A comparison of lower bounds for the symmetric circulant traveling salesman problem

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on the optimal value that may be computed in polynomial time. We derive a new linear programming (LP) relaxation of the SCTSP from the semidefinite programming (SDP) relaxation in [E. de Klerk, D.V. Pasechnik, R. Sotirov, On semidefinite programming relaxation of the traveling salesman problem, SIAM Journal of Optimization 19 (4) (2008) 1559-1573]. Further, we discuss theoretical and empirical comparisons between this new bound and three well-known bounds from the literature, namely the Held-Karp bound [M. Held, R.M. Karp, The traveling salesman problem and minimum spanning trees, Operations Research 18 (1970) 1138-1162], the 1-tree bound, and the closed-form bound for SCTSP proposed in [J.A.A. van der Veen, Solvable cases of TSP with various objective functions, Ph.D. Thesis, Groningen University, The Netherlands, 1992].     

Thermo-hydraulic characterization of a louvered fin and flat tube heat exchanger

In the present study, a whole heat exchanger with a hydraulic diameter of 2.3 mm is tested, which is a minichannel heat exchanger according to the Kandlikar classification. This is a louvered fin and flat tube heat exchanger currently used in car cooling systems, also known as radiator. A glycol-water mixture (60/40 in volume) circulates through the tubes at flows ranging from 100 to 7800 l/h and at a supply temperature of 90 °C. This fluid is cooled with ambient air at a temperature of 20 °C and at frontal air velocities varying between 0.5 and 7 m/s. The thermohydraulic performance of the heat exchanger is compared with the classical correlations given in the literature for the heat transfer and the friction factor calculation. On the glycol-water side the heat exchanger is characterized for Reynolds numbers from 30 to 8000. A first comparison is carried out with the correlations available in the literature with a purely predictive model by obtaining a predictive value with a systematic under prediction lower than 10%. In a second step a semi-empirical model is considered to identify the experimental heat transfer coefficients for this application.     

Analysis of sheet metal formability through isotropic and kinematic hardening models

The present paper aims at analysing the sheet metal formability through several isotropic and kinematic hardening models. Specifically, a special attention is paid to the physically-based hardening model of Teodosiu and Hu (1995), which accounts for the anisotropic work-hardening induced by the microstructural evolution at large strains, as well as to some more conventional hardening models, including the isotropic Swift strain-hardening power law, and the Voce saturation strain-hardening law, combined with a non-linear kinematic hardening described by the Armstrong–Frederick law. The onset of localized necking is simulated by an advanced sheet metal forming limit model which connects, through the Marciniak–Kuczinsky analysis, the hardening models with the anisotropic yield criterion Yld2000-2d (Barlat et al., 2003). Both linear and complex strain paths are taken into account. The selected material is a DC06 steel sheet. The validity of each model is assessed by comparing the predicted forming limits with experimental results carefully obtained on this steel. The origin of discrepancy in the predicted results using different hardening models is thoroughly analyzed.     

Interior gradient estimates for solutions to the linearized Monge–Ampère equation

Let ? be a convex function on a convex domain Ω⊂Rn, n?1. The corresponding linearized Monge–Ampère equation istrace(ΦD²u)=f, where is the matrix of cofactors of D²?. We establish interior Hölder estimates for derivatives of solutions to such equation when the function f on the right-hand side belongs to Lp(Ω) for some p>n. The function ? is assumed to be such that with ?=0 on ∂Ω and the Monge–Ampère measure is given by a density g∈C(Ω) which is bounded away from zero and infinity.     

