Degenerate Phases Research Articles

Phase transition between the cholesteric and twist grain boundaryCphases

The upper critical temperature Tc2 for the phase transition between the Cholesteric phase (N*) and the Twist Grain Boundary C phase with the layer inclination tilted to the pitch axis (TGBct) in thermotropic liquid crystals is determined by the mean field Chen-Lubensky approach. We show that the N*-TGBct phase transition is split in two with the appearance of either the TGBA or the TGB2q phase in a narrow temperature interval below Tc2. The latter phase is novel in being superposed from two degenerate TGBct phases with different (left and right) layers inclinations to the pitch axis.

Effective pairing model for a one-dimensional dimerized system

Dimerization in a one-dimensional chain is modelled using an alternating potential model. Within the mean field approximation, the present model includes an effective pairing contribution between the bonding electrons as well as the Su-Schrieffer-Heeger Hamiltonian. It is shown that the effective pairing introduces the soliton and the energy gap in the dimerized one- dimensional system. It is also found that superconductivity in the dimerized system is prevented by the energy barrier between the two degenerate phases.

On a stopping process for oscillatory integrals

In this paper we introduce a stopping process to analyze oscillatory integral operators with degenerate phases. The resulting bounds give smoothing properties for averages along variable families of curves inR n with two-sided torsion.

Desorption or disordering from diffraction peak intensity decay?

Abstract When an ordered overlayer is heated at a high enough temperature, there is loss of order that can be monitored through the decay of the peak intensity of diffraction spots. This is caused by either particle loss to the gas phase or the onset of diffusion that disorders the overlayer. With the use of model simulations on a c(2 × 2) ordered overlayer, we show how the peak intensity decay can differentiate between the two cases. We further examine the growth laws describing the growth of disorder to see if they obey similar laws as the reverse ordering processes. When no interfaces separating degenerate phases are present, disordering and ordering processes do not obey the same growth laws.

Desorption or disordering from diffraction peak intensity decay?

When an ordered overlayer is heated at a high enough temperature, there is loss of order that can be monitored through the decay of the peak intensity of diffraction spots. This is caused by either particle loss to the gas phase or the onset of diffusion that disorders the overlayer. With the use of model simulations on a c(2 × 2) ordered overlayer, we show how the peak intensity decay can differentiate between the two cases. We further examine the growth laws describing the growth of disorder to see if they obey similar laws as the reverse ordering processes. When no interfaces separating degenerate phases are present, disordering and ordering processes do not obey the same growth laws.

Theoretical concepts of conducting polymers

The central theoretical concepts in quasi one dimensional conducting polymers were discussed. The topics include 1. 1. the interacting electron-phonon system; 2. 2. spontaneous symmetry breaking and dimerization; 3. 3. soliton, polaron and bipolaron excitations; 4. 4. charge-spin separation and fractionally charged kinks; 5. 5. photogeneration of soliton-antisoliton pairs and the nonlinear lattice dynamics that ensues; 6. 6. soliton confinement in polymers having non degenerate broken symmetry phases; 7. 7. electron-electron Coulomb repulsion effects; 8. 8. effects of quantum fluctuations of the phonon field; 9. 9. large doping and the pseudo metallic phase. Since these and related topics have been discussed in detail in a recent review article by A.J. Heeger, S. Kivelson, W.P. Su and the author, Reviews of Modern Physics, 60 781–849 (1988), the reader is referred to this source for details concerning these topics.

Statistical mechanics of neural networks near saturation

The Hopfield model of a neural network is studied near its saturation, i.e., when the number p of stored patterns increases with the size of the network N, as p = αN. The mean-field theory for this system is described in detail. The system possesses, at low α, both a spin-glass phase and 2 p dynamically stable degenerate ferromagnetic phases. The latter have essentially full macroscopic overlaps with the memorized patterns, and provide effective associative memory, despite the spin-glass features. The network can retrieve patterns, at T = 0, with an error of less than 1.5% for α < α c = 0.14. At α c the ferromagnetic (FM) retrieval states disappear discontinuously. Numerical simulations show that even above α c the overlaps with the sored patterns are not zero, but the level of error precludes meaningful retrieval. The difference between the statistical mechanics and the simulations is discussed. As α decreases below 0.05 the FM retrieval states become ground states of the system, and for α < 0.03 mixture states appear. The level of storage creates noise, akin to temperature at finite p. Replica symmetry breaking is found to be salient in the spin-glass state, but in the retrieval states it appears at extremely low temperatures, and is argued to have a very weak effect. This is corroborated by simulations. The study is extended to survey the phase diagram of the system in the presence of stochastic synaptic noise (temperature), and the effect of external fields (neuronal thresholds) coupled to groups of patterns. It is found that a field coupled to many patterns has a very limited utility in enhancing their learning. Finally, we discuss the robustness of the network to the relaxation of various underlying assumptions, as well as some new trends in the study of neural networks.

