Study On Buoyancy Convection Phenomenon In The Crystal Growth Process

Real-time phase shift Mach-Zehnder interference technique, imaging technique, and computer image processing technique were combined to perform a real-time diagnosis of NaClO3 crystal, which described both the dissolution process and the crystallization process of the NaClO3 crystal in real-time condition. The dissolution fringes and the growth fringes in the process were obtained. Moreover, a distribution of concentration field in this process was obtained by inversion calculation. Finally, the buoyancy convection phenomenon caused by gravity in the crystal growth process was analyzed. The results showed that this convection phenomenon directly influences the growth rate of each crystal face in the crystal.

Bifurcation in a reaction diffusion system

The bifurcation and nonlinear stability properties of the Meinhardt-Gierer model for biochemical pattern formation are studied. Analyses are carried out in parameter ranges where the linearized system about a trivial solution loses stability through one to three eigenfunctions, yielding both time independent and periodic final states. Solution branches are obtained that exhibit secondary bifurcation and imperfection sensitivity and that appear, disappear, or detach themselves from other branches.

Steady capillary-gravity waves on deep water

The properties of capillary-gravity waves of permanent form on deep water are studied. Two different formulations to the problem are given. The theory of simple bifurcation is reviewed. For small amplitude waves a formal perturbation series is used. The Wilton ripple phenomenon is reexamined and shown to be associated with a bifurcation in which a wave of permanent form can double its period. It is shown further that Wilton's ripples are a special case of a more general phenomenon in which bifurcation into subharmonics and factorial higher harmonics can occur. Numerical procedures for the calculation of waves of finite amplitude are developed. Bifurcation and limit lines are calculated. Pure and combination waves are continued to maximum amplitude. It is found that the height is limited in all cases by the surface enclosing one or more bubbles. Results for the shape of gravity waves are obtained by solving an integra-differential equation. It is found that the family of solutions giving the waveheight or equivalent parameter has bifurcation points. Two bifurcation points and the branches emanating from them are found specifically, corresponding to a doubling and tripling of the wavelength. Solutions on the new branches are calculated.

Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.

Some modified bifurcation problems with application to imperfection sensitivity in buckling

The branching theory of solutions of certain nonlinear elliptic partial differential equations is developed, when the nonlinear term is perturbed from unforced to forced. We find families of branching points and the associated nonisolated solutions which emanate from a bifurcation point of the unforced problem. Nontrivial solution branches are constructed which contain the nonisolated solutions, and the branching is exhibited. An iteration procedure is used to establish the existence of these solutions, and a formal perturbation theory is shown to give asymptotically valid results. The stability of the solutions is examined and certain solution branches are shown to consist of minimal positive solutions. Other solution branches which do not contain branching points are also found in a neighborhood of the bifurcation point.

The qualitative features of branching points and their associated nonisolated solutions are used to obtain useful information about buckling of columns and arches. Global stability characteristics for the buckled equilibrium states of imperfect columns and arches are discussed. Asymptotic expansions for the imperfection sensitive buckling load of a column on a nonlinearly elastic foundation are found and rigorously justified.

Bifurcation theory of nonlinear boundary value problems

The theory of bifurcation of solutions to two-point boundary value problems is developed for a system of nonlinear first order ordinary differential equations in which the bifurcation parameter is allowed to appear nonlinearly. An iteration method is used to establish necessary and sufficient conditions for bifurcation and to construct a unique bifurcated branch in a neighborhood of a bifurcation point which is a simple eigenvalue of the linearized problem. The problem of bifurcation at a degenerate eigenvalue of the linearized problem is reduced to that of solving a system of algebraic equations. Cases with no bifurcation and with multiple bifurcation at a degenerate eigenvalue are considered.

The iteration method employed is shown to generate approximate solutions which contain those obtained by formal perturbation theory. Thus the formal perturbation solutions are rigorously justified. A theory of continuation of a solution branch out of the neighborhood of its bifurcation point is presented. Several generalizations and extensions of the theory to other types of problems, such as systems of partial differential equations, are described.

The theory is applied to the problem of the axisymmetric buckling of thin spherical shells. Results are obtained which confirm recent numerical computations.

