P-Sequential Spaces and Cleavability

∗ Supported by the Serbian Scientific Foundation, grant No 04M01

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

A squeezed state holomorphic phase space representation of equations of motion

A mapping scheme is presented which takes quantum operators associated to bosonic degrees of freedom into complex phase space integral kernel representatives. The procedure consists of using the Schrödinger squeezed state as the starting point for the construction of the integral mapping kernel which, due to its inherent structure, is suited for the description of second quantized operators. Products and commutators of operators have their representatives explicitly written which reveal new details when compared to the usual q-p phase space description. The classical limit of the equations of motion for the canonical pair q-p is discussed in connection with the effect of squeezing the quantum phase space cellular structure. © 1993.

First-principles quantum dynamics in interacting Bose gases: I. The positive P representation

The performance of the positive P phase-space representation for exact many- body quantum dynamics is investigated. Gases of interacting bosons are considered, where the full quantum equations to simulate are of a Gross-Pitaevskii form with added Gaussian noise. This method gives tractable simulations of many-body systems because the number of variables scales linearly with the spatial lattice size. An expression for the useful simulation time is obtained, and checked in numerical simulations. The dynamics of first-, second- and third-order spatial correlations are calculated for a uniform interacting 1D Bose gas subjected to a change in scattering length. Propagation of correlations is seen. A comparison is made with other recent methods. The positive P method is particularly well suited to open systems as no conservation laws are hard-wired into the calculation. It also differs from most other recent approaches in that there is no truncation of any kind.

High-strain composites and dual-matrix composite structures

Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.

The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.

A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.

High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.

Smooth Banach spaces and approximations

If E and F are real Banach spaces let C^p,q(E, F) O ≤ q ≤ p ≤ ∞, denote those maps from E to F which have p continuous Frechet derivatives of which the first q derivatives are bounded. A Banach space E is defined to be C^p,q smooth if C^p,q(E,R) contains a nonzero function with bounded support. This generalizes the standard C^p smoothness classification.

If an L^p space, p ≥ 1, is C^q smooth then it is also C^q,q smooth so that in particular L^p for p an even integer is C^∞,∞ smooth and L^p for p an odd integer is C^p-1,p-1 smooth. In general, however, a C^p smooth B-space need not be C^p,p smooth. C_o is shown to be a non-C^2,2 smooth B-space although it is known to be C^∞ smooth. It is proved that if E is C^p,1 smooth then C_o(E) is C^p,1 smooth and if E has an equivalent C^p norm then c_o(E) has an equivalent C^p norm.

Various consequences of C^p,q smoothness are studied. If f ϵ C^p,q(E,F), if F is C^p,q smooth and if E is non-C^p,q smooth, then the image under f of the boundary of any bounded open subset U of E is dense in the image of U. If E is separable then E is C^p,q smooth if and only if E admits C^p,q partitions of unity; E is C^p,psmooth, p ˂∞, if and only if every closed subset of E is the zero set of some C^P function.

f ϵ C^q(E,F), 0 ≤ q ≤ p ≤ ∞, is said to be C_p,q approximable on a subset U of E if for any ϵ ˃ 0 there exists a g ϵ C^p(E,F) satisfying

sup/xϵU, O≤k≤q ‖ D^k f(x) - D^k g(x) ‖ ≤ ϵ.

It is shown that if E is separable and C^p,q smooth and if f ϵ C^q(E,F) is C_p,q approximable on some neighborhood of every point of E, then F is C_p,q approximable on all of E.

In general it is unknown whether an arbitrary function in C¹(l², R) is C_2,1 approximable and an example of a function in C¹(l², R) which may not be C_2,1 approximable is given. A weak form of C_∞,q, q≥1, to functions in C^q(l², R) is proved: Let {U_α} be a locally finite cover of l² and let {T_α} be a corresponding collection of Hilbert-Schmidt operators on l². Then for any f ϵ C^q(l²,F) such that for all α

sup ‖ D^k(f(x)-g(x))[T_αh]‖ ≤ 1.

xϵU_α,‖h‖≤1, 0≤k≤q

Crystallization and characterization of substoichiometric compound (W0.5Al0.5)C-0..5 obtained by solid-state reaction

(W0.5Al0.5)C-0.5 substoichiometric compound is synthesized by a combination of mechanical milling and high-pressure reactive sintering. X-ray diffraction is used to monitor the phase changes and crystallization of (W0.5Al0.5) C-0.5 during the whole reaction process. As a result, (W0.5Al0.5) C-0.5 is identified as the hexagonal WC-type belonging to the P-6m2 space group (No. 187), and the lattice parameters of (W0.5Al0.5)C-0.5 are calculated to be a = 2.907 (1) angstrom, c = 2.838 (1) angstrom, which are very similar to those of WC even if there are approximately 50 pct carbon vacancies in the cell of (W0.5Al0.5)C-0.5 as compared with WC. The substoichiometric (W0.5Al0.5)C-0.5 compound has a Vickers microhardness of 2385 +/- 70 kg mm(-2), which is as high as that of WC, while its density is far lower than that of WC.