The poly-polyphenanthrene family of multi-phase π-network polymers in a valence-bond picture

A family of long polymer strips ranging from the extremes of polyacetylene to graphite are considered from a truncated valence-bond (VB) view. It is argued that several phases with different long range-ordering in electronic structure are possible. Calculations reveal that in some cases there should be nearly degenerate ground-state phases, with consequent low energy solitonic excitations. For the non-degenerate cases bound bisolitonic excitations should occur. Similarities and contrasts between VB and band-theoretic molecular-orbital views are noted.

The poly-polyacene family of multi-phase π-network polymers in a valence-bond picture

A family of long polymer strips are argued to exhibit distinct phases each with a different long-range ordering in electronic structure. Degenerate ground-state phases necessarily occur (due to symmetry) for odd width strips, and may also occur for even width strips. A new type of solitonic excitation is indicated; it may be viewed as consisting of a group of bound solitons that cannot mutually annihilate (i.e. there are no antisolitons in the group). Valence-bond and band-theoretic molecular-orbital views are compared.

Germination and establishment of seedlings in different phases of theCalluna life cycle in a Scottish heathland

Previous authors have suggested that cyclical succession takes place inCalluna-dominated heathland, and is determined by the different growth phases of the dominant. Characteristic species are said to invade at different stages of the life cycle ofCalluna, particularly in the initial and pioneer phases and in the degenerate phase. In the last phase, gaps are formed due to separation and dying of the oldest frame branches. This paper aims to analyze in which microhabitat and in which phase of theCalluna life cycle seedling emergence and establishment is possible. More seedlings appear in pioneerCalluna than in matureCalluna stands in experimentally manipulated micro-sites. In pioneerCalluna establishment is affected only by application of litter, in matureCalluna by increased illumination. The differences between treatments disappeared after three years, but not the difference in establishment between stands. Seedling emergence from species sown experimentally was different in the successive phases ofCalluna. Highest emergence was in the pioneer stand. In a seedling survey also most seedlings appeared and established in the pioneer phase. The number of recently germinated seeds was high in all phases. However, seedling survival was very low, except in the pioneer stands. This study does not of itself show evidence for cyclical succession inCalluna-dominated heath vegetation. Colonization of gaps by seedlings ofCalluna in mature or degenerate phases is possible, but must be an infrequent occurrence.

Birch regeneration in heath vegetation

SynopsisThe relationship between stand structure of Calluna vulgaris and the ability of Betula spp. to establish was examined at Dinnet Moor, Aberdeenshire. As a result of management by burning, a series of even-aged stands of Calluna is available including recently-burnt examples and stands with Calluna in the pioneer, building, mature and degenerate phases. Uneven-aged stands were included for comparison. The density of birch was found to be high very shortly after burning, much less in pioneer phase stands and minimal in the building and mature phases, indicating high mortality as the stand ages. Some indication of slightly higher densities in degenerate stands was obtained, suggesting some recruitment at this stage. Comparisons of the age of individual birches (seedlings or saplings) with that of the adjacent Calluna showed that, in general, birch is established very shortly after Calluna begins to regenerate, the surviving birch individuals being consistently one or two years younger than the Calluna. Again, results indicated little or no recruitment after the Calluna stands enter the building phase. Experimental introduction of birch seedlings to stands of various age since burning showed that survival and performance was best in the pioneer stands, and poorest in building stands.It is concluded that birch is virtually excluded by dense Calluna stands in the building and mature phases, and that carefully controlled management involving regular burning may therefore prevent the entry of birch. However, occasional fires followed by slow or patchy Calluna regeneration may provide ideal conditions for birch establishment.

Phase diagram of the square-lattice Ising model with first- and second-neighbour interactions

The phase diagram of the square-lattice Ising model with first- and second-neighbour interactions in an external magnetic field has been calculated by the interface method. The first-neighbour interactions are assumed to be antiferromagnetic while the interaction ratio, R, assumes arbitrary values. Closed-form second-order phase boundaries are obtained for three ordered phases (here called antiferromagnetic, layered and degenerate phases). This is not in agreement with Monte Carlo (MC) computations which proposed two ordered phases (called antiferro- and superantiferromagnetic phase). A proof is given that the layered and degenerate phase are two separate phases. For R>or=0 all transitions are second-order order-disorder transitions. For R<0 the transition from the ordered (antiferromagnetic) to the disordered phase is first order at low temperatures, and a tricritical-point estimate, which is in good agreement with MC and renormalisation-group calculations, is found. An estimate for the critical chemical potential of the hard-squares lattice gas with first- and second-neighbour exclusion is found. This is about 70% higher than the currently accepted value.

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ≳1022Mx) and smaller elements ranging down to flux fibres (≲ 1018Mx). Some implications of similar features in other stars are discussed.