Effect of darting phenomenon of African catfish Heterobranchus longifilis (Burchell 1822) on growth performance of Nile tilapia: Oreochromis niloticus (Linnaeus, 1758)

Replicate Ponds of 0.02ha stocked at 500 catfishes with 20,000 tilapia/ha were used to assess growth performance of O.niloticus, average weight 50.4g with (i) darted catfish; H.longifilis (shooters) average weight 60.3g (ii) non-shooters of H.longifilis, average weight 35.4g. Final mean weight, mean growth rate, specific growth rate and food conversion ratio were 499.5g 26g/day, 1.36% and 5.58% respectively for O.niloticus stocked with longifilis (shooters and 440.4g 2.3g/day 1.23% and 5.58% respectively for O.niloticus stocked withH.longifilis (non- shooters) and 246.9g, 1.2g/day, 0.93, 6.30% respectively for tilapia in monoculture. The least growth was noted for O. niloticus in monoculture while the best growth was recorded O. niloticus in polyculture with darted catfish

Effect of darting phenomenon of African catfish Heterobranchus longifilis (Burchell 1822) on growth performance of Nile tilapia: Oreochromis niloticus (Linnaeus, 1758)

Replicate Ponds of 0.02ha stocked at 500 catfishes with 20,000 tilapia/ha were used to assess growth performance of O.niloticus, average weight 50.4g with (i) darted catfish; H.longifilis (shooters) average weight 60.3g (ii) non-shooters of H.longifilis, average weight 35.4g. Final mean weight, mean growth rate, specific growth rate and food conversion ratio were 499.5g 26g/day, 1.36% and 5.58% respectively for O.niloticus stocked with longifilis (shooters) and 440.4g 2.3g/day 1.23% and 5.58% respectively for O.niloticus stocked with H.longifilis (non- shooters) and 246.9g, 1.2g/day, 0.93, 6.30% respectively for tilapia in monoculture. The least growth was noted for O. niloticus in monoculture while the best growth was recorded O. niloticus in polyculture with darted catfish

Flowering in British Lemna: A rare, cyclic or simply overlooked phenomenon?

It is largely presumed that reproduction in British Lemna, as in other British Lemnaceae, is almost entirely asexual, with new daughter fronds being produced from the side pouches of older mother fronds. Sexual reproduction is considered to be a rather rare event or even absent and because of this rarity the sexual features of Lemna, such as anthers and fruit, are often considered to be of little taxonomic value. It was with some surprise, therefore, that widespread flowering was observed in all British Lemna during the summer of 1995. Initial observations in Shropshire during June recorded flowers in minor and trisulca, with fruit production in trisulca. L.gibba, minor and minuta were noted as being in flower on several occasions in Kent, during July and August, probably fruit production occurring in both species. To what extent these events are truly representative of the sexual reproduction rate of British Lemna on a year-to-year basis, or simply reflect the unusually high summer temperatures of 1995, is unclear.

Abnormal phenomenon of ac Stark splitting in magneto-optical traps

We experimentally study the ac Stark splitting in D2 line of cold Rb-87 atoms. The frequency span between the Autler-Townes doublets is obviously larger than that derived from theoretical calculation. Two physical effects, which increase the effective Rabi frequency, contribute to the splitting broadening. First, atoms tend to distribute in strong lield places of a inhomogeneous red-detuned light field. Second, atoms reabsorb scattered light when they are huge in number and high in density.

Analysis on fluorescence intensity reverse photonic phenomenon between red and green fluorescence of oxyfluoride nanophase vitroceramics

An interesting fluorescence intensity reverse photonic phenomenon between red and green fluorescence is investigated. The dynamic range. of intensity reverse between red and green fluorescence of Er( 0.5) Yb( 3): FOV oxyfluoride nanophase vitroceramics, when excited by 378.5nm and 522.5nm light respectively, is about 4.32 x 10(2). It is calculated that the phonon- assistant energy transfer rate of the electric multi- dipole interaction of {(4)G(11/2)( Er3+) -> F-4(9/2)( Er3+), F-2(7/2)( Yb3+). F-2(5/2)( Yb3+)} energy transfer of Er( 0.5) Yb( 3): FOV is around 1.380 x 10(8) s(-1), which is much larger than the relative multiphonon nonradiative relaxation rates 3.20 x 10(5) s(-1). That energy transfer rate for general material with same rare earth ion's concentration is about 1.194 x 10(5) s(-1). These are the reason to emerge the unusual intensity reverse phenomenon in Er( 0.5) Yb( 3): FOV. (C) 2007 Optical Society of America.