The Thermodynamic Limit in Mean Field Spin Glass Models

 We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N ₁ and N ₂ sites, respectively, with N ₁ +N ₂ =N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site. Received: 19 April 2002 / Accepted: 22 April 2002 Published online: 6 August 2002     

Poly(ethylene terephthalate) terpolyesters containing isophthalic and 5‐tert‐butylisophthalic units

Poly(ethylene terephthalate‐co‐isophthalate‐co‐5‐tert‐butylisophthalate) (PETI^tBI) terpolymers were investigated with reference to poly(ethylene terephthalate) (PET) homopolymer and poly(ethylene terephthalate‐co‐isophthalate) (PETI) copolymers. Three series of PETI^tBI terpolyesters, characterized by terephthalate contents of 90, 80, and 60 mol %, respectively, with different isophthalate/5‐tert‐butylisophthalate molar ratios, were prepared from ethylene glycol and mixtures of dimethyl terephthalate, dimethyl isophthalate, and 5‐tert‐butylisophthalic acid. The composition of the terpolymers and the composition of the feed agreed. All terpolymers had a random microstructure and number‐average molecular weights ranging from 10,000 to 20,000. The PETI^tBI terpolyesters displayed a higher glass‐transition temperature and a lower melting temperature than the PETI copolymers having the same content of terephthalic units. Thermal stability appeared essentially unchanged upon the incorporation of the 5‐tert‐butylisophthalic units. The PETI^tBIs were crystalline for terephthalate contents higher than 80 mol %, and they crystallized at lower rates than PETI. The crystal structure of the crystalline terpolymers was the same as that of PET with the 1,3‐phenylene units being excluded from the crystalline phase. Incorporation of isophthalate comonomers barely affected the tensile modulus and strength of PET, but the brittleness of the terpolymers decreased for higher contents in 5‐tert‐butylisophthalic units. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 124–134, 2003     

Aromatic homo‐ and copolyesters from naturally occurring monosaccharides: PET and PEI analogs derived from L‐arabinitol and xylitol

The synthesis and characterization of new aromatic homo‐ and copolyesters based on l‐arabinitol and xylitol are described. These polymers were obtained by polycondensation reaction of the 2,3,4‐tri‐O‐methyl‐l‐arabinitol or 2,3,4‐tri‐O‐methyl‐xylitol, or their mixtures with ethylene glycol, with terephthaloyl chloride or isophthaloyl chloride in o‐dichlorobenzene or in the melt phase from the corresponding methyl phthalates. All the polymers were characterized by GPC, IR, and NMR. Their M_w values ranged between 11,500 and 46,500, with polydispersities from 1.5 to 2.3. They were found to be soluble in chloroform, but insoluble in water. In contrast with the homopolymers completely made with EG, they showed a significant hygroscopicity. DSC and TGA studies showed that the melting temperature of polyethylene terephthalate is depressed by the presence of pentitol units, whereas the thermal stability is kept above 350 °C. Only copolyesters containing 10% or less of pentitol units showed melting and produced X‐ray diffraction patterns characteristic of crystalline material. d‐Arabinitol‐based homopolyesters appeared to be more crystalline than those derived from xylitol and also presented a higher thermal stability. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6394–6410, 2005     

Sensitivity analysis in linear semi-infinite programming: Perturbing cost and right-hand-side coefficients

This paper analyzes the effect on the optimal value of a given linear semi-infinite programming problem of the kind of perturbations which more frequently arise in practical applications: those which affect the objective function and the right-hand-side coefficients of the constraints. In particular, we give formulae which express the exact value of a perturbed problem as a linear function of the perturbation.     

Holographic optical elements as scanning lidar telescopes

We have developed and investigated the use of holographic optical elements (HOEs) and holographic transmission gratings for scanning lidar telescopes. Rotating a flat HOE in its own plane with the focal spot on the rotation axis makes a very simple and compact conical scanning telescope. We developed transmission and reflection HOEs for use at the first three harmonic wavelengths of Nd:YAG lasers. The diffraction efficiency, diffraction angle, focal length, focal spot size and optical losses were measured for several HOEs and holographic gratings, and found to be suitable for use as lidar receiver telescopes, and in many cases could also serve as the final collimating and beam steering optic for the laser transmitter. Two lidar systems based on this technology have been designed, built, and successfully tested in atmospheric science applications. This technology will enable future spaceborne lidar missions by significantly lowering the size, weight, power requirement and cost of a large aperture, narrow field of view scanning telescope.     

Chloroform sorption in nanoporous crystalline and amorphous phases of syndiotactic polystyrene

The transport of chloroform in films of atactic polystyrene and of semicrystalline syndiotactic polystyrene in its nanoporous form (δ‐form) has been investigated by gravimetric analysis. Experimental tests have been performed at 35, 49, and 56 °C and at several vapor pressures ranging from 0.5 to 100 Torr. Nonequilibrium lattice fluid prediction of the amorphous sorption behavior was used to enucleate the sorption contribution of the crystalline nanoporous phase from semicrystalline samples. Sorption behavior of the crystalline phase has been interpreted on the basis of Langmuir equation. Moreover, the chloroform sorption at low activities in the crystalline nanoporous phase has been predicted by using Grand Canonical Monte Carlo molecular simulations. Isosteric heats of sorption were also experimentally evaluated for the crystalline phase, and compared with the corresponding prediction of molecular simulation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 8–15, 2008     

A measurement of the azimuthal angle dependence of the process ep → enπ+ near threshold

The azimuthal angle dependence of the process ep → enπ⁺ has been measured by detecting the electron and neutron in coincidence. Data are presented for momentum transfers (?k²) between 0.08 and 0.32 $\text{(}\text{GeV}\text{c}\text{)}{}^2$ and at energies close to threshold. Fixed-t dispersion relation models give predictionsin good qualitative agreement with the data.     

Scalar quantum electrodynamics on lattice correlation inequalities and infinite volume limit

We consider Wilson's lattice approximation to scalar Quantum Electrodynamics. We establish correlation inequalities of Griffiths-Kelly-Sherman type and a rigorous transfer matrix formalism, from which existence and non triviality of the infinite volume limit follow.