Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Finitely coordinated models for low-temperature phases of amorphous systems

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behaviour of finite-dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von Karman-type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double-well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well-known universal glassy low-temperature anomalies when quantum effects are taken into account. © 2007 IOP Publishing Ltd.

Growth phases in the life of a lichen thallus

The growth rates of thalli of foliose saxicolous lichens before and after the linear phase of growth were measured in 1973. Changes in the radial growth rate (measured as mm/year) with thallus size in the prelinear phase (thalli less than approximately 1.5 cm in diameter) were consistent with the hypothesis that early growth of these lichens is loagarithmic. When growth in the prelinear phase was measured as a relative growth rate (measured as sq cm/sq cm/year) there was a rapid rise in growth rate until about 3 mm thallus diameter and then a decline in growth rate. The radial growth rate of non-fragmenting thalli when compared with fragmenting thalli at different stages of fragmentation suggested that radial growth rate does not significantly decline after fragmentation of the thallus. This result is not consistent with a postlinear phase in the radial growth of a lichen thallus.

The effect of flow regimes in the distillation of systems containing two liquid phases

Single phase solutions containing three components have been observed to exhibit foaminess near a single to two liquid phase boundary. It was seen, in a sintered plate column under mass transfer conditions, that distillation systems where the liquid appeared as one phase in one part of a column and two phases in another part, exhibited foaminess when the liquid concentration was near the one phase to two phase boundary. Various ternary systems have been studied in a 50 plate. 30mm i.d. Oldershaw column and it was observed that severe foaming occurred in the middle section of the column near the one liquid phase to two liquid phase boundary and no foaming occurred at the end of the column where liquid was either one phase or two phase. This is known as Ross type foam. Mass transfer experiments with Ross type ternary systems have been carried out in a perspex simulator with small and large hole diameter trays. It was observed that by removal of the more volatile component, Ross type foam did not build up on the tray. Severe entrainment of liquid was observed in all cases leading to a 'dry' tray, even with a low free area small diameter hole tray which was expected to produce a bubbly mixture. Entrainment was more severe for high gas superficial velocities and large hole diameters. This behaviour is quite different from the build up of foam observed when one liquid phase/two liquid phase Ross systems were contacted with air above a small sintered disc or with vapour in an Oldershaw distillation column. This observation explains why distillation columns processing mixtures which change from one liquid phase to two liquid phases (or vice versa) must be severely derated to avoid flooding. Single liquid phase holdups at the spray to bubbly transition were measured using a perspex simulator similar to that of Porter & Wong (17). i.e. with no liquid cross flow. A light transmission technique was used to measure the transition from spray regime to bubbly regime. The effect of tray thickness and the ratio of hole diameter to tray thickness on the transition was evaluated using trays of the same hole diameter and free area but having thickness of 2.38 mm, 4 mm, and 6.35 mm. The liquid holdup at the transition was less with the thin metal trays. This result may be interpreted by the theory of Lockett (101), which predicts the transition liquid holdup in terms of the angle of the gas iet leaving the holes in the sieve plate. All the existing correlations have been compared and none were found to be satisfactory and these correlations have been modified in view of the experimental results obtained. A new correlation has been proposed which takes into account the effect of the hole diameter to tray thickness ratio on the transition and good agreement was obtained between the experimental results and the correlated values of the liquid holdup at the transition. Results have been obtained for two immiscible liquids [kerosene and water] on trays to determine whether foaming can be eliminated by operating in the spray regime. Kerosene was added to a fixed volume of water or water was added to a fixed volume of kerosene. In both cases, there was a transition from spray to bubbly. In the water fixed system. the liquid holdup at the transition was slightly less than the pure kerosene system. Whilst for the kerosene fixed system, the transition occurred at much lower liquid holdups. Trends In the results were similar to those for single liquid phase. New correlations have been proposed for the two cases. It has been found that Ross type foams, observed in a sintered plate column and in the Oldershaw column can be eliminated by either carrying out the separation in a packed column or by the addition of defoaming additives.

Triassic stratigraphy and sedimentology in central England

The Triassic rocks of Central England consist of three major stratigraphic units: Sherwood Sandstone Group, Mercia Mudstone Group, and Penarth Group. The lower part of the Sherwood Sandstone Group represented by the Kidderminster, Cannock Chase, and Polesworth Formations represents pebbly braided river deposits carried by a major fluvial system flowing to the North-Northwest. The upper part of the Sherwood Sandstone Group includes the Wildmoor and Bromsgrove Sandstone Formations, the deposits of a sandy alluvial system. The Mercia Mudstone Group represents quiet-water deposits of marginal palya type which were subjected to occasional marine flooding. The overlying Penarth Group represent shallow marine and lagoonal environment associated with the Rhaetian marine transgression. The mineralogy of the Triassic sandstones indicates that the main source was from medium to low rank metamorphic rocks with additional supplies from igneous and metamorphic rocks. The study of size-composition trends shows that the climate was semiarid in early Triassic time and became more humid later. The Triassic sandstones show a variety of diagenetic features typical of continental red beds; these include: 1. the dissolution of unstable ferromagnesian silicates, 2. the replacement of detrital grains by clay, 3. the pseudomorphism of biotite by haematite, and 4. the formation of a suite of authigenic minerals including quartz, illite, mixed-layer illite-montmorillonite, kaolinite, k-feldspar, haematite, titanium oxide and later carbonate cement. Palaeomagnetic studies of selected samples show that the magnetization is muticomponent with the various components being carried by different textural phases of haematite.

