Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

Evaluation of the sonically induced narrowing of nuclear magnetic resonance spectra of solids

The Nuclear Magnetic Resonance (NMR) spectra of liquids contain a wealth of quantitative information that may be derived, for instance, from chemical shifts and spin-spin couplings. The available information depends on the incoherent rapid molecular motion that causes complicating effects present in the solid state to average to zero. Whereas liquid state NMR spectra show narrow lines, the corresponding NMR spectra from the solid state are normally composed of exceedingly broad resonance lines due to highly restricted molecular motion. It is, therefore, difficult to obtain directly as detailed information from the spectra of solids as from those derived from the liquid state. Studies on a new technique (SINNMR, the sonically induced narrowing of the NMR spectra of solids) to remove line broadening effects in the NMR spectra of the solid state are reported within this thesis. SINNMR involves narrowing the NMR absorptions from solid particles by irradiating them with ultrasound when they are suspended in a support liquid. It is proposed that ultrasound induces incoherent motion of the suspended particles, producing motional characteristics of the particles similar to those of rather large molecules. The first report of apparently successful experiments involving SINNMR[1] emphasised both the irreproducibility of the technique and the uncertainty regarding its true origin. If SINNMR can be made reproducible and the effect definitively attributed to the sonically induced incoherent motional averaging of particles, the technique could offer a simple alternative to the now classical magic-angle spinning (MAS) NMR[2] and the recently reported dynamic angle spinning (DAS)[3] and double rotation (DOR)[4] techniques. Evidence is presented in this thesis to support the proposal that ultrasound may be used to narrow the NMR spectral resonances from solids by inducing incoherent motion of particles suspended in support liquids and, additionally, for some solids, by inducing rotational motion of molecular constituents in the lattices of solids. Successful SINNMR line narrowing using 20 kHz ultrasound is reported for a variety of samples: including trisodium orthophosphate, polytetrafluoroethylene and aluminium alloys. Investigations of SINNMR line narrowing in trisodium phosphate have revealed the relationship between ultrasonic power, particle size and support liquid density for the production of optimum SINNMR conditions. It is also proposed that the incoherent motion of particles induced by 20 kHz ultrasound can originate from interactions between acoustically induced cavitation microjets and particles.

Continous annular chromatography for the separation of carbohydrate mixtures

The continuous separation of beet molasses resulting in a sucrose rich product and a non-sugar waste product was carried out using a rotating annular chromatograph. The annulus was 12 mm wide and 1.4 m long and was packed with a sodium charged 5.5% cross-linked polystyrene ion exchange resin. Separation was achieved by the simultaneous mechanisms of ion exclusion, size exclusion and partition chromatography. The entire packed bed was slowly rotated while beet molasses was fed continuously through a stationary feed nozzle to the top of the bed. Each molasses constituent having a different relative affinity for the packing and the deionised water mobile phase describes a characteristic helical path as it progresses from the stationary feed point to the bottom of the rotating bed. Each solute then elutes from the annulus at a different angular distance from the feed and separation of the multicomponent mixture is thereby achieved. When a 35% w/w sucrose beet molasses feed was used the throughput achievable was 45.1 kg sucrose m~3 resin h"1. In addition to beet molasses separation other carbohydrate mixtures were separated. In particular the separation of glucose and fructose by Ligand exchange chromatography on a calcium charged ion exchange bed was carried out. The effects of flowrates, concentration, rotation rate, temperature and particle size on resolution and dilution of constituents in the mixtures to be separated were studied. A small test rig was designed and built to determine the cause of liquid maldistribution around the annulus. The problem was caused by the porous bed support media becoming clogged with fines being introduced by eluent flows and off the resin. An outer ring was constructed to house the bed support which could be quickly replaced with the onset of maldistribution. The computer simulation of the operation of the rotating annular chromatograph has been carried out successfully.