Community dynamics in relation to management of heathland vegetation in Scotland

The paper describes studies of post-fire succession in heathland vegetation in N.E. Scotland, dominated by Calluna vulgaris. A preliminary model (Legg, 1978) suggested good agreement between simulation of succession on the basis of a Markov chain and observations of stands at different stages of development after burning, at least in the earlier stages. Vegetation transitions are currently being recorded in permanent plots on burnt areas. First results confirm the view that (a) the post-fire succession has the properties of a Markov process, (b) this type of model remains valid when constructed from records of actual transitions, rather than data obtained by inference from evidence of transition. Comparing successional events in stands where, at the time of burning, the Calluna population was in pioneer-, building-, mature-and degenerate phases, shows that transition matrices generally agree with the Markov hypothesis, but not in the case of stands where Calluna was degenerate when burnt. The composition of establishing vegetation 1 year after fire is not confined to species normally associated with the early stages of succession, but reflects the composition of the stand before burning. Redevelopment after fire is described in terms of an initial floristic composition of species with strategies permitting early re-establishment, selected by the recurrence of the fire factor. Subsequent transitions represent changes in their relative abundance due to differing growth properties and competitive interactions. This interpretation applies only under conditions of recurrent incidence of fire (normally once in 10–15 yr). If fire does not recur, Calluna stands pass into the degenerate phase, where changes in the nature of relay floristics may come into play (e.g. with tree colonization).

Litter Accumulation Under Calluna Vulgaris on a Lowland Heathland in Britain

The pattern of organic matter production by the above-ground vegetation of Calluna heathland in lowland Britain has been described by Chapman, Hibble & Rafarel (1975) and accounts of the overall nutrient budget and root standing crop for the same area are given by Chapman (1967, 1970). The litter layer accumulating on the surface of the soil is important as a storage bank for plant nutrients that can be released by the activity of the decomposers. In an ecosystem where available nutrients are present in limited quantities only and the rate of decomposition is low the litter layer becomes increasingly important in the overall nutrient regime of the system. The litter layer is an important habitat for members of the soil fauna, a high proportion of the biomass of the soil fauna actually living in this layer. In a potentially cyclical system, such as heathland, where the vegetation passes through building, mature and degenerate phases of development, the accumulation and characteristics of the litter layer are important regarding germination and establishment of both Calluna vulgaris (L.) Hull and invading tree and shrub species. This paper attempts to characterize the process of litter accumulation in relation to litter production, general considerations of decomposition, and the release of plant nutrients in the litter layer of an area of lowland heathland in southern Britain (in Dorset). Details of the sites under discussion have been described by Chapman (1967, 1970) and by Chapman et al. (1975).

Cryptogam Complement and Biomass in Dry Calluna Heath of Different Ages

The heath types studied (Yorkshire, England) are shown to be more closely related to those of the Netherlands than to other regions of the British Isles. The nine sample plots from pioneer, building, mature and degenerate phases of the Calluna life cycle have been sampled for cryptogams using ten 20 x 20 cm sub-samples and the biomass for each cryptogam species calculated in g/10 m2 (kg/hectare). Based on biomass and species development three communities are recognised in association with the development of the heath following burning - Pioneer (Lecideo-Callunetum), Building (Pohlio-Callunetum) and Mature-degenerate (Cladonio-Callunetum). The dominance and diversity relationships of the stages of the life cycle are discussed via the use of Simpson's index of dominance concentration. Dominance-diversity curves are shown to fit simple geometric progressions in all stages except the mature stages where

CuSe2, a Marcasite Type Superconductor

CuSe2 occurs in a room temperature form of the marcasite type1 and a high-pressure high-temperature modification of the pyrite type2. In both the marcasite and pyrite structures the cations are coordinated by six anions forming a distorted octahedron while the anions are bonded to three cations and another anion. In the pyrite structure the anion octahedra are connected by shared corners and in the marcasite structure the octahedra form chains by sharing edges. In the pyrites and the normal marcasites the deformation of the anion octahedra is not very marked. The marcasite family, however, has another branch, the loellingites, in which the deformation of the anion octahedra is much more pronounced and of opposite sign. The ratio of the octahedron edge parallel and perpendicular to the cation chains is roughly 1.1 in the normal marcasites and about 0.75 in the loellingites3,4. Different electronic structures of the cations account for the different distortions. Loellingites are found only in non-metallic phases containing d2 and d4 cations and distortions then result from the Jahn–Teller effect. Pyrites with dn cations occur for n≧5, while normal marcasites are known only for n≧6. In both the pyrite and the normal marcasite phases non-metallic properties are possible only if the cations have completely occupied d subbands, such as de3dγ2, de6, de6dγ2 and d10. Examples of these configurations are MnS2, RuS2, NiS2 and ZnS2(p) respectively. (The symbols (r), (h), (p) indicate room temperature, high temperature and high pressure modifications, respectively.) Because large distortions would be required to separate the energies of the degenerate dγ states, all d7 and d9 phases are metallic and adopt either the pyrite or the normal marcasite structure.