Symbolic Dynamics in the Free-Fall Equal-Mass Three-Body Problem

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

High energy three -body breakup of three -nucleon systems

The main goal of this dissertation was to study two- and three-nucleon Short Range Correlations (SRCs) in high energy three-body breakup of 3He nucleus in 3He(e, e'NN) N reaction. SRCs are characterized by quantum fluctuations in nuclei during which constituent nucleons partially overlap with each other. ^ A theoretical framework is developed within the Generalized Eikonal Approximation (GEA) which upgrades existing medium-energy methods that are inapplicable for high momentum and energy transfer reactions. High momentum and energy transfer is required to provide sufficient resolution for probing SRCs. GEA is a covariant theory which is formulated through the effective Feynman diagrammatic rules. It allows self-consistent calculation of single and double re-scatterings amplitudes which are present in three-body breakup processes. The calculations were carried out in detail and the analytical result for the differential cross section of 3He(e, e'NN)N reaction was derived in a form applicable for programming and numerical calculations. The corresponding computer code has been developed and the results of computation were compared to the published experimental data, showing satisfactory agreement for a wide range of values of missing momenta. ^ In addition to the high energy approximation this study exploited the exclusive nature of the process under investigation to gain more information about the SRCs. The description of the exclusive 3He( e, e'NN)N reaction has been done using the formalism of the nuclear decay function, which is a practically unexplored quantity and is related to the conventional spectral function through the integration of the phase space of the recoil nucleons. Detailed investigation showed that the decay function clearly exhibits the main features of two- and three-nucleon correlations. Four highly practical types of SRCs in 3He nucleus were discussed in great detail for different orders of the final state re-interactions using the decay function as an unique identifying tool. ^ The overall conclusion in this dissertation suggests that the investigation of the decay function opens up a completely new venue in studies of short range nuclear properties. ^

High energy three-body breakup of three-nucleon systems

The main goal of this dissertation was to study two- and three-nucleon Short Range Correlations (SRCs) in high energy three-body breakup of 3He nucleus in 3He(e, e'NN)N reaction. SRCs are characterized by quantum fluctuations in nuclei during which constituent nucleons partially overlap with each other. A theoretical framework is developed within the Generalized Eikonal Approximation (GEA) which upgrades existing medium-energy methods that are inapplicable for high momentum and energy transfer reactions. High momentum and energy transfer is required to provide sufficient resolution for probing SRCs. GEA is a covariant theory which is formulated through the effective Feynman diagrammatic rules. It allows self-consistent calculation of single and double re-scatterings amplitudes which are present in three-body breakup processes. The calculations were carried out in detail and the analytical result for the differential cross section of 3He(e, e'NN)Nreaction was derived in a form applicable for programming and numerical calculations. The corresponding computer code has been developed and the results of computation were compared to the published experimental data, showing satisfactory agreement for a wide range of values of missing momenta. In addition to the high energy approximation this study exploited the exclusive nature of the process under investigation to gain more information about the SRCs. The description of the exclusive 3He(e, e'NN)N reaction has been done using the formalism of the nuclear decay function, which is a practically unexplored quantity and is related to the conventional spectral function through the integration of the phase space of the recoil nucleons. Detailed investigation showed that the decay function clearly exhibits the main features of two- and three-nucleon correlations. Four highly practical types of SRCs in 3He nucleus were discussed in great detail for different orders of the final state re-interactions using the decay function as an unique identifying tool. The overall conclusion in this dissertation suggests that the investigation of the decay function opens up a completely new venue in studies of short range nuclear properties.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Novel correlations in two dimensions: Two-body problem

We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyse in detail the two-body problem which is completely solvable. We show that the solution of the two-body problem reduces to solving a known differential equation due to Heun. We show that the two-body spectrum becomes remarkably simple for large interaction strengths and the level structure resembles that of the Landau levels. We also clarify the 'ultraviolet' regularization which is needed to define an inverse-square potential properly and discuss its implications for our model.