Simultaneous biochemical reaction and separation in a continuous rotating annular chromatograph

The aim of this work has been to investigate the behaviour of a continuous rotating annular chromatograph (CRAC) under a combined biochemical reaction and separation duty. Two biochemical reactions have been employed, namely the inversion of sucrose to glucose and fructose in the presence of the enzyme invertase and the saccharification of liquefied starch to maltose and dextrin using the enzyme maltogenase. Simultaneous biochemical reaction and separation has been successfully carried out for the first time in a CRAC by inverting sucrose to fructose and glucose using the enzyme invertase and collecting continuously pure fractions of glucose and fructose from the base of the column. The CRAC was made of two concentric cylinders which form an annulus 140 cm long by 1.2 cm wide, giving an annular space of 14.5 dm3. The ion exchange resin used was an industrial grade calcium form Dowex 50W-X4 with a mean diameter of 150 microns. The mobile phase used was deionised and dearated water and contained the appropriate enzyme. The annular column was slowly rotated at speeds of up to 240°h-1 while the sucrose substrate was fed continuously through a stationary feed pipe to the top of the resin bed. A systematic investigation of the factors affecting the performance of the CRAC under simultaneous biochemical reaction and separation conditions was carried out by employing a factorial experimental procedure. The main factors affecting the performance of the system were found to be the feed rate, feed concentrations and eluent rate. Results from the experiments indicated that complete conversion could be achieved for feed concentrations of up to 50% w/v sucrose and at feed throughputs of up to 17.2 kg sucrose per m3 resin/h. The second enzymic reaction, namely the saccharification of liquefied starch to maltose employing the enzyme maltogenase has also been successfully carried out on a CRAC. Results from the experiments using soluble potato starch showed that conversions of up to 79% were obtained for a feed concentration of 15.5% w/v at a feed flowrate of 400 cm3/h. The product maltose obtained was over 95% pure. Mathematical modelling and computer simulation of the sucrose inversion system has been carried out. A finite difference method was used to solve the partial differential equations and the simulation results showed good agreement with the experimental results obtained.

Transfer coefficients over inclined tube banks

The thesis presents experimental results for shell-side transfer coefficients and pressure drops across four different tube banks, using small-scale models, with yawed tubes, as found in many types of heat exchangers, boilers and nuclear reactors. The tube banks investigated have a staggered tube layout on a rotated square pitch, with a 1.25 pitch-to-diameter ratio. The angle of attack was varied between 45o and 90o. An extensive range of Reynolds number, i.e. 0.5. to 12,600, covering so-called laminar, transition and turbulent flows, was investigated. A diffusion-controlled electrochemical mass transfer technique has been employed to measure mass transfer coefficients. The heat transfer coefficients may be then readily obtained from the mass transfer values by applying the well-established Chilton-Colburn analogy. The results for the normal tube bank, which forms the base case for the study on inclined tube banks, show close agreement with previous work. The transfer coefficients and pressure drops of the inclined tube banks are compared with results from the ideal normal tube bank to examine the effect of inclination angle on heat transfer and pressure drop variations. The variation of the transfer coefficients row-by-row and the entrance and exit effects have also been investigated. An auxilary investigation has been carried out on the role of natural convection. A preliminary correlation of transfer coefficients and pressure drops against the variation in the yaw angle has been attempted. The results are discussed in the light of the few existing theoretical treatments and experimental data for these situations, and recommendations made for future work.

Isotropic compression of mixtures of hard and soft spheres

The compaction behaviour of powders with soft and hard components is of particular interest to the paint processing industry. Unfortunately, at the present time, very little is known about the internal mechanisms within such systems and therefore suitable tests are required to help in the interpretative process. The TRUBAL, Distinct Element Method (D.E.M.) program was the method of investigation used in this study. Steel (hard) and rubber (soft) particles were used in the randomly-generated, binary assemblies because they provided a sharp contrast in physical properties. For reasons of simplicity, isotropic compression of two-dimensional assemblies was also initially considered. The assemblies were first subject to quasi-static compaction, in order to define their behaviour under equilibrium conditions. The stress-strain behaviour of the assemblies under such conditions was found to be adequately described by a second-order polynomial expansion. The structural evolution of the simulation assemblies was also similar to that observed for real powder systems. Further simulation tests were carried out to investigate the effects of particle size on the compaction behaviour of the two-dimensional, binary assemblies. Later work focused on the quasi-static compaction behaviour of three-dimensional assemblies, because they represented more realistic particle systems. The compaction behaviour of the assemblies during the simulation experiments was considered in terms of percolation theory concepts, as well as more familiar macroscopic and microstructural parameters. Percolation theory, which is based on ideas from statistical physics, has been found to be useful in the interpretation of the mechanical behaviour of simple, elastic lattices. However, from the evidence of this study, percolation theory is also able to offer a useful insight into the compaction behaviour of more realistic particle assemblies.