Asymptotics of solutions to the periodic problem for a Burgers type equation

We study large time asymptotic behavior of solutions to the periodic problem for the nonlinear Burgers type equation

Rare earth doped cobalt ferrite thin films deposited by PLD

CoFe₂O₄ thin films with preferential texture structure, small grain size, and perpendicular magnetic anisotropy can be obtained by the pulsed laser deposition (PLD) technique. In this work, we studied the influence of the Fe³⁺ ions substitution by three elements from lanthanide group (Dy, La, and Gd) on the structural properties of the thin films. The samples were deposited by Nd:YAG laser (λ=532 nm, 10 ns) ablation of CoFe_1.8RE_0.2O₄, (RE=Dy, La, Gd) targets at various substrate temperatures ranging from room temperature to 600 °C. The microstructure and chemical composition of the thin films were investigated by Raman spectroscopy, XRD, SEM-EDS, and ToF-SIMS. The XRD patterns and Raman spectra of the thin films indicated the formation of a single spinel structure. Thus, the desired substitution of the iron ions in the spinel lattice with the RE elements was achieved in the thin films, although in the bulk material, their presence determined the formation of a residual phase with a perovskite-type structure.     

Accelerated iterative strategy for the divergent synthesis of dendritic macromolecules using a combination of living radical polymerization and an irreversible terminator multifunctional initiator

Our laboratory has reported the elaboration of an iterative strategy for the synthesis of dendritic macromolecules from conventional monomers. This synthetic method involves a combination of self‐regulated metal‐catalyzed living radical polymerization initiated from arenesulfonyl chlorides and an irreversible terminator multifunctional initiator (TERMINI). The previous TERMINI, (1,1‐dimethylethyl)[[1‐[3,5‐bis(S‐phenyl‐4‐N,N′ diethylthiocarbamate)phenyl]ethenyl]oxy]dimethylsilane, was prepared in nine reaction steps. The replacement of the previous TERMINI with one that requires only three steps for its synthesis, diethylthiocarbamic acid S‐{3‐[1‐(tert‐butyl‐dimethyl‐silanyloxy)‐vinyl]‐5‐diethylcarbamoylsulfanyl‐phenyl} ester, and the use of the more reactive Cu₂S/2,2′‐bipyridine rather than the Cu₂O/2,2′‐bipyridine self‐regulated catalyst have generated an accelerated method for the synthesis of dendritic macromolecules. This method provides rational design strategies for the synthesis of dendritic macromolecules with different compaction by the use of a single monomer. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4894–4906, 2005     

Arenesulfonyl iodides: The third universal class of functional initiators for the metal‐catalyzed living radical polymerization of methacrylates and styrenes

The metal‐catalyzed living radical polymerization of methyl methacrylate and styrene initiated with freshly prepared p‐toluenesulfonyl iodide (TsI) and catalyzed with CuX/2,2′‐bipyridine (bpy), where X is Cl, Br, or I, and various self‐regulated copper‐based catalytic systems, such as copper/bpy, copper(I) oxide/bpy, copper(I) sulfide/bpy, copper(I) selenide/bpy, and copper(I) telluride/bpy, is reported. The exchange of C? I into C? Br and C? Cl takes place when the living radical polymerization of methyl methacrylate is catalyzed by copper(I) bromide/bpy and copper(I) chloride/bpy, respectively. Therefore, the use of the TsI initiator facilitates the synthesis, starting from a single initiator, of poly(methyl methacrylate) containing C? I, C? Br, and C? Cl chain ends. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3920–3931, 2005     

Arenesulfonyl bromides: The second universal class of functional initiators for the metal‐catalyzed living radical polymerization of methacrylates,acrylates, and styrenes

The metal‐catalyzed living radical polymerization of methyl methacrylate, n‐butyl acrylate, and styrene, initiated with p‐toluenesulfonyl bromide and phenoxybenzene‐4,4′‐disulfonyl bromide and catalyzed with CuBr/2,2′‐bipyridine (bpy) and various self‐regulated Cu‐based catalytic systems such as Cu₂O/bpy, Cu₂S/bpy, Cu₂Se/bpy, and Cu₂Te/bpy, is reported. Similarities and differences between the arenesulfonyl chloride and arenesulfonyl bromide initiators are discussed. The arenesulfonyl bromide initiators require reduced reaction times to produce polymers in high conversions under milder reaction conditions than the corresponding arenesulfonyl chloride initiators. At the same time, they exhibit 100% initiator efficiency and generate polymers with narrow molecular weight distributions and functional chain ends. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 319–330, 2005     

The complexity of proving chaoticity and the Church-Turing thesis

Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.