Effective aperture of X-ray compound refractive lenses

2017 ◽  
Vol 24 (3) ◽  
pp. 609-614 ◽  
Author(s):  
V. G. Kohn
Keyword(s):  
Integral Intensity ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
The Real ◽  
A Value ◽  
Effective Aperture ◽  
The One ◽  
Definition Of ◽  
Focusing Properties

A new definition of the effective aperture of the X-ray compound refractive lens (CRL) is proposed. Both linear (one-dimensional) and circular (two-dimensional) CRLs are considered. It is shown that for a strongly absorbing CRL the real aperture does not influence the focusing properties and the effective aperture is determined by absorption. However, there are three ways to determine the effective aperture in terms of transparent CRLs. In the papers by Kohn [(2002). JETP Lett. 76, 600–603; (2003). J. Exp. Theor. Phys. 97, 204–215; (2009). J. Surface Investig. 3, 358–364; (2012). J. Synchrotron Rad. 19, 84–92; Kohn et al. (2003). Opt. Commun. 216, 247–260; (2003). J. Phys. IV Fr, 104, 217–220], the FWHM of the X-ray beam intensity just behind the CRL was used. In the papers by Lengeler et al. [(1999). J. Synchrotron Rad. 6, 1153–1167; (1998). J. Appl. Phys. 84, 5855–5861], the maximum intensity value at the focus was used. Numerically, these two definitions differ by 50%. The new definition is based on the integral intensity of the beam behind the CRL over the real aperture. The integral intensity is the most physical value and is independent of distance. The new definition gives a value that is greater than that of the Kohn definition by 6% and less than that of the Lengeler definition by 41%. A new approximation for the aperture function of a two-dimensional CRL is proposed which allows one to calculate the two-dimensional CRL through the one-dimensional CRL and to obtain an analytical solution for a complex system of many CRLs.

A one-dimensional cobalt(II) coordination polymer based on 2,4′-oxydibenzoic acid: poly[[[diaquabis[2-(4-carboxyphenoxy)benzoato-κO1]cobalt(II)]-μ-4,4′-bipyridine-κ2N:N′] dihydrate]

2014 ◽  
Vol 70 (7) ◽  
pp. 654-658 ◽  
Author(s):  
Long Tang ◽  
Feng Fu ◽  
Ji-Jiang Wang ◽  
Qi-Rui Liu ◽  
Hang-Hang Zhao
Keyword(s):  
Coordination Polymer ◽  
Hydrothermal Condition ◽  
Dimensional Chain ◽  
Supramolecular Architecture ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
One Dimensional ◽  
X Ray ◽  
The One ◽  
Two Sides

The reaction of CoSO4with 2,4-oxydibenzoic acid (H2oba) and 4,4′-bipyridine (bipy) under hydrothermal condition yielded a new one-dimensional cobalt(II) coordination polymer, {[Co(C14H9O5)2(C10H8N2)(H2O)2]·2H2O}n, which was characterized by elemental analysis, IR spectroscopy, thermogravimetric analysis, magnetic properties and single-crystal X-ray diffraction. The CoIIions are connected by bipy ligands into infinite one-dimensional chains. The Hoba−ligands extend out from the two sides of the one-dimensional chain. O—H...O hydrogen bonding extends these chains into a two-dimensional supramolecular architecture.

