Search results for "EXPANSION"
showing 10 items of 630 documents
On lacunary Toeplitz determinants
2014
By using Riemann--Hilbert problem based techniques, we obtain the asymptotic expansion of lacunary Toeplitz determinants $\det_N\big[ c_{\ell_a-m_b}[f] \big]$ generated by holomorhpic symbols, where $\ell_a=a$ (resp. $m_b=b$) except for a finite subset of indices $a=h_1,\dots, h_n$ (resp. $b=t_1,\dots, t_r$). In addition to the usual Szeg\"{o} asymptotics, our answer involves a determinant of size $n+r$.
Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles
2014
Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodic…
Identification of small inhomogeneities: Asymptotic factorization
2007
We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral …
Charge-density analysis of 1-nitroindoline: refinement quality using free R factors and restraints
2011
Nitramines and related N-nitro compounds have attracted significant attention owing to their use in rocket fuel and as explosives. The charge density of 1-nitroindoline was determined experimentally and from theoretical calculations. Electron-density refinements were performed using the multipolar atom formalism. In order to design the ideal restraint strategy for the charge-density parameters, R-free analyses were performed involving a series of comprehensive refinements. Different weights were applied to the charge-density restraints, namely the similarity between chemically equivalent atoms and local symmetry. Additionally, isotropic thermal motion and an anisotropic model calculated by …
Thermal Expansion in Small Metal Clusters and its Impact on the Electric Polarizability
2000
The thermal expansion coefficients of $\mathrm{Na}_{N}$ clusters with $8 \le N \le 40$ and $\mathrm{Al}_{7}$, $\mathrm{Al}_{13}^-$ and $\mathrm{Al}_{14}^-$ are obtained from {\it ab initio} Born-Oppenheimer LDA molecular dynamics. Thermal expansion of small metal clusters is considerably larger than that in the bulk and size-dependent. We demonstrate that the average static electric dipole polarizability of Na clusters depends linearly on the mean interatomic distance and only to a minor extent on the detailed ionic configuration when the overall shape of the electron density is enforced by electronic shell effects. The polarizability is thus a sensitive indicator for thermal expansion. We …
Orthorhombic Phase of Crystalline Polyethylene: A Monte Carlo Study
1996
In this paper we present a classical Monte Carlo simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles and periodic boundary conditions. We used a recently developed algorithm which apart from standard Metropolis local moves employs also global moves consisting of displacements of the center of mass of the whole chains in all three spatial directions as well as rotations of the chains around an axis parallel to the crystallographic c-direction. Our simulations are performed in the NpT ensemble, at zero pressure, and extend over the whole range of temperatures in which the orthorhombic phase is experime…
Ab initiolattice dynamical studies of silicon clathrate frameworks and their negative thermal expansion
2014
The thermal and lattice dynamical properties of seven silicon clathrate framework structures are investigated with ab initio density functional methods (frameworks I, II, IV, V, VII, VIII, and H). The negative thermal expansion (NTE) phenomenon is investigated by means of quasiharmonic approximation and applying it to equal time displacement correlation functions. The thermal properties of the studied clathrate frameworks, excluding the VII framework, resemble those of the crystalline silicon diamond structure. The clathrate framework VII was found to have anomalous NTE temperature range up to 300 K and it is suitable for further studies of the mechanisms of NTE. Investigation of the displa…
Thermodynamic properties at the phase transition of Pb(Zr, Sn, Ti)O3solid solutions
2000
Abstract Field induced deformation and electrocaloric effect are investigated in the vicinity of phase transition at 163°C. The sharp increase of electrostriction below Tc is explained by the field induced ferroelectric to antiferroelectric phase transition. The antiferroelectric phase appears and remains stable below Tc in the absence of field. Elastic compliance and thermal expansion as functions of temperature are studied.
Phase transitions of Pb0.99Nb0.02(Zr0.75Sn0.20Ti0.05)O3ceramics
2001
Abstract The dielectric, elastic and electromechanical properties, electrocaloric effect and thermal expansion of poled and depoled Pb0.99Nb0.02(Zr0.75Sn0.20Ti0.05)O3 samples are presented to evaluate the nature of polar phases existing in the solid solution above room temperature. The Kittel's free energy expansion is used to explain some essential features of physical properties.
Anomalies in low-temperature lattice parameters of ErFeO3 and ErAlO3 single crystals: correlation with magnetic properties
2005
Abstract The paper presents the results of an experimental study of thermal expansion of isostructural orthorhombic ErFeO3 and ErAlO3 single crystals. Changes of lattice parameters have been investigated by X-ray measurements in the 10–300 K temperature range. Above ∼150 K, experimental results correspond well to the phonon mechanism. At low temperatures distinct anisotropic anomalies were observed in both compounds; and a correlation with the magnetic properties of the relevant ions is noted.