Search results for "Lattice"
showing 10 items of 3278 documents
Bhabha Scattering and a special pencil of K3 surfaces
2018
We study a pencil of K3 surfaces that appeared in the $2$-loop diagrams in Bhabha scattering. By analysing in detail the Picard lattice of the general and special members of the pencil, we identify the pencil with the celebrated Ap\'ery--Fermi pencil, that was related to Ap\'ery's proof of the irrationality of $\zeta(3)$ through the work of F. Beukers, C. Peters and J. Stienstra. The same pencil appears miraculously in different and seemingly unrelated physical contexts.
On monadic quantale algebras: basic properties and representation theorems
2010
Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.
Finitary shadows of compact subgroups of $$S(\omega )$$
2020
AbstractLet LF be the lattice of all subgroups of the group $$SF(\omega )$$SF(ω) of all finitary permutations of the set of natural numbers. We consider subgroups of $$SF(\omega )$$SF(ω) of the form $$C\cap SF(\omega )$$C∩SF(ω), where C is a compact subgroup of the group of all permutations. In particular, we study their distribution among elements of LF. We measure this using natural relations of orthogonality and almost containedness. We also study complexity of the corresponding families of compact subgroups of $$S(\omega )$$S(ω).
Beyond frames: Semi-frames and reproducing pairs
2017
Frames are nowadays a standard tool in many areas of mathematics, physics, and engineering. However, there are situations where it is difficult, even impossible, to design an appropriate frame. Thus there is room for generalizations, obtained by relaxing the constraints. A first case is that of semi-frames, in which one frame bound only is satisfied. Accordingly, one has to distinguish between upper and lower semi-frames. We will summarize this construction. Even more, one may get rid of both bounds, but then one needs two basic functions and one is led to the notion of reproducing pair. It turns out that every reproducing pair generates two Hilbert spaces, conjugate dual of each other. We …
A Lattice-Geometric Proof of Wedderburn’s Theorem
1993
This note presents a proof of Wedderburn’s theorem concerning the classification of semisimple rings within the conceptual frame of projective lattice geometry.
Monolayers of asymmetrical diethylalkanoat disulfides on gold(111):.the influence of chain length difference on atomic force microscope images
1998
Several symmetrical and asymmetrical long-chain diethylalkanoat disulfides were synthesized and character- ized. The differences in the chain lengths of the disul- fides ranged between zero and five methylene units. Self- assembled monolayers of these disulfides formed on Au(111) surfaces were studied by atomic force microscopy (AFM) in order to obtain information about the origin of the image contrast. Domains with hexagonal lattices (lattice constants 5:2- 5:3 A) were detected for all derivatives, independent of the chain length differences. This indicates that the contrast arises roughly at a depth of 4- 8 A in the monolayers at imag- ing forces between 0: 2a nd 3n N. For SAMs of diethyl…
Linear chain surfactants at a planar interface: a comparative Monte Carlo study of several lattice models
1993
Linear chain surfactants in a densely packed arrangement (such as alkane chains in lipid monolayers in the “uniform tilt” structures) are described by a crude coarse-grained model where the endgroups grafted on the interface form a regular lattice and the chains are described by the bond fluctuation model with chains containing N = 4 effective monomers only. Square-well interactions between the monomers are studied for both the attractive and repulsive case for three choices of the interaction range. None of these models exhibits a structure with uniform tilt. For attractive interactions the last bond has a strong tendency to fold back thus leading to a very high density close to the interf…
Defects in yttrium aluminium perovskite and garnet crystals: atomistic study
2000
Native and impurity point defects in both yttrium aluminium perovskite (YAP) and garnet (YAG) crystals are studied in the framework of the pair-potential approximation coupled with the shell model description of the lattice ions. The calculated formation energies for native defects suggest that the antisite disorder is preferred over the Frenkel and Schottky-like disorder in both YAP and YAG. The calculated values of the distortion caused by the antisite YAl x in the lattice turn out to be in an excellent agreement with the EXAFS measurements. In non-stoichiometric compounds, the calculated reaction energies indicate that excess Y2 O3 or Al2 O3 is most likely to be accommodated by the forma…
Finite-size scaling of charge carrier mobility in disordered organic semiconductors
2016
Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a macroscopic, nondispersive mobility from the system-size dependence of a microscopic one. The method is validated against a temperature-based extrapolation [A. Lukyanov and D. Andrienko, Phys. Rev. B 82, 193202 (2010)]. In addition, we provide an analytic estimate of system sizes required to perform nondispersive charge transport simulations in systems with finite charge carrier density, derived from a truncated Gaussian distribution. This estimate is not limited t…
Cooling of Hot Electrons in Amorphous Silicon
1997
ABSTRACTMeasurements of the cooling rate of hot carriers in amorphous silicon are made with a two-pump, one-probe technique. The experiment is simulated with a rate-equation model describing the energy transfer between a population of hot carriers and the lattice. An energy transfer rate proportional to the temperature difference is found to be consistent with the experimental data while an energy transfer independent of the temperature difference is not. This contrasts with the situation in crystalline silicon. The measured cooling rates are sufficient to explain the difficulty in observing avalanche effects in amorphous silicon.