Results from the multi-species Benchmark Problem 3 (BM3) using two-dimensional models

2004 ◽  
Vol 49 (11-12) ◽  
pp. 169-176 ◽  
Author(s):  
D.R. Noguera ◽  
C. Picioreanu
Keyword(s):  
Numerical Solutions ◽  
Mathematical Framework ◽  
Two Dimensional ◽  
Benchmark Problem ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Bulk Substrate ◽  
The One ◽  
Definition Of ◽  
Multidimensional Models

In addition to the one-dimensional solutions of a multi-species benchmark problem (BM3) presented earlier (Rittmann et al., 2004), we offer solutions using two-dimensional (2-D) models. Both 2-D models (called here DN and CP) used numerical solutions to BM3 based on a similar mathematical framework of the one-dimensional AQUASIM-built models submitted by Wanner (model W) and Morgenroth (model M1), described in detail elsewhere (Rittmann et al., 2004). The CP model used differential equations to simulate substrate gradients and biomass growth and a particle-based approach to describe biomass division and biofilm growth. The DN model simulated substrate and biomass using a cellular automaton approach. For several conditions stipulated in BM3, the multidimensional models provided very similar results to the 1-D models in terms of bulk substrate concentrations and fluxes into the biofilm. The similarity can be attributed to the definition of BM3, which restricted the problem to a flat biofilm in contact with a completely mixed liquid phase, and therefore, without any salient characteristics to be captured in a multidimensional domain. On the other hand, the models predicted significantly different accumulations of the different types of biomass, likely reflecting differences in the way biomass spread within the biofilm is simulated.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Assembly of C-propyl-pyrogallol[4]arene with bipyridine-based spacers and solvent molecules

2020 ◽  
Vol 75 (4) ◽  
pp. 341-345
Author(s):  
Xiao-Li Liu ◽  
Jing-Long Liu ◽  
Hong-Mei Yang ◽  
Ai-Quan Jia ◽  
Qian-Feng Zhang
Keyword(s):  
Mixed Solvent ◽  
Polymer Structure ◽  
Brick Wall ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
X Ray Crystallography ◽  
Wave Trough ◽  
Hydrogen Bonding Networks ◽  
Solvent Molecules

AbstractCo-crystallization of C-propyl-pyrogallol[4]arene (PgC3) with 4,4′-bipyridine (bpy) in ethanol afforded a multi-component complex (PgC3) · 3(bpy) ·(EtOH) (1) that consists of a one-dimensional brick-wall framework, which was formed by four pyrogallol[4]arene molecules and two juxtaposed bpy molecules, entrapping two other bpy molecules as guests within each cavity. Heating a mixture of PgC3 and trans-1,2-bis-(4-pyridyl)ethylene (bpe) in an ethanol-water mixed solvent allowed the isolation of a multi-component complex (PgC3) ·(bpe) · 2(EtOH) ·(H2O) (2), which has a two-dimensional wave-like polymer structure with the bpe molecules embedded in the wave trough between two PgC3 molecules. Single-crystal X-ray crystallography was utilized to investigate the hydrogen bonding networks of the multi-component complexes 1 and 2.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

2022 ◽  
Author(s):  
Bharti bharti ◽  
Debabrata Deb
Keyword(s):  
Molecular Dynamics ◽  
Liquid Crystals ◽  
Molecular Dynamics Simulations ◽  
Liquid Crystalline ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Dynamics Simulations

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the...

Polysulfonylamine, CXXV [1]. Neue Komplexe von Disulfonylaminen mit Kronenethern - im voraus entworfen oder zufällig entdeckt / Polysulfonylamines, CXXV [1]. New Complexes of Disulfonylam ines with Crown Ethers - Preconceived or Discovered by Serendipity

2000 ◽  
Vol 55 (3-4) ◽  
pp. 299-316 ◽  
Author(s):  
Dagmar Henschel ◽  
Karna Wijaya ◽  
Oliver Moers ◽  
Armand Blaschette ◽  
Peter G. Jones
Keyword(s):  
Hydrogen Bonds ◽  
X Ray Diffraction ◽  
Ladder Structure ◽  
Triclinic Space Group ◽  
One Dimensional ◽  
X Ray ◽  
Bonding System ◽  
Supramolecular Aggregate ◽  
Guest Species ◽  
The One

