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The long-time behavior of the incompressible Navier-Stokes equations on a 2-torus is computed using several discretizations in space and in time. We compare several nonlinear Galerkin methods (NGMs) with the standard Galerkin method (SGM) in both their ability to capture the dynamic and geometric behavior of a turbulent flow accurately, and the computational efficiency with which they are solved using variable time-step integration schemes. To measure the convergence of the chaotic attractor we employ Poincare section plots as well as density functions of instantaneous Lyapunov exponents. As expected, for the smooth (single mode) force used, the NGMs fare no better than the SGM in reproducing the correct behavior. As the number of modes for each method is increased, however, a distinct advantage in computational cost emerges for the NGMs. This trend suggests that the correct solution may be computed at considerable savings for a nonsmooth force, at higher Reynolds numbers.

An algebraic approximation of global attractors introduced by Foias and Temam is developed into a numerically stable algorithm and implemented for the Lorenz system and Kuramoto-Sivashinsky equation. An error estimate is derived for the numerical computation of a sequence of improper integrals needed for the polynomials. The zero sets of the approximating polynomials are observed to approach the global attractor at rates which seem to vary with the recurrence of the solution orbits.

Nonlinear Galerkin methods (NGMs) based on pproximate inertial manifolds are applied to a weakly dissipative nonlinear Schrodinger equation. The purpose is to capture critical and chaotic behavior with as few modes as possible. Density functions are used on both the energy and instantaneous Lyapunov exponents to determine convergence of a chaotic attractor as the number of modes is increased. The computations presented here indicate a substantial reduction in the number of modes needed for the NGMs, compared to that needed for the traditional Galerkin method.

It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts such as spurious turning points and inaccurate solution branches. These shortcomings were attributed to a lack of dissipation in the forms used. We show analytically and verify numerically that with an appropriate adjustment we can eliminate these numerical artifacts. The motivation for this adjustment is to enforce dissipation, while maintaining the same order of approximation. We demonstrate with computations that the most natural remedy, namely, preparation of the equation, can be highly sensitive to assumptions on the size of the absorbing ball. In addition, we show that certain implicit forms are dissipative without any adjustment. As an illustrative example we use here the Kuramoto-Sivashinsky equation.

In the present studies an attempt has been made to elucidate the karyomorphological details in some important mulberry cultivars of exotic origin

The Kuramoto-Sivashinsky equation is a dissipative evolution equation in one space dimension which, despite its apparent simplicity, gives rise to a very rich dynamical behavior, as evidenced for instance by the study in [16], of its complicated set of stationary solutions and stationary and Hopf bifurcations. The large time behavior of the solutions is usually embodied by the attractor and the inertial manifolds which have been the object of many studies. In the present article, explicit expressions which can be completely evaluated are obtained for the dimension of an inertial manifold for the Kuramoto-Sivashinsky equation. This involves reworking the analysis in [1] to estimate the radius of the absorbing ball. From there, the choice of phase space, spectral gap condition, and preparation of the equation outside the absorbing ball are varied and the results compared over a moderate domain length. A new preparation of the equation is introduced which leads to the smallest dimension of those compared. The dimension is also obtained for the equation prepared using radii smaller than that of the known absorbing ball, down to the radius of the global attractor suggested by computations.

The need to validate and improve numerical models of the MPD thruster flow, using detailed comparisons with experimentally determined plasma properties, is essential in the effort to improve MPD thruster efficiency. This research represents an attempt to experimentally identify trends, in the variation of plasma properties inside of a self-field MPD thruster, which could be meaningfully compared with numerical results. Experimental results, consistent with the numerical model in trend, show an axial variation of the electron temperature along the anode which exhibits a very distinctive double-peaked profile. Experimental axial profiles of the electron number density and current density were also consistent with the numerical model in trend. Such evidence, along with results of the numerical model, suggest that an oblique shock is present near the inlet, and is required to establish the radial pressure gradient so prevalent in the MPD thruster. This work marks one of the first non-trivial, successful comparisons between a numerical model and experimentally determined plasma properties inside the MPD thruster.

Tetraploidy was successfully induced in mulberry cultivar RFS-135 (male), with 0.3 and 0.4% colchicine applied to sprouting buds for 6 and 8 hours for three consecutive days. The tetraploids are characterized by stunted growth, large, thick, coarse and dark green leaves, elongated and broad petiole and long inflorescences. Considerable increase in respect of stomatal chloroplast, weight and water content of leaves and pollen diameter and reduction in frequency of stomata per unit area, number of primary branches and internodal distance have been recorded. Meiosis is irregular. Various types of chromosomal associations, presence of univalents, unequal distribution and precocious movement of chromosomes, laggards, bridges at metaphase I and II, cytomixis at metaphase I and at dyad stage and varying number of microspores have been frequently observed in the PMCs. The reduced pollen fertility has been attributed to the loss of chromatin material due to meiotic abnormalities and multivalent associations.