Bending and orientational characteristics of long period gratings written in D-shaped optical fiber

Long period gratings (LPGs) were written into a D-shaped single-mode fiber. These LPGs were subjected to a range of curvatures, and it was found that as curvature increased, there was increasingly strong coupling to certain higher order cladding modes without the usual splitting of the LPGs stopbands. A bend-induced stopband yielded a spectral sensitivity of 12.55 nm · m for curvature and 2.2 × 10-2 nm°C-1 for temperature. It was also found that the wavelength separation between adjacent bend-induced stopbands varied linearly as a function of curvature. Blue and red wavelength shifts of the stopbands were observed as the sensor was rotated around a fixed axis for a given curvature; thus, in principle, this sensor could be used to obtain bending and orientational information. The behavior of the stopbands was successfully modeled using a finite element approach.

An optical study of human ocular dimensions

Many workers have studied the ocular components which occur in eyes exhibiting differing amounts of central refractive error but few have ever considered the additional information that could be derived from a study of peripheral refraction. Before now, peripheral refraction has either been measured in real eyes or has otherwise been modelled in schematic eyes of varying levels of sophistication. Several differences occur between measured and modelled results which, if accounted for, could give rise to more information regarding the nature of the optical and retinal surfaces and their asymmetries. Measurements of ocular components and peripheral refraction, however, have never been made in the same sample of eyes. In this study, ocular component and peripheral refractive measurements were made in a sample of young near-emmetropic, myopic and hyperopic eyes. The data for each refractive group was averaged. A computer program was written to construct spherical surfaced schematic eyes from this data. More sophisticated eye models were developed making use of linear algebraic ray tracing program. This method allowed rays to be traced through toroidal aspheric surfaces which were translated or rotated with respect to each other. For simplicity, the gradient index optical nature of the crystalline lens was neglected. Various alterations were made in these eye models to reproduce the measured peripheral refractive patterns. Excellent agreement was found between the modelled and measured peripheral refractive values over the central 70o of the visual field. This implied that the additional biometric features incorporated in each eye model were representative of those which were present in the measured eyes. As some of these features are not otherwise obtainable using in vivo techniques, it is proposed that the variation of refraction in the periphery offers a very useful optical method for studying human ocular component dimensions.

Persistence in a random bond ising model of socio-econo dynamics

We study the persistence phenomenon in a socio-econo dynamics model using computer simulations at a nite temperature on hypercubic lattices in dimensions up to ve. The model includes a \social" local eld which contains the magnetization at time t. The nearest neighbour quenched interactions are drawn from a binary distribution which is a function of the bond concentration, p. The decay of the persistence probability in the model depends on both the spatial dimension and p. We nd no evidence of \blocking" in this model. We also discuss the implications of our results for possible applications in the social and economic elds. It is suggested that the absence, or otherwise, of blocking could be used as a criterion to decide on the validity of a given model in dierent scenarios.

