Statistical stability of three and more body hierarchical systems in celestial mechanics

itqquad Then to the Heav'n itself I cried,qquad Asking, `What Lamp had destiny to guideqquad Her little Children stumbling in the Dark?'qquad And - `A blind understandingMissing data. Heav'n replied. qquadqquadqquad Rubaiyat of Omar Khayyam It seems that not everybody in Persia in the eleventh century was as convinced as the astrologers that the movements of the heavens controlled the destiny of Man. Nevertheless, for many centuries before and since, kings and emperors rewarded handsomely those astronomer/astrologers who could give them advice based on the movements of the planets and other celestial bodies. (There may be some astronomers today who would wish for similar generous patronage). Since the advent of modern celestial mechanics with the work of Isaac Newton, orbital motion has been studied for its own sake, and in the last thirty years, for the purposes of sending artificial satellites and manned craft into space. Yet for 300 years, one of the most important questions posed by celestial mechanics remains unanswered: are the motions of the planets in the Solar System stable? Could planets collide or even escape? Countless workers since Newton's time have sought Lamps to the destiny of the Solar System, but our Understanding is still obscured by many blind-spots. This thesis does not claim to give any definitive answers to these questions. It does indicate how to obtain quantitative estimates of the likelihood of certain events occurring. Simple statistical methods are applied to the results of numerical experiments and give probabilities of planetary orbits crossing or bodies escaping dynamical systems altogether. In Chapter 1 a general review of the problem of the Solar System's stability is given along with brief descriptions of methods and definitions of stability which have been used in the past. This thesis studies the stability of real and fictitious dynamical systems not necessarily associated with the Solar System. It investigates one particular definition of stability, namely hierarchical stability, using special perturbation methods. The definitions of hierarchical systems, hierarchical stability and empirical stability parameters are reviewed in Chapter 2. These will form the basis for subsequent numerical experiments. One further definition of stability - Hill stability is an important condition for hierarchical stability. It has been studied in a mathematically rigorous way in the problem of three massive bodies in mutually perturbed orbits. This analysis as well as some new numerical results are given in Chapter 3. Numerical integration experiments were carried out, with the aid of a mainframe computer, to study the period of time for which various three-body systems remain stable. Several hundred fictitious systems with different masses and starting conditions were studied. In each case, all three bodies' orbits lay in the same plane. In some systems, all the bodies orbited in the same direction (direct); for other systems, one body orbited in the opposite direction from the other two (retrograde). The results of these experiments are presented in Chapter 4 (for retrograde systems) and Chapter 5 (for direct systems). The results are grouped in such a way that analytical curves may be fitted to the data. This allows predictions of stability lifetimes for similar systems without the need for lengthy numerical integration experiments. Systems whose masses, initial positions and initial velocities fall into certain ranges are always stable. These regions of hierarchical stability are mapped out and compared with corresponding regions of Hill stability. In the case of direct systems, commensurabilities give rise to large fluctuations in stability lifetimes, if the initial conditions are varied slightly. Additional statistical methods are described in Chapter 5 to cope with this effect. In Chapter 6, the results of Chapters 4 and 5 are compared with real three-body systems within the Solar System. Possible origins of the Solar System are discussed in the light of the results

Performance and Stability Gain in Zero-Dimensional Perovskite Solar Cells after >2 Years when Hybridized with Silicon Nanocrystals

We report highly stable zero-dimensional (CH(3)NH(3))(3)Bi(2)I(9) photovoltaic cells which demonstrate a 33% increase in performance after 2 years when hybridized with silicon nanocrystals (SiNCs). The natural oxidation of SiNCs is expected to consume radical species and improve the SiNC/(CH(3)NH(3))(3)Bi(2)I(9) interface and electronic coupling whilst also inhibiting defect-induced degradation

Proinsulin is stable at room temperature for 24 hours in EDTA:A clinical laboratory analysis (adAPT 3)

AIMS:Reference laboratories advise immediate separation and freezing of samples for the assay of proinsulin, which limit its practicability for smaller centres. Following the demonstration that insulin and C-peptide are stable in EDTA at room temperature for at least 24hours, we undertook simple stability studies to establish whether the same might apply to proinsulin. METHODS:Venous blood samples were drawn from six adult women, some fasting, some not, aliquoted and assayed immediately and after storage at either 4°C or ambient temperature for periods from 2h to 24h. RESULTS:There was no significant variation or difference with storage time or storage condition in either individual or group analysis. CONCLUSION:Proinsulin appears to be stable at room temperature in EDTA for at least 24h. Immediate separation and storage on ice of samples for proinsulin assay is not necessary, which will simplify sample transport, particularly for multicentre trials

Tuning the Bandgap Character of Quantum-Confined Si–Sn Alloyed Nanocrystals

Nanocrystals in the regime between molecules and bulk give rise to unique electronic properties. Here, a thorough study focusing on quantum-confined nanocrystals (NCs) is provided. At the level of density functional theory an approximate (quasi) band structure which addresses both the molecular and bulk aspects of finite-sized NCs is calculated. In particular, how band-like features emerge with increasing particle diameter is shown. The quasiband structure is used to discuss technological-relevant direct bandgap NCs. It is found that ultrasmall Sn NCs have a direct bandgap in their at-nanoscale-stable α-phase and for high enough Sn concentration (≈41%) alloyed Si–Sn NCs transition from indirect to direct bandgap semiconductors. The calculations strongly support recent experiments suggesting a direct bandgap for these systems. For a quantitative comparison many-body GW + Bethe–Salpeter equation (BSE) calculations are performed. The predicted optical gaps are close to the experimental data and the calculated absorbance spectra compare well with the corresponding measurements