A rare case of interspecific hybridization between the Indian oak feeding silkworm Antheraea roylei (n=31) and Chinese oak feeding silkworm A. pernyi (n=49) yielding fertile and vigorous offspring is reported. The F1 and the backcross (A. roylei X A. pernyi X A. pernyi male individuals of the above cross and the F23 and F32 male offspring derived from an earlier cross between another race of A. roylei (n=30) and A. pernyi (n=49) were cytogenetically analysed in order to study their chromosome dynamics. The F1 hybrids showed 18 trivalents and 13 bivalents in the first meiotic prophase and metaphase. The backcross individuals possessed either 9 trivalents and 31 bivalents or 49 bivalents, in Metaphase I cells. The F23 and F32 individuals were karyotypically alike and exhibited 49 bivalents. The following conclusions were drawn from the above observations: (a) in spite of allopatry and karyotypic divergence in number, a high degree of homology exists between the chromosomal complements of the two species; (b) A. pernyi possibly evolved from A. roylei, during the course of which 18 chromosomes of the latter underwent fission to give rise to the 36 chromosomes of the former. This is demonstrated by trivalent formation and pairing affinities in F1 hybrids; (c) selection has favoured the elimination of large A. roylei chromosomes which participated in trivalent formation in successive generations of inbred hybrids to establish a stable Karyotype like that of A. pernyi.

Triploids were successfully evolved in mulberry by diploidizing female gamete cells of Morus alba var. Kanva-2 with 0.2%, 0.3% and 0.4% colchicine treated for 8 hours for consecutive 3 days and by crossing them with monoecious diploid mutant. The triploids are characterized by increased growth and rooting habit; weight, size and water content of leaves, size of stomata and number of stomatal chloroplast and reduction in frequency of stomata per unit area and internodal distance have been recorded. Meiosis is highly irregular and characterized by the presence of a high frequency of trivalents and univalents. Various types of chromosomal associations, presence of tetravalents, unequal distribution and precocious movements of chromosomes, laggards, bridges at metaphase I and II, cytomixis at metaphase I and II, telophase I and II, dyads and tetrads stages and varying number of microspores have been frequently observed in the PMCs. The reduced pollen fertility has been attributed to various meiotic anomalies. Maintenance and commerical exploitation of triploids with desirable characters on large scale is feasible by vegetative multiplication.

The anther development conforms to the monocotyledonous type. The tapetal cells are glandular and polynucleate. The pollen tetrads are of tetrahedral (68%), decussate (18%) and isobilateral (14%) types. The pollen grains are shed at 2-celled stage. The ovule is anatropous, crassinucellate and bitegmic. The development of embryo sac is of polygonum type. The endosperm is nuclear. The embryo development follows Urtica variation of Asterad type. The seed coat is 3 layered. The pericarp consists of 3 zones. The seed is endospermic.

Qualitative assessment of nine promising mulberry varieties with two check cultivars was evaluated with silkworm, Bombyx mon (L.). The feeding experiment revealed that ACC-143 and ACC-203 (S-135) varieties were superior to other varieties and check cultivars in all the economic characters of cocoon. The variety x season interaction was highly significant. ACC-143 and ACC-203 showed significantly better results over other varieties.

A modified Galerkin (the “Euler-Galerkin”) algorithmj for the computational of inertial manifolds is described and applied to reaction diffusion and the Kuramoto-Sivashinsky (KS) equation. In the context of the (KS) equation, a low-dimensional Euler-Galerkin approximation ( n = 3) is distinctly superior to the traditional Galerkin of the same dimension, and comparable to a traditional Galerkin of a much higher dimension ( n = 16).

1. 1. The proteolytic enzyme, cocoonase, from Antheraea mylitta has been compared to other cocoonases and bovine trypsin and found to be similar in (1) molecular weight, (2) amino acid composition, (3) specificity and reactivity toward Nα-benzoyl- l -arginine ethyl ester, (4) proteolytic specificities toward glucagon, B-chain of insulin and lysozome, (5) rate of proteolysis of modified lysozyme and (6) NH2-terminal amino acid sequence. 2. 2. The A. mylitta cocoonase, however, activated chymotrypsinogen A at a rate 3200-fold slower than bovine trypsin which suggested subtle and important differences in the structures of these two enzymes.

Genetical studies withAntheraea mylitta have revealed that larval body colour is controlled by 2 independently assorting pairs of alleles. Yellow body is designatedYYbb, blueyyBB; greenYYBB (wild variety); and almond bodyyybb.

IN order to test the effect of the hydrogen ion concentration of the cell-sap on stomatal movement, experiments were made with the stomata of Tulipa, Scilla, Iris, and Tradescantia. It was found that the hydrogen ion concentration of the cell-sap of the guard-cells was approximately 4.5, while the epidermal cells were slightly less acid. The stripped epidermis was placed in buffer mixtures of known hydrogen ion concentration and left for two, six, twelve, and twenty-four hours respectively. The mixture used was the B.D.H. ‘Universal Buffer Mixture’. For each time interval, one set was kept in the light and another in the dark for comparison. It was found that, in the case of Tulipa, the stomata were closed between pH 1 and pH 5, and at pH 6,7, and 9 they were open, the maximum being at pH 7. In the dark the stomata were open at pH 5, 6, 7, and 9, the maximum being at pH 5. In the case of Scilla, the closure continued up to pH 6 in light, to pH 5 in the dark, with a maximum at pH 7.