Semantics of query-driven communication of exact values

We address the question of how to communicate among distributed processes valuessuch as real numbers, continuous functions and geometrical solids with arbitrary precision, yet efficiently. We extend the established concept of lazy communication using streams of approximants by introducing explicit queries. We formalise this approach using protocols of a query-answer nature. Such protocols enable processes to provide valid approximations with certain accuracy and focusing on certain locality as demanded by the receiving processes through queries. A lattice-theoretic denotational semantics of channel and process behaviour is developed. Thequery space is modelled as a continuous lattice in which the top element denotes the query demanding all the information, whereas other elements denote queries demanding partial and/or local information. Answers are interpreted as elements of lattices constructed over suitable domains of approximations to the exact objects. An unanswered query is treated as an error anddenoted using the top element. The major novel characteristic of our semantic model is that it reflects the dependency of answerson queries. This enables the definition and analysis of an appropriate concept of convergence rate, by assigning an effort indicator to each query and a measure of information content to eachanswer. Thus we capture not only what function a process computes, but also how a process transforms the convergence rates from its inputs to its outputs. In future work these indicatorscan be used to capture further computational complexity measures. A robust prototype implementation of our model is available.

Shaping acoustic fields as a toolset for microfluidic manipulations in diagnostic technologies

Ultrasonics offers the possibility of developing sophisticated fluid manipulation tools in lab-on-a-chip technologies. Here we demonstrate the ability to shape ultrasonic fields by using phononic lattices, patterned on a disposable chip, to carry out the complex sequence of fluidic manipulations required to detect the rodent malaria parasite Plasmodium berghei in blood. To illustrate the different tools that are available to us, we used acoustic fields to produce the required rotational vortices that mechanically lyse both the red blood cells and the parasitic cells present in a drop of blood. This procedure was followed by the amplification of parasitic genomic sequences using different acoustic fields and frequencies to heat the sample and perform a real-time PCR amplification. The system does not require the use of lytic reagents nor enrichment steps, making it suitable for further integration into lab-on-a-chip point-of-care devices. This acoustic sample preparation and PCR enables us to detect ca. 30 parasites in a microliter-sized blood sample, which is the same order of magnitude in sensitivity as lab-based PCR tests. Unlike other lab-on-a-chip methods, where the sample moves through channels, here we use our ability to shape the acoustic fields in a frequency-dependent manner to provide different analytical functions. The methods also provide a clear route toward the integration of PCR to detect pathogens in a single handheld system.

Double machine operation and psychological strain

This study examines the effects of double machine operation on psychological strain. CNC drilling machine operators' reactions to their job were monitored as they rotated between three different work conditions; single machine operation, double machine operation, and double machine operation with additionally high responsibility for products. Results show no effect of double machine operation on strain where responsibility was low. Double machine operation under the condition of high responsibility, however, was found to increase strain.

A new inventory model for aircraft spares

A special inventory problem is presented: aircraft spares that are repaired and returned to spares, called rotable inventory. Rotable inventory is not consumed so does not change in the medium term, but is rotated through operational, maintenance and stock phases. The objective for inventory performance is fleet Service Level (SL), which effects aircraft dispatch performance. A model is proposed where the fleet SL drives combined stock levels such that cost is optimized. By holding greater numbers of lower-cost items and holding lower levels of more expensive items, it is possible to achieve substantial cost savings while maintaining performance. This approach is shown to be an advance over the current literature and is tested with case data, with conclusive results.

Epitaxial growth and magnetic properties of half-metallic Fe3O4 on GaAs(100)

The growth and magnetic properties of epitaxial magnetite Fe3O4 on GaAs(100) have been studied by reflection high-energy electron diffraction, x-ray photoelectron spectroscopy, magneto-optical Kerr effect, and x-ray magnetic circular dichroism. The epitaxial Fe3O4 films were synthesized by in situ post growth annealing of ultrathin epitaxial Fe films at 500K in an oxygen partial pressure of 5×10−5mbar. The XMCD measurements show characteristic contributions from different sites of the ferrimagnetic magnetite unit cell, namely, Fetd3+, Feoh2+, and Feoh3+. The epitaxial relationship was found to be Fe3O4(100)⟨011⟩∕∕GaAs(100)⟨010⟩ with the unit cell of Fe3O4 rotated by 45° to match that of GaAs(100) substrate. The films show a uniaxial magnetic anisotropy in a thickness range of about 2.0–6.0nm with the easy axes along the [011] direction of the GaAs(100) substrate.

When does a Bounded Domain Cover a Projective Manifold? (Survey)

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and Technology