Complex surfaces polarized by an ample and spanned line bundle of genus three

Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K _X L))/2=3 are classified by means of the main techniques of adjunction theory.     

New promising bulk thermoelectrics: intermetallics,pnictides and chalcogenides

The need of alternative “green” energy sources has recently renewed the interest in thermoelectric (TE) materials, which can directly convert heat to electricity or, conversely, electric current to cooling. The thermoelectric performance of a material can be estimated by the so-called figure of merit, zT = σ α ² T/λ (α the Seebeck coefficient, σ α ² the power factor, σ and λ the electrical and thermal conductivity, respectively), that depends only on the material. In the middle 1990s the “phonon glass and electron crystal” concept was developed, which, together with a better understanding of the parameters that affect zT and the use of new synthesis methods and characterization techniques, has led to the discovery of improved bulk thermoelectric materials that start being implemented in applications. During last decades, special focus has been made on skutterudites, clathrates, half-Heusler alloys, Si_1?x Ge _x-, Bi₂Te_3- and PbTe-based materials. However, many other materials, in particular based on intermetallics, pnictides, chalcogenides, oxides, etc. are now emerging as potential advanced bulk thermoelectrics. Herein we discuss the current understanding in this field, with special emphasis on the strategies to reduce the lattice part of the thermal conductivity and maximize the power factor, and review those new potential thermoelectric bulk materials, in particular based on intermetallics, pnictides and chalcogenides. A final chapter, discussing different shaping techniques leading to bulk materials (eventually from nanostructured TE materials), is also included.     

Applicability of medium-size basis sets in calculations of molecular dynamic polarisabilities

Static and dynamic average polarisabilities and polarisability anisotropies of seven linear non-polar and polar molecules are calculated within the CCS, CC2, and CC3 approximations using a range of medium-sized basis sets: the polarised LPol-n (n = ds, dl, fs, fl), the aug-pc-n (n = 1, 2), the def2-SVPD, and -TZVPD basis sets. Reference values are obtained using a hierarchy of Dunning's (d-)aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The results are discussed together with the available CCSD values in terms of basis set and correlation method errors, and their ratio. Detailed analysis shows that already the def2-SVPD basis set can be used in CCS polarisability calculations. When affordable, the slightly larger aug-pc-1 basis set is recommended, as it leads to significant reduction of basis set error. The def2-TZVPD, LPol-ds, and aug-pc-2 basis sets are optimal choice within the CC2 approximation, with the latter allowing to approach the CC2 basis set limit. The LPol-ds, -dl, and def2-TZVPD sets outperform the aug-cc-pVTZ set in average polarisability CCSD calculations, with the def2-TZVPD being competitive to other reduced-size sets also in determination of polarisability anisotropy. The aug-pc-2 basis is a particularly attractive choice for CCSD, giving the accuracy of aug-cc-pVQZ at a significantly reduced computational cost. The polarisability anisotropy is shown to be more computationally demanding than the average polarisability, in particular with respect to the accuracy of the correlation method and an accurate evaluation of this property requires at least the CCSD model.     

MCSCF calculation of response properties of Argon

Summary Analytic equations of the multiconfigurational SCF (MCSCF) response theory are combined with the finite-field (FF) approach to compute static and frequency dependent electric and magnetic properties of the Argon atom. A complete active space (CAS SCF) function including the 3s, 3p, 3d, 4s and 4p orbitals in the active space and a large (17s 13p 7d 5f 3g) basis set are employed. This permits an accurate determination of various linear and non-linear response properties such as e.g. electric dipole polarisability and second hyperpolarisability, Verdet constant, magnetisability and second hyperpolarisability. The results, both for the static values and for the frequency dependence of these properties, compare well with other most recent experimental and theoretical data.Dedicated to Jan Linderberg on the occasion of his 60th birthday     

On Metastability in FPU

We present an analytical study of the Fermi–Pasta–Ulam (FPU) α–model with periodic boundary conditions. We analyze the dynamics corresponding to initial data with one low frequency Fourier mode excited. We show that, correspondingly, a pair of KdV equations constitute the resonant normal form of the system. We also use such a normal form in order to prove the existence of a metastability phenomenon. More precisely, we show that the time average of the modal energy spectrum rapidly attains a well defined distribution corresponding to a packet of low frequencies modes. Subsequently, the distribution remains unchanged up to the time scales of validity of our approximation. The phenomenon is controlled by the specific energy.     

Analytic stratifications and the cut locus of a class of distance functions

We study the analytic singularities of viscosity solutions of equations of eikonal type and obtain that the analytic singular support of these functions has an analytic stratification. The singular support can be identified with the cut locus of the distance to the boundary of an open set, when the interior is equipped with a degenerate Riemannian metric. We apply the result to elliptic equations as well as to model operators of Grušin type.