Nanostructured Perovskite Solar Cells

Funding: UK EPSRC EP/K022237/1, EP/M024938/1 and EP/R023638/1.Over the past decade, lead halide perovskites have emerged as one of the leading photovoltaic materials due to their long carrier lifetimes, high absorption coefficients, high tolerance to defects, and facile processing methods. With a bandgap of ~1.6 eV, lead halide perovskite solar cells have achieved power conversion efficiencies in excess of 25%. Despite this, poor material stability along with lead contamination remains a significant barrier to commercialization. Recently, low-dimensional perovskites, where at least one of the structural dimensions is measured on the nanoscale, have demonstrated significantly higher stabilities, and although their power conversion efficiencies are slightly lower, these materials also open up the possibility of quantum-confinement effects such as carrier multiplication. Furthermore, both bulk perovskites and low-dimensional perovskites have been demonstrated to form hybrids with silicon nanocrystals, where numerous device architectures can be exploited to improve efficiency. In this review, we provide an overview of perovskite solar cells, and report the current progress in nanoscale perovskites, such as low- dimensional perovskites, perovskite quantum dots, and perovskite-nanocrystal hybrid solar cells.Publisher PDFPeer reviewe

Zero-dimensional methylammonium iodo bismuthate solar cells and synergistic interactions with silicon nanocrystals

This work was supported by EPSRC (EP/K022237/1 and EP/M024938/1) and by the New Energy and Industrial Technology Development Organization (NEDO).Organometal trihalide perovskite solar cells have attracted monumental attention in recent years. Today's best devices, based on a three-dimensional perovskite structure of corner-sharing PbI6 octahedra, are unstable, toxic, and display hysteresis in current-voltage measurements. We present zero-dimensional organic-inorganic hybrid solar cells based on methylammonium iodo bismuthate (CH3NH3)3(Bi2I9) (MABI) comprising a Bi2I9 bioctahedra and observe very low hysteresis for scan rates in the broad range of 150 mV s-1 to 1500 mV s-1 without any interfacial layer engineering. We confirm good stability for devices produced and stored in open air without humidity control. The MABI structure can also accommodate silicon nanocrystals, leading to an enhancement in the short-circuit current. Through the material MABI, we demonstrate a promising alternative to the organometal trihalide perovskite class and present a model material for future composite third-generation photovoltaics.PostprintPeer reviewe

Carrier extraction from metallic perovskite oxide nanoparticles

This work was supported by EPSRC (EP/K022237/1, EP/M024938/1 and EP/R023638/1), the EPSRC Supergen SuperSolar Hub, the Department for Employment and Learning (DEL) of Northern Ireland Studentship, and by the New Energy and Industrial Technology Development Organization (NEDO).We observe the extraction of carriers excited between two types of bands in the perovskite oxide, Sr-deficient strontium niobate (Sr0.9NbO3). Sr0.9NbO3 exhibits metallic behaviour and high conductivity, whilst also displaying broad absorption across the ultraviolet, visible, and near-infrared spectral regions, making it an attractive material for solar energy conversion. Furthermore, the optoelectronic properties of strontium niobate can easily be tuned by varying the Sr fraction or through doping. Sr-deficient strontium niobate exhibits a split conduction band, which enables two types of optical transitions: intraband and interband. However, whether such carriers can be extracted from an unusual material as such remains unproven. In this report, we have overcome the immense challenge of photocarrier extraction by fabricating an extremely thin absorber layer of Sr0.9NbO3 nanoparticles. These findings open up great opportunities to harvest a very broad solar spectral absorption range with reduced recombination losses.Publisher PDFPeer reviewe

Crypt fusion as a homeostatic mechanism in the human colon.

OBJECTIVE: The crypt population in the human intestine is dynamic: crypts can divide to produce two new daughter crypts through a process termed crypt fission, but whether this is balanced by a second process to remove crypts, as recently shown in mouse models, is uncertain. We examined whether crypt fusion (the process of two neighbouring crypts fusing into a single daughter crypt) occurs in the human colon. DESIGN: We used somatic alterations in the gene cytochrome c oxidase (CCO) as lineage tracing markers to assess the clonality of bifurcating colon crypts (n=309 bifurcating crypts from 13 patients). Mathematical modelling was used to determine whether the existence of crypt fusion can explain the experimental data, and how the process of fusion influences the rate of crypt fission. RESULTS: In 55% (21/38) of bifurcating crypts in which clonality could be assessed, we observed perfect segregation of clonal lineages to the respective crypt arms. Mathematical modelling showed that this frequency of perfect segregation could not be explained by fission alone (p<10-20). With the rates of fission and fusion taken to be approximately equal, we then used the distribution of CCO-deficient patch size to estimate the rate of crypt fission, finding a value of around 0.011 divisions/crypt/year. CONCLUSIONS: We have provided the evidence that human colonic crypts undergo fusion, a potential homeostatic process to regulate total crypt number. The existence of crypt fusion in the human colon adds a new facet to our understanding of the highly dynamic and plastic phenotype of the colonic epithelium.wellcome trust royal societ