The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem. (c) 2004 Elsevier B.V. All rights reserved.

Does calcium deposition play a role in the stability of atheroma? Location may be the key

Background: Rupture of vulnerable atheromatous plaque in the carotid and coronary arteries often leads to stroke and heart attack respectively. The role of calcium deposition and its contribution to plaque stability is controversial. This study uses both an idealized and a patient-specific model to evaluate the effect of a calcium deposit on the stress distribution within an atheromatous plaque. Methods: Using a finite-element method, structural analysis was performed on an idealized plaque model and the location of a calcium deposit within it was varied. In addition to the idealized model, in vivo high-resolution MR imaging was performed on 3 patients with carotid atheroma and stress distributions were generated. The individual plaques were chosen as they had calcium at varying locations with respect to the lumen and the fibrous cap. Results: The predicted maximum stress was increased by 47.5% when the calcium deposit was located in the thin fibrous cap in the model when compared with that in a model without a deposit. The result of adding a calcium deposit either to the lipid core or remote from the lumen resulted in almost no increase in maximal stress. Conclusion: Calcification at the thin fibrous cap may result in high stress concentrations, ultimately increasing the risk of plaque rupture. Assessing the location of calcification may, in the future, aid in the risk stratification of patients with carotid stenosis.

Dynamics of crystal size distributions with size-dependent rates

The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

The intensity distribution and thermal stability of InnoSlab laser

Partially end-pumped slab laser is an innovative solid state laser, namely InnoSlab. Combining the hybrid resonator with partially end-pumping, the output power can be scaled with high beam quality. In this paper, the output intensity distributions are simulated by coordinate transformation fast Fourier transform (FFT) algorithm, comparing the thermal lens influence. As the simulated curves showed, the output mode is still good when the thermal lens effect is strong, indicating the good thermal stability of InnoSlab laser. Such a new kind of laser can be designed and optimized on the base of this simulation.

Studies on the stability of polyazamacrocycle-Eu (Tb) by potentiometry and its catalytic hydrolysis on phosphate diester

The stability constants and species distributions of complexes of two lanthanide ions, Eu (III) and Tb(III), with a macrocyclic ligand, 3,6, 9, 17 20, 23-hexaazo-29, 30-dihydroxy-13, 27-dimethyl-tricylco-[23,3,1,1(11,15)] triaconta-1 (28) 11,13,15 (30), 25 26-hexane (BDBPH), in 1: 1 and 2: 1 system, were determined potentiometrically in 50% ethanol solution, at 35.0 degrees C and I = 0.100 mol/L (KCl). The two metal ions could form deprotonated mono- or dinuclear complexes with BDBPH with high stability after the three protons of the ligand completely neutralized. At higher pH values, Eu(M) could not form hydroxo complexes with BDBPH, while Tb(III) could form hydroxo complexes in the types of M2L(OH) M2L(OH)(2) and M2L (OH)(2). The kinetic study on the hydrolysis reaction of his (4-nitrophenyl) phosphate (BNPP) catalyzed by Tb-BDBPH system (2:1) was carried out in aqueous solution (pH 7.0 similar to 10.0) at 35 degrees C with I = 0.1000 mol/L (KCl). The second-order rate constant k(BNPP) (2.3 x 10(-3) (mol/L)(-1)center dot s(-1)) was determined. The dinuclear monohydroxo species, L-Tb-2-OH, is kinetically active species.

Perturbations to trophic interactions and the stability of complex food webs

The pattern of predator-prey interactions is thought to be a key determinant of ecosystem processes and stability. Complex ecological networks are characterized by distributions of interaction strengths that are highly skewed, with many weak and few strong interactors present. Theory suggests that this pattern promotes stability as weak interactors dampen the destabilizing potential of strong interactors. Here, we present an experimental test of this hypothesis and provide empirical evidence that the loss of weak interactors can destabilize communities in nature. We ranked 10 marine consumer species by the strength of their trophic interactions. We removed the strongest and weakest of these interactors from experimental food webs containing >100 species. Extinction of strong interactors produced a dramatic trophic cascade and reduced the temporal stability of key ecosystem process rates, community diversity and resistance to changes in community composition. Loss of weak interactors also proved damaging for our experimental ecosystems, leading to reductions in the temporal and spatial stability of ecosystem process rates, community diversity, and resistance. These results highlight the importance of conserving species to maintain the stabilizing pattern of trophic interactions in nature, even if they are perceived to have weak effects in the system.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

