On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Superconvergence error estimates of discontinuous Galerkin time stepping for singularly perturbed parabolic problems

Numerical Algorithms - A parabolic convection-diffusion-reaction problem is discretized by the non-symmetric interior penalty Galerkin (NIPG) method in space and discontinuous Galerkin (DG) method...     

Ag+ ion transport studies in a polyvinyl alcohol-based polymer electrolyte system

Thick films of pure polyvinyl alcohol and polyvinyl alcohol doped with silver nitrate with different compositions have been prepared by solution cast technique. The FT-IR spectrum confirms the complexation process. The conductivity of the pure polyvinyl alcohol is of the order of 10⁻⁷ Sm⁻¹ at 90 °C, and its value increases by two orders of magnitude when doped with 20 wt% of AgNO₃. The activation energy, calculated from the Arrhenius plot for all compositions of the poly vinyl alcohol doped with silver nitrate, is between 0.24 and 0.35 eV. The migration energy for the ion in polymer electrolyte has been calculated from the modulus spectrum, and is in good agreement with the activation energy calculated from the Arrhenius plot. The modulus spectra indicate the non-Debye nature of the material.     

Ciprofloxacin-protected gold nanoparticles

The antibacterial drug ciprofloxacin (cfH) has been used to protect gold nanoparticles of two different mean diameters, 4 and 20 nm. The protection is complete with about 65 and 585 cfH molecules covering 4 and 15 nm particles, respectively. The nature of binding has been investigated by several analytical techniques. The nitrogen atom of the NH moiety of piperazine group binds on the gold surface, as revealed by voltammetric and spectroscopic studies. The cfH-adsorbed particles are stable in the dry state as well as at room temperature, and as a result, redispersion is possible. The rate of release of the drug molecule from the nanoparticles is more in the basic medium than in pure water, and the kinetics depend on the size of the particle; faster desorption is seen in smaller particles. The bound cfH is fluorescent, and this property could be used in biological investigations. This study shows that metal nanoparticles could be useful carriers for cfH and fluoroquinolone molecules. Most of the bound molecules could be released over an extended period of time.     

Conductivity anomalies in Y–Ba–Cu–O at 40K and 100K under high quasihydrostatic pressures

Electrical resistance measurements at low temperatures and high quasihydrostatic pressures on superconducting and non-superconducting varieties of Y_0.8Ba_1.2Cu₂O₅ (obtained by annealing in oxygen and air respectively) show striking anomalies in the vicinity of 100K and 40K. Arguments are presented to show that these anomalies as also the occurrence of T 's in the oxide superconductors either in the vicinity of 100K or of 40K are connected with their layered structure containing planes of Cu-O otahedral complexes.     

Phosphorene Supported Single-Atom Catalysts for CO Oxidation: A Computational Study

Single-atom catalysts (SACs) have attracted extensive attention owing to their high catalytic activity. The development of efficient SACs is crucial for applications in heterogeneous catalysis. In this article, the geometric configuration, electronic structure, stabilitiy and catalytic performance of phosphorene (Pn) supported single metal atoms (M=Ru, Rh, Pd, Ir, Pt, and Au) have been systematically investigated using density functional theory calculations and ab initio molecular dynamics simulations. The single atoms are found to occupy the hollow site of phosphorene. Among the catalysts studied, Ru-decorated phosphorene is determined to be a potential catalyst by evaluating adsorption energies of gaseous molecules. Various mechanisms including the Eley-Rideal (ER), Langmuir-Hinshelwood (LH) and trimolecular Eley-Rideal (TER) mechanisms are considered to validate the most favourable reaction pathway. Our results reveal that Ru−Pn exhibits outstanding catalytic activity toward CO oxidation reaction via TER mechanism with the corresponding rate-determining energy barrier of 0.44 eV, making it a very promising SAC for CO oxidation under mild conditions. Overall, this work may provide a new avenue for the design and fabrication of two-dimensional materials supported SACs for low-temperature CO oxidation.     

The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction–diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter–uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

An investigation of Staudinger reactions involving cis-1,3,5-triazidocyclohexane and tri(alkylamino)phosphines

The reaction of 1,3,5-cis-triazidocyclohexane with the electron-rich tris(dialkylamino)phosphines P(NMe(2))(3) (1) and N(CH(2)CH(2)NMe)(3)P (2b) in acetonitrile for 3 h furnished the corresponding tris-phosphazides 1,3,5-cis-(R(3)PN(3))(3)C(6)H(9), 3a (R(3)P = 1) and 3b (R(3)P = 2b), in 90% and 92% yields, respectively. The same reaction with the relatively electron-poor tris(dialkylamino)phosphine MeC(CH(2)NMe)(3)P (4) for 2 days gave the tris-iminophosphorane, 1,3,5-cis-(R(3)PN)(3)C(6)H(9), 5a (R(3)P = 4), in 60% yield. Compound 3b is a thermally stable solid that did not lose dinitrogen when refluxed in toluene for 24 h or when heated as a neat sample at 100 degrees C /0.5 Torr for 10 h. By contrast, tris-phosphazide 3a decomposed to the tris-iminophosphorane 1,3,5-cis-(R(3)PN)(3)C(6)H(9), 5b (R(3)P = 1), in 3 h in quantitative yield upon heating to 100 degrees C in toluene. Factors influencing the formation of the phosphazides or the iminophosphoranes in these reactions are discussed. The reaction of 3b with 4 equiv of benzoic acid gave [N(CH(2)CH(2)NMe)(3)P=NH(2)]PhCO(2) ([6bH]PhCO(2)) in quantitative yield along with benzene (56% yield) and dinitrogen. The same reaction with 3a gave [(Me(2)N)(3)P=NH(2)]PhCO(2) ([7aH]PhCO(2)) (quantitative yield), benzene (15% yield), and dinitrogen(.) Treatment of [6bH]PhCO(2) with KO(t)Bu afforded N(CH(2)CH(2)NMe)(3)P=NH (6b) in 40% overall yield. Compound 6b upon treatment with PhCH(2)CH(2)Br produced [6bH]Br in 90% yield along with styrene. The new compounds were characterized by analytical and spectroscopic methods, and selected compounds (3b, 5a, and [6bH]Br) were structured by X-ray crystallography. A special feature of 3b is its capability to function as a starting material for 6b, which was not accessible by other synthetic routes.