Effects of body size and water temperature on food consumption and growth in the sea cucumber Apostichopus japonicus (Selenka) with special reference to aestivation

To investigate the effects of body size and water temperature on feeding and growth in the sea cucumber Apostichopus japonicus (Selenka), the maximum rate of food consumption in terms of energy (C-maxe; J day(-1)) and the specific growth rate in terms of energy (SGRe; % day(-1)) in animals of three body sizes (mean +/- SE) - large (134.0 +/- 3.5 g), medium (73.6 +/- 2.2 g) and small (36.5 +/- 1.2 g) - were determined at water temperatures of 10, 15, 20, 25 and 30 degrees C. Maximum rate of food consumption in terms of energy increased and SGRe decreased with increasing body weight at 10, 15 and 20 degrees C. This trend, however, was not apparent at 25 and 30 degrees C, which could be influenced by aestivation. High water temperatures (above 20 degrees C) were disadvantageous to feeding and growth of this animal; SGRe of A. japonicus during aestivation was negative. The optimum temperatures for food consumption and for growth were similar and were between 14 and 15 degrees C, and body size seemed to have a slight effect on the optimal temperature for food consumption or growth. Because aestivation of A. japonicus was temperature dependent, the present paper also documented the threshold temperatures to aestivation as indicated by feeding cessation. Deduced from daily food consumption of individuals, the threshold temperature to aestivation for large and medium animals (73.3-139.3 g) was 24.5-25.5 degrees C, while that for small animals (28.9-40.7 g) was between 25.5 and 30.5 degrees C. These values are higher than previous reports; differences in sign of aestivation, experimental condition and dwelling district of test animals could be the reasons.

Obesity associated severe asthma represents a distinct clinical phenotype - Analysis of the British Thoracic Society Difficult Asthma Registry patient cohort according to body mass index

BACKGROUND: Obesity has emerged as a risk factor for the development of asthma and it may also influence asthma control and airways inflammation. However, the role of obesity in severe asthma remains unclear. OBJECTIVE: To explore the association between obesity (defined by BMI) and severe asthma. METHODS: Data from the National Registry for dedicated UK Difficult Asthma Services were used to compare patient demographics, disease characteristics and healthcare utilisation between three body mass index (BMI) categories (normal weight: 18.5 -24.99, overweight: 25 -29.99, obese: =30) in a well characterised group of severe asthmatic adults. RESULTS: The study population consisted of 666 severe asthmatics with a median BMI of 29.8 (interquartile range 22.5 -34.0). The obese group exhibited greater asthma medication requirements in terms of maintenance corticosteroid therapy (48.9% versus 40.4% and 34.5% in the overweight and normal weight groups, respectively), steroid burst therapy and short-acting ß2-agonist (SABA) use per day. Significant differences were seen with gastro-oesophageal reflux disease (GORD) (53.9% versus 48.1% and 39.7% in the overweight and normal weight groups, respectively) and proton pump inhibitor (PPI) use. Bone density scores were higher in the obese group, whilst pulmonary function testing revealed a reduced FVC and raised Kco. Serum IgE levels decreased with increasing BMI and the obese group were more likely to report eczema, but less likely to have a history of nasal polyps. CONCLUSIONS: Severe asthmatics display particular characteristics according to BMI that support the view that obesity associated severe asthma may represent a distinct clinical phenotype.1Royal Brompton Hospital, London, UK;2Department of Computing, Imperial College, UK3Airways Disease, National Heart & Lung Institute, Imperial College, UK;4Centre for infection and immunity, Queen's University of Belfast, UK;5University of Leicester, UK;6The University of Manchester and University Hospital of South Manchester, UK;7Birmingham Heartlands Hospital, University of Birmingham, UK;8Gartnavel General Hospital, University of Glasgow, UK;9Glasgow Royal Infirmary, Glasgow, UKCorrespondence: Dr Andrew N. Menzies-Gow, Royal Brompton Hospital, Fulham Road, London SW3 6HP.

Microabrasion-corrosion of cast CoCrMo alloy in simulated body fluids

Wear and corrosion of metal-on-metal hip replacements results in wear debris and metal-ion release in vivo, which may subsequently cause pain and hypersensitivity for patients. Retrieved metal-on-metal hip replacements have revealed that two-body sliding wear and three-body abrasive wear are the predominant wear mechanisms. However, there is a lack of understanding of the combined effects of wear/corrosion, especially the effect of abrasion-corrosion.