On Truncated Versions of Certain Measures of Inequality and Stability

The present study focuses attention on defining certain measures of income inequality for the truncated distributions and characterization of probability distributions using the functional form of these measures, extension of some measures of inequality and stability to higher dimensions, characterization of bivariate models using the above concepts and estimation of some measures of inequality using the Bayesian techniques. The thesis defines certain measures of income inequality for the truncated distributions and studies the effect of truncation upon these measures. An important measure used in Reliability theory, to measure the stability of the component is the residual entropy function. This concept can advantageously used as a measure of inequality of truncated distributions. The geometric mean comes up as handy tool in the measurement of income inequality. The geometric vitality function being the geometric mean of the truncated random variable can be advantageously utilized to measure inequality of the truncated distributions. The study includes problem of estimation of the Lorenz curve, Gini-index and variance of logarithms for the Pareto distribution using Bayesian techniques.

Stability of Random Sums and Extremes

This study is about the stability of random sums and extremes.The difficulty in finding exact sampling distributions resulted in considerable problems of computing probabilities concerning the sums that involve a large number of terms.Functions of sample observations that are natural interest other than the sum,are the extremes,that is , the minimum and the maximum of the observations.Extreme value distributions also arise in problems like the study of size effect on material strengths,the reliability of parallel and series systems made up of large number of components,record values and assessing the levels of air pollution.It may be noticed that the theories of sums and extremes are mutually connected.For instance,in the search for asymptotic normality of sums ,it is assumed that at least the variance of the population is finite.In such cases the contributions of the extremes to the sum of independent and identically distributed(i.i.d) r.vs is negligible.

Biomineralisation by earthworms: an investigation into the stability and distribution of amorphous calcium carbonate

Background Many biominerals form from amorphous calcium carbonate (ACC), but this phase is highly unstable when synthesised in its pure form inorganically. Several species of earthworm secrete calcium carbonate granules which contain highly stable ACC. We analysed the milky fluid from which granules form and solid granules for amino acid (by liquid chromatography) and functional group (by Fourier transform infrared (FTIR) spectroscopy) compositions. Granule elemental composition was determined using inductively coupled plasma-optical emission spectroscopy (ICP-OES) and electron microprobe analysis (EMPA). Mass of ACC present in solid granules was quantified using FTIR and compared to granule elemental and amino acid compositions. Bulk analysis of granules was of powdered bulk material. Spatially resolved analysis was of thin sections of granules using synchrotron-based μ-FTIR and EMPA electron microprobe analysis. Results The milky fluid from which granules form is amino acid-rich (≤ 136 ± 3 nmol mg−1 (n = 3; ± std dev) per individual amino acid); the CaCO3 phase present is ACC. Even four years after production, granules contain ACC. No correlation exists between mass of ACC present and granule elemental composition. Granule amino acid concentrations correlate well with ACC content (r ≥ 0.7, p ≤ 0.05) consistent with a role for amino acids (or the proteins they make up) in ACC stabilisation. Intra-granule variation in ACC (RSD = 16%) and amino acid concentration (RSD = 22–35%) was high for granules produced by the same earthworm. Maps of ACC distribution produced using synchrotron-based μ-FTIR mapping of granule thin sections and the relative intensity of the ν2: ν4 peak ratio, cluster analysis and component regression using ACC and calcite standards showed similar spatial distributions of likely ACC-rich and calcite-rich areas. We could not identify organic peaks in the μ-FTIR spectra and thus could not determine whether ACC-rich domains also had relatively high amino acid concentrations. No correlation exists between ACC distribution and elemental concentrations determined by EMPA. Conclusions ACC present in earthworm CaCO3 granules is highly stable. Our results suggest a role for amino acids (or proteins) in this stability. We see no evidence for stabilisation of ACC by incorporation of inorganic components.