Textural and microstructural studies of zinc sulfide and associated phases in certain base metal deposits

A textural and microstructural study of a variety of zinc sulfide-containing ores has been undertaken, and the possible depositional and deformational controls of textural and microstructural development considered. Samples for the study were taken from both deformed and undeformed zinc ores of the Central U.S. Appalachians, and deformed zinc ores of the English Pennines. A variety of mineralogical techniques were employed, including transmitted and reflected light microscopy of etched and unetched material, transmission electron microscopy and electron microprobe analysis. For the Pennine zinc sulfides, spectroscopic, x-ray diffraction and fluid inclusion studies were also undertaken. Optical and electron optical examination of the Appalachian material confirmed the suitability of zinc sulfide for detailed study with such techniques. Growth and deformation-related microstructures could be distinguished from specimen-preparation induced artifacts. A deformationally-mduced lamelliform optical anisotropy is seen to be developed in areas hosting a dense planar microstructure of {111} twin- and slip-planes. The Pennine zinc sulfide texturally records a changing depositional environment. Thus, for example, delicately growth- zoned crystals are truncated and cross-cut by solution disconformities. Fluid inclusion studies indicate a highly saline (20-25 wt. % equiv. NaCl), low temperature (100-150°C.) fluid. Texturally, two varieties of zinc sulfide can be recognised; a widely developed, iron- banded variety, and a paragenetically early variety, banded due to horizons rich in crystal defects and microscopic inclusions. The zinc sulfide takes the form of a disordered 3C-polytype, with much of the disorder being deformational in origin. Twin- and slip-plane fabrics are developed . A deformation-related optical anisotropy is seen to overprint growth-related anisotropy, along with cuprian alteration of certain {111} deformation planes.

Two-phases control of DSRC Vehicle networks for road intersection coexisting safety applications

In this paper we propose a two phases control method for DSRC vehicle networks at road intersection, where multiple road safety applications may coexist. We consider two safety applications, emergency safety application with high priority and routine safety applications with low priority. The control method is designed to provide high availability and low latency for emergency safety applications while leave as much as possible bandwidth for routine applications. It is expected to be capable of adapting to changing network conditions. In the first phase of the method we use a simulation based offline approach to find out the best configurations for message rate and MAC layer parameters for given numbers of vehicles. In the second phase we use the configurations identified by simulations at roadside access point (AP) for system operation. A utilization function is proposed to balance the QoS performances provided to multiple safety applications. It is demonstrated that the proposed method can largely improve the system performance when compared to fixed control method.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Total solution of Gibilaro and Rowe model for a segregating fluidised bed

This study re-examines the one-dimensional equilibrium model of Gibilaro and Rowe (1974) for a segregating gas fluidized bed. The model was based on volumetric jetsam concentration and divided the bed contents into bulk and wake phases, taking account of bulk and wake flux, segregation, exchange between the bulk and wake phases, and axial mixing. Due to the complex nature of the model and its unstable solution, the lack of computing power at the time prevented the authors from doing little more than the analytical solutions to specific cases of this model. This paper provides a numerical total solution and allows the effect of the respective parameters to be compared for the first time. There is also a comparison with experimental results, which showed a reasonable agreement.

Functional recombinant protein is present in the pre-induction phases of Pichia pastoris cultures when grown in bioreactors, but not shake-flasks

Background - Pichia pastoris is a widely-used host for recombinant protein production; expression is typically driven by methanol-inducible alcohol oxidase (AOX) promoters. Recently this system has become an important source of recombinant G protein-coupled receptors (GPCRs) for structural biology and drug discovery. The influence of diverse culture parameters (such as pH, dissolved oxygen concentration, medium composition, antifoam concentration and culture temperature) on productivity has been investigated for a wide range of recombinant proteins in P. pastoris. In contrast, the impact of the pre-induction phases on yield has not been as closely studied. In this study, we examined the pre-induction phases of P. pastoris bioreactor cultivations producing three different recombinant proteins: the GPCR, human A2a adenosine receptor (hA2aR), green fluorescent protein (GFP) and human calcitonin gene-related peptide receptor component protein (as a GFP fusion protein; hCGRP-RCP-GFP). Results - Functional hA2aR was detected in the pre-induction phases of a 1 L bioreactor cultivation of glycerol-grown P. pastoris. In a separate experiment, a glycerol-grown P. pastoris strain secreted soluble GFP prior to methanol addition. When glucose, which has been shown to repress AOX expression, was the pre-induction carbon source, hA2aR and GFP were still produced in the pre-induction phases. Both hA2aR and GFP were also produced in methanol-free cultivations; functional protein yields were maintained or increased after depletion of the carbon source. Analysis of the pre-induction phases of 10 L pilot scale cultivations also demonstrated that pre-induction yields were at least maintained after methanol induction, even in the presence of cytotoxic concentrations of methanol. Additional bioreactor data for hCGRP-RCP-GFP and shake-flask data for GFP, horseradish peroxidase (HRP), the human tetraspanins hCD81 and CD82, and the tight-junction protein human claudin-1, demonstrated that bioreactor but not shake flask cultivations exhibit recombinant protein production in the pre-induction phases of P. pastoris cultures. Conclusions - The production of recombinant hA2aR, GFP and hCGRP-RCP-GFP can be detected in bioreactor cultivations prior to methanol induction, while this is not the case for shake-flask cultivations of GFP, HRP, hCD81, hCD82 and human claudin-1. This confirms earlier suggestions of leaky expression from AOX promoters, which we report here for both glycerol- and glucose-grown cells in bioreactor cultivations. These findings suggest that the productivity of AOX-dependent bioprocesses is not solely dependent on induction by methanol. We conclude that in order to maximize total yields, pre-induction phase cultivation conditions should be optimized, and that increased specific productivity may result in decreased biomass yields.