This study investigates the sliding-corrosion and abrasion-corrosion performance of a cast CoCrMo alloy in simulated hip joint environments using a microabrasion rig integrated with an electrochemical cell. Tests have been conducted in 0.9% NaCl, phosphate buffered saline solution, 25% and 50% bovine serum solutions with 0 or 1 g cm(-3) SiC at 37 degrees C. Experimental results reveal that under abrasion-corrosion test conditions, the presence of proteins increased the total specific wear rate. Conversely, electrochemical noise measurements indicated that the average anodic current levels were appreciably lower for the proteinaceous solutions when compared with the inorganic solutions. A severely deformed nanocrystalline layer was identified immediately below the worn surface for both proteinaceous and inorganic solutions. The layer is formed by a recrystallisation process and/or a strain-induced phase transformation that occurs during microabrasion-corrosion. (C) 2008 Elsevier Ltd. All rights reserved.

Two and three nucleon induced photon absorption

We have investigated the mechanisms leading to two and three body photon absorption in nuclei. At photon energies around the pion production threshold we obtain a fraction of three body absorption of less than 10% of the total, contradicting previous theoretical claims that it dominates the absorption process. The strength of the three body channel grows smoothly with the photon energy reaching a maximum of about 60% of the total direct absorption at energies of the photon around 400 MeV.

Many-body energy decomposition of hydrogen-bonded glycine clusters in gas-phase

A detailed analysis of the many-body contribution to the interaction energies of the gas-phase hydrogen-bonded glycine clusters, (Gly)(N), N = 1-4 is presented. The energetics of the hydrogen-bonded dimer, trimer and tetramer complexes have been analyzed using density-functional theory. The magnitude of the two-through four-body energy terms have been calculated and compared. The relaxation energy and the two-body energy terms are the principal contributors to the total binding energy. Four-body contribution is negligible. However, the three-body contribution is found to be sizable and the formation of the cyclic glycine trimer presents geometric strains that make it less favorable. (C) 2010 Elsevier B.V. All rights reserved.

Performance of body fat and body mass index cutoffs in elevated blood pressure screening among male children and adolescents

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Scaling in few-body nuclear physics

The nuclear matter calculations with realistic nucleon-nucleon potentials present a general scaling between the nucleon-nucleus binding energy, the corresponding saturation density, and the triton binding energy. The Thomas-Efimov three-body effect implies in correlations among low-energy few-body and many-body observables. It is also well known that, by varying the short-range repulsion, keeping the two-nucleon information (deuteron and scattering) fixed, the four-nucleon and three-nucleon binding energies lie on a very narrow band known as a Tjon line. By looking for a universal scaling function connecting the proper scales of the few-body system with those of the many-body system, we suggest that the general nucleus-nucleon scaling mechanism is a manifestation of a universal few-body effect.

Stability of atomic condensed systems with attractive two-body interactions

In the present report, we review recent investigations that we have conducted on the stability of atomic condensed systems, when the two-body interaction is attractive. In particular, the dynamics that occurs in the condensate due to nonconservative terms is considered in the context of an extension of the mean-field Gross-Pitaevskii approximation. Considering the relative intensity of the nonconservative parameters, chaotic and solitonic solutions are verified. Also discussed is the possibility of a liquid-gas phase transition in the presence of positive three-body elastic collisions.

Three-boson recombination at ultralow temperatures

The effects of trimer continuum resonances are considered in the three-body recombination rate of a Bose system at finite energies for large and negative two-body scattering lengths (a). The thermal average of the rate allows to apply our formula to Bose gases at ultra-low temperatures. We found a good quantitative description of the experimental three-body recombination length of cesium atoms to deeply bound molecules up to 500 nK. Consistent with the experimental data, the increase of the temperature moves the resonance peak of the three-body recombination rate to lower values of vertical bar a vertical bar exhibiting a saturation behavior. (C) 2006 Elsevier B.V. All rights reserved.

Three helium atoms and the scaling limit

We show that a scaling limit approach, previously applied in three-body low-energy nuclear physics, is realized for the first excited state of He-4 trimer. The present result suggests that such approach has a wider application.