Effect of high pressure homogenisation and heat treatment on physical properties and stability of almond and hazelnut milks

The effect of high pressure homogenisation (HPH) and heat treatments on physicochemical properties and physical stability of almond and hazelnut milks was studied. Vegetable milks were obtained and homogenised by applying 62, 103 and 172 MPa (MF1, MF2 and MF3, respectively). Untreated and MF3 samples were also submitted to two different heat treatments (85 °C/30 min (LH) or 121 °C/15 min (HH)). Physical and structural properties of the products were greatly affected by heat treatments and HPH. In almond milk, homogenised samples showed a significant reduction in particle size, which turned from bimodal and polydisperse to monodisperse distributions. Particle surface charge, clarity and Whiteness Index were increased and physical stability of samples was improved, without affecting either viscosity or protein stability. Hazelnut beverages showed similar trends, but HPH notably increased their viscosity while change their rheological behaviour, which suggested changes in protein conformation. HH treatments caused an increment of particle size due to the formation oil droplet-protein body clusters, associated with protein denaturation. Samples submitted to the combined treatment MF3 and LH showed the greatest stability.

A Bayesian approach for assessing the stability of genotypes

Several statistical models can be used for assessing genotype X environment interaction (GEI) and studying genotypic stability. The objectives of this research were to show how (i) to use Bayesian methodology for computing Shukla's phenotypic stability variance and (ii) to incorporate prior information on the parameters for better estimation. Potato [Solanum tuberosum subsp. andigenum (Juz. & Bukasov) Hawkes], wheat (Triticum aestivum L.), and maize (Zea mays L.) multi environment trials (MET) were used for illustrating the application of the Bayes paradigm. The potato trial included 15 genotypes, but prior information for just three genotypes was used. The wheat trial used prior information on all 10 genotypes included in the trial, whereas for the maize trial, noninformative priors for the nine genotypes was used. Concerning the posterior distribution of the genotypic means, the maize MET with 20 sites gave less disperse posterior distributions of the genotypic means than did the posterior distribution of the genotypic means of the other METs, which included fewer environments. The Bayesian approach allows use of other statistical strategies such as the normal truncated distribution (used in this study). When analyzing grain yield, a lower bound of zero and an upper bound set by the researcher's experience can be used. The Bayesian paradigm offers plant breeders the possibility of computing the probability of a genotype being the best performer. The results of this study show that although some genotypes may have a very low probability of being the best in all sites, they have a relatively good chance of being among the five highest yielding genotypes.

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

Environmental correlates of species rank − abundance distributions in global drylands

Theoretical models predict lognormal species abundance distributions (SADs) in stable and productive environments, with log-series SADs in less stable, dispersal driven communities. We studied patterns of relative species abundances of perennial vascular plants in global dryland communities to: (i) assess the influence of climatic and soil characteristics on the observed SADs, (ii) infer how environmental variability influences relative abundances, and (iii) evaluate how colonisation dynamics and environmental filters shape abundance distributions. We fitted lognormal and log-series SADs to 91 sites containing at least 15 species of perennial vascular plants. The dependence of species relative abundances on soil and climate variables was assessed using general linear models. Irrespective of habitat type and latitude, the majority of the SADs (70.3%) were best described by a lognormal distribution. Lognormal SADs were associated with low annual precipitation, higher aridity, high soil carbon content, and higher variability of climate variables and soil nitrate. Our results do not corroborate models predicting the prevalence of log-series SADs in dryland communities. As lognormal SADs were particularly associated with sites with drier conditions and a higher environmental variability, we reject models linking lognormality to environmental stability and high productivity conditions. Instead our results point to the prevalence of lognormal SADs in heterogeneous environments, allowing for more evenly distributed plant communities, or in stressful ecosystems, which are generally shaped by strong habitat filters and limited colonisation. This suggests that drylands may be resilient to environmental changes because the many species with intermediate relative abundances could take over ecosystem functioning if the environment becomes suboptimal for dominant species.