Abstract In a study aim ed at the „deconstruction“ of the supramolecular aggregate 3(18C6) · 2HN( SO2Me)2 (1,18C6 = 18-crown-6), which is known to display a ladder structure with two isotactic [18C6 - Me SO2N(H)SO2Me···)∞ polymers forming the uprights and symmetrically N - H···O bonded 18C6 rings providing the rungs, the following crystalline complexes were isolated and (except for 2b) characterized by low-temperature X-ray diffraction: 18C6-ClN (SO2Me)2 (2a, triclinic, space group P1̅, Z = 2), 18C6-PhN (SO2Me)2 (2b), 18C6 -MeN(SO2Me)2 (3, monoclinic, P21/c, Z = 8), Bz18C6-HN(SO2Me)2 (4, Bz18C6 = benzo-18-crown-6, monoclinic, P21/n, Z = 4), 18C6-2 MeN (SO2Me)2 (5, triclinic, P1̅, Z = 1), 18C6-Me2SO- HN( SO2Me) (SO2Ph) (13, triclinic, P1̅, Z = 2), and 18C6-H2OMe2SO·2HN(SO2Me)2 (14, triclinic, P1̅, Z = 2). Each of the one-dimensional polymers 2a (syndiotactic), 3 (disyndiotactic) and 4 (isotactic) mimics a single upright of 1; in contrast to 1 and 2a, where the intra-catemer connectivity solely relies on S - Me ··· crow n and crown ··· O = S hydrogen bonds, this bonding system is reinforced in 3 by N -Me ··· crown and in 4 by N - H ··· crown hydrogen bonds. Complex 5 is monomeric and matches a fragment formally extruded from the catemer 3; moreover, 3 and 5 represent a rare case of two structurally characterized 18C6 complexes containing the same uncharged guest species in distinct molecular ratios. The surprising structure of the quaternary adduct 14 exhibits an [18C6 ··· MeSO2N(H)SO2Me ··· ]∞ chain, which can be regarded both as an isolated, though unmodified upright from the ladder 1 and, being syndiotactic, as a stereochemical analogue of 2a; the potentially rung-forming *NH functions in the chain are blocked by hydrogenbonded side chains of the type * N - H ··· water ··· sulfoxide ··· H - N (SO2Me)2. The ternary complex 13 consists of chains [18C6 ··· Me2SO ··· H - N (SO2Ph)SO2Me···]∞ and is not closely related to the other structures

scholarly journals Water storage in wetted strips under irrigated coffee trees with different criteria of irrigation management

2013 ◽  
Vol 33 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Alberto Colombo ◽  
Lívia A. Alvarenga ◽  
Myriane S. Scalco ◽  
Randal C. Ribeiro ◽  
Giselle F. Abreu
Keyword(s):  
Dimensional Analysis ◽  
Drip Irrigation ◽  
Irrigation Management ◽  
Water Storage ◽  
Moisture Distribution ◽  
Water Volume ◽  
Two Dimensional ◽  
One Dimensional ◽  
Irrigation Interval ◽  
The One

The increasing demand for water resources accentuates the need to reduce water waste through a more appropriate irrigation management. In the particular case of irrigated coffee planting, which in recent years presented growth with the predominance of drip irrigation, the improvement of drip irrigation management techniques is a necessity. The proper management of drip irrigation depends on the knowledge of the spatial pattern of soil moisture distribution inside the wetted strip formed under the irrigation lines. In this study, grids of 24 tensiometers were used to determine the water storage within the wetted strip formed under drippers, with a 3.78 L h-1 discharge, evenly spaced by 0.4 m, subjected to two different management criteria (fixed irrigation interval and 60 kPa tension). Estimates of storage based on a one-dimensional analysis, that only considers depth variations, were compared with two-dimensional estimates. The results indicate that for high-frequency irrigation the one-dimensional analysis is not appropriate. However, under less frequent irrigation, the two-dimensional analysis is dispensable, being the one-dimensional sufficient for calculating the water volume stored in the wetted strip.

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