Structure and order of the discotic compound 2,3,6,7,10,11-hexakispentyloxytriphenylene as revealed by diffraction and molecular simulation studies

The aggregate structure of the discotic compound 2,3,6,7,10,11-hexakispentyloxytriphenylene (HPT) was studied both for the crystalline state and the liquid crystalline state by using electron crystallography and a molecular simulation approach. In the crystalline state, HPT was found to adopt an orthorhombic P-2212 space group with cell parameters a = 36.73 Angstrom, b = 27.99 Angstrom and c = 4.91 Angstrom. Molecular packing calculations were conducted to elucidate the molecular conformation and mutual orientational characteristics in the different states. Phase transitions and relationships are discussed from a structural point of view.

On trip planning queries in spatial databases

In this paper we discuss a new type of query in Spatial Databases, called Trip Planning Query (TPQ). Given a set of points P in space, where each point belongs to a category, and given two points s and e, TPQ asks for the best trip that starts at s, passes through exactly one point from each category, and ends at e. An example of a TPQ is when a user wants to visit a set of different places and at the same time minimize the total travelling cost, e.g. what is the shortest travelling plan for me to visit an automobile shop, a CVS pharmacy outlet, and a Best Buy shop along my trip from A to B? The trip planning query is an extension of the well-known TSP problem and therefore is NP-hard. The difficulty of this query lies in the existence of multiple choices for each category. In this paper, we first study fast approximation algorithms for the trip planning query in a metric space, assuming that the data set fits in main memory, and give the theory analysis of their approximation bounds. Then, the trip planning query is examined for data sets that do not fit in main memory and must be stored on disk. For the disk-resident data, we consider two cases. In one case, we assume that the points are located in Euclidean space and indexed with an Rtree. In the other case, we consider the problem of points that lie on the edges of a spatial network (e.g. road network) and the distance between two points is defined using the shortest distance over the network. Finally, we give an experimental evaluation of the proposed algorithms using synthetic data sets generated on real road networks.

Structure and thermal reactivity of Zn(II) salts of isocinchomeronic acid (2,5-pyridinedicarboxylic acid)

The synthesis, an improved refined crystal and molecular structure re-determination, and the thermal decomposition behavior of two Zn(II) derivatives of isocinchomeronic acid (2,5-pyridinedicarboxylic acid or H(2)2,5-pydc) are presented. [Zn(2,5-pydc)(H(2)O)(3)Zn(2,5-pydc)(H(2)O)(2)](2) (1) crystallizes in the triclinic P-1 space group with a = 7.106(2), b = 11.450(2), c = 11.869(1) angstrom, alpha = 107.29(1), beta = 104.08(1), gamma = 90.32(2)degrees, and Z = 2. [Zn(2,5-pydc)(H(2)O)(2)] center dot H(2)O (2) is orthorhombic (P2(1)2(1)2(1) space group), with a = 7.342(1), b = 9.430(1), c = 13.834(2) angstrom, and Z = 4. The structures were refined to agreement R(1)-factors of 0.0315 (1) and 0.0336 (2). Complex (1) is arranged as molecular Zn(4)(2,5-pydc)(4)(H(2)O)(10) tetramers, the cages of which define channels that remain unblocked by anions. Compound (2) is polymeric with Zn(2,5-pydc)(H(2)O)(2) and Zn(2,5-pydc)(H(2)O)(3) units linked through bridging ligands. Both compounds were synthesized under mild conditions in aqueous media, without need to resort to hydrothermal media. Changing the pH from 4.51 to 5.75 suffices to direct the chemical processes toward the orthorhombic compound rather than to the triclinic one.

Spectroscopic characterization and crystal structure of cis-Bis(N-(2-benzoyl)-N ',N '-diphenylthioureato-k O-2,S)nickel(II)

The title compound [Ni(C20H15N2OS)(2)] is prepared by the reaction of metal acetate with the corresponding acylthiourea derivative. The complex is characterized by elemental analysis, IR, H-1 and C-13 NMR, and its structure is determined by single crystal X-ray diffraction. The Ni(II) ion is coordinated by the S and O atoms of two N-benzoyl-N',N'-diphenylthiourea ligands in a slightly distorted square-planar coordination geometry. The two O and two S atoms are mutually cis to each other. The substance crystallizes triclinic (P-1 space group) with cell dimensions a = 10.7262(9) , b = 12.938(3) , c = 14.2085(12) , alpha = 74.650(4)A degrees, beta = 78.398(4)A degrees, gamma = 68.200(5)A degrees, and two formula units in the unit cell. The structure is very close to the related N-(2-furoyl) Ni complex reported previously.

Flexible structure control laboratory development and technology demonstration /

"Final report for the period July 1985 to July 1987."

Another Generalization of Arhangel'skii's Theorem

MSC 2010: 54A25, 54A35.