm. Our code can solve realistically sized problems on a microcomputer. We give an example to illustrate the tradeoffs between the three objectives, which are inevitable in such a location problem.This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada (OGP 25481), and by the Nova Fellowship of the Faculty of Business, University of Alberta.     

Ant Colony Optimisation for Machine Layout Problems

Flexible machine layout problems describe the dynamic arrangement of machines to optimise the trade-off between material handling and rearrangement costs under changing and uncertain production environments. A previous study used integer-programming techniques to solve heuristically reduced versions of the problem. As an alternative, this paper introduces an ant colony optimisation (ACO) algorithm to generate good solutions. Experimental results are presented, with ACO obtaining better solutions than the reduction heuristic.     

On the Continuity of Stochastic Exit Time Control Problems

We determine a weaker sufficient condition than that of Theorem 5.2.1 in Fleming and Soner (2006) for the continuity of the value functions of stochastic exit time control problems.     

Synthesis of a series of triple-bridged cyclotriphosphazene hexa-alkoxy derivatives and investigation of their structural and mesomorphic properties

Triple diamino-bridged cyclotriphosphazene (1) was reacted in a 1:8 stoichiometry with the sodium derivatives of long-chain diols [1-octanol, 1-decanol, 1-dodecanol, 1-hexadecanol] tetrahydrofuran (THF) at room temperature to form hexa-substituted cyclotriphosphazene derivatives (2, 3, 4 and 5, respectively), whose mesomorphic behaviours were investigated for their possible applications as liquid crystals. The cylindrical-type cyclotriphosphazene derivatives (2–5) were characterised by mass and elemental analyses and by Fourier transform infrared spectroscopy (FT-IR), ¹H and ³¹P {¹H} NMR spectroscopies. The thermal and mesomorphic properties were investigated by differential scanning calorimetry and by polarising optical microscopy, respectively. It was found that liquid crystal materials could be obtained from compounds 3 and 4 with alkoxy chains rather than using aromatic ring(s) as mesogens as published previously.     

Isothermal Entropy Change for the Spin-1 Blume-Capel Model on the Bethe Lattice

The isothermal entropy change of spin-1 Blume-Capel (BC) is investigated on the Bethe lattice (BL) with the variations of coordination numbers (q), crystal field (D) and external magnetic field (H) in the vicinity of critical temperatures, i.e. about the second- and first-order phase transition temperatures. The calculation is carried on the BL in terms of exact recursion relations. It is found that the peaks of the isothermal entropy variation obtained for both magnetization and quadrupole moments are observed to be increasing with increasing values of H for given D and q, decreasing with the increasing q for fixed D and H and also decreasing with the increasing values of D for constant q and H. The peaks of the curves for the quadrupole moment is less sharper then the ones obtained for the magnetization.

     

Trait-based heterogeneous populations plus (TbHP+ ) genetic algorithm

This study developed a variant of genetic algorithm (GA) model called the trait-based heterogeneous populations plus (TbHP+). The developed TbHP+ model employs a memory concept in the form of immunity and instinct to provide the populations with a more efficient guidance. Also, it has an ability to vary the number of individuals during the search process, thus allowing an automatic determination of the size of the population based on the individual qualities such as character fitness and credit for immunity. The algorithm was tested against the classical GA model in convergence and minimum error performance. For this purpose, 5 different mathematical functions from the literature were employed. The selected functions have different topological characteristics, ranging from simple convex curves with 2 variables to complex trigonometric ones having several hilly shapes with more than 2 variables. The developed model and the classical GA model were applied to finding the global minima of the functions. The comparison of the results revealed that the developed TbHP+ model outperformed the classical GA in faster convergence and minimum errors, which may be explained by the adaptive nature of the new paradigm.