Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

Hexagonal patterns in a model for rotating convection

We study a model equation that mimics convection under rotation in a fluid with temperature- dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kuppers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and os- cillating hexagons quite well, and include the Busse?Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.

Conformational influences of glycosylation of a peptide: A possible model for the effect of glycosylation on the rate of protein folding

Improved strategies for synthesis make it possible to expand the range of glycopeptides available for detailed conformational studies. The glycopeptide 1 was synthesized using a new solid phase synthesis of carbohydrates and a convergent coupling to peptide followed by deprotection. Its conformational properties were subjected to NMR analysis and compared with a control peptide 2 prepared by conventional solid phase methods. Whereas peptide 2 fails to manifest any appreciable secondary structure, the glycopeptide 1 does show considerable conformational bias suggestive of an equilibrium between an ordered and a random state. The implications of this ordering effect for the larger issue of protein folding are considered.

Thermal model for charring rate calculation in wooden cellular slabs under fire

Wood is a natural and traditional building material, as popular today as ever, and presents advantages. Physically, wood is strong and stiff, but compared with other materials like steel is light and flexible. Wood material can absorb sound very effectively and it is a relatively good heat insulator. But dry wood burns quite easily and produces a great deal of heat energy. The main disadvantage is the high level of combustion when exposed to fire, where the point at which it catches fire is from 200–400°C. After fire exposure, is need to determine if the charred wooden structures are safe for future use. Design methods require the use of computer modelling to predict the fire exposure and the capacity of structures to resist those action. Also, large or small scale experimental tests are necessary to calibrate and verify the numerical models. The thermal model is essential for wood structures exposed to fire, because predicts the charring rate as a function of fire exposure. The charring rate calculation of most structural wood elements allows simple calculations, but is more complicated for situations where the fire exposure is non-standard and in wood elements protected with other materials. In this work, the authors present different case studies using numerical models, that will help professionals analysing woods elements and the type of information needed to decide whether the charred structures are adequate or not to use. Different thermal models representing wooden cellular slabs, used in building construction for ceiling or flooring compartments, will be analysed and submitted to different fire scenarios (with the standard fire curve exposure). The same numerical models, considering insulation material inside the wooden cellular slabs, will be tested to compare and determine the fire time resistance and the charring rate calculation.

Thermal model for charring rate calculation in wooden cellular slabs under fire

Wood is a natural and traditional building material, as popular today as ever, and presents advantages. Physically, wood is strong and stiff, but compared with other materiais like steel is light and flexible. Wood material can absorb sound very effectively and it is a relatively good heat insulator. But dry wood does bum quite easily md produces a great deal ofheat energy. The main disadvantage is the high levei ofcombustion when exposed to fíre, where the point at which it catches fire is fi-om 200-400°C. After fu-e exposure, is need to determine if the charred wooden stmctures are safe for future use. Design methods require the use ofcomputer modelling to predict the fíre exposure and the capacity ofstructures to resist fhose action. Also, large or small scale experimental tests are necessary to calibrate and verify the numerical models. The thermal model is essential for wood stmctures exposed to fire, because predicts the charring rate as a fünction offire exposure. The charring rate calculation ofmost stmctural wood elements allows simple calculations, but is more complicated for situations where the fire exposure is non-standard and in wood elements protected with other materiais.

Assessment of rural nonpoint source pollution : a model based on the Universal soil loss equation /

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Solution of the dual reflection equation for A(n-1)((1)) solid-on-solid model

We obtain a diagonal solution of the dual reflection equation for the elliptic A(n-1)((1)) solid-on-solid model. The isomorphism between the solutions of the reflection equation and its dual is studied. (C) 2004 American Institute of Physics.

Relationship between ash content and R-70 self-heating rate of Callide Coal

Borecore samples from the Trap Gully pit at Callide have been assessed using the R-70 self-heating test. The highest R-70 self-heating rate value was 16.22 degrees C/h, which is consistent with the subbituminous rank of the coal. R-70 decreases significantly with increasing mineral matter content, as defined by the ash content of the coal. This effect is due to the mineral matter in the coal acting as a heat sink. A trendline equation has been fitted to the borecore data from the Trap Gully pit: R-70 = 0.0029 x ash(2) - 0.4889 x ash + 20.644, where all parameters are on a dry-basis. This relationship can be used to model the self-heating hazard of the pit, both vertically and laterally. (c) 2005 Elsevier B.V All rights reserved.

Time scale analysis for fluidizedbedmeltgranulation-II: binder spreading rate

The spreading time of liquid binder droplet on the surface a primary particle is analyzed for Fluidized Bed Melt Granulation (FBMG). As discussed in the first paper of this series (Chua et al., in press) the droplet spreading rate has been identified as one of the important parameters affecting the probability of particles aggregation in FBMG. In this paper, the binder droplet spreading time has been estimated using Computational Fluid Dynamic modeling (CFD) based on Volume of Fluid approach (VOF). A simplified analytical solution has been developed and tested to explore its validity for predicting the spreading time. For the purpose of models validation, the droplet spreading evolution was recorded using a high speed video camera. Based on the validated model, a generalized correlative equation for binder spreading time is proposed. For the operating conditions considered here, the spreading time for Polyethylene Glycol (PEG1500) binder was found to fall within the range of 10-2 to 10-5 s. The study also included a number of other common binders used in FBMG. The results obtained here will be further used in paper III, where the binder solidification rate is discussed.