FEATURES AND APPLICATIONS OF BERTALANFFY-RICHARDS‘ AND SCHNUTE'S GROWTH EQUATIONS

ABSTRACT. Based on various ranges of the parameter m (or b), the paper analyzes the features and the integral forms of the Schnute and the Bertalanffy-Richards growth equations as well as the two aspects of their special cases (such as Gompertz, logistic and monomolecular models). It is a first attempt to investigate all the corresponding relationships among parameters of the models derived from the Schnute and the Bertalanffy-Richards growth equations. All the models from the two are empirically fitted by different data sets for eucalypt plantations. Unlike earlier papers, the results of this paper show that either of the two growth equations can be considered as a model for estimating forest growth given a parameter range, and both can produce similar growth performances. Some other aspects of the two growth equations are discussed so that the two can be used correctly.     

Double-diffusive parallel flow induced in a horizontal Brinkman porous layer subjected to constant heat and mass fluxes: analytical and numerical studies

Fluid flow and heat and mass transfer induced by double-diffusive natural convection in a horizontal porous layer subjected to vertical gradients of temperature and concentration are studied analytically and numerically using the Brinkman-extended Darcy model. Both cases of rigid and free horizontal boundaries are examined in the present study. The parameters governing the problem are the Rayleigh number R_T, the Lewis number Le, the buoyancy ratio N, the Darcy number Da and the aspect ratio Ar. The analytical solution is based on the parallel flow approximation. The critical Rayleigh number corresponding to the onset of the parallel flow in this system is determined analytically as a function of Le, N and Da. For sufficiently small Da, both free and rigid boundaries yield results which are identical to those predicted by the Darcy model. The present investigation shows that there exists a region in the plane (N, Le) where the convective flow is not possible in the layer regardless of the Rayleigh and Darcy numbers considered. Received on 21 December 1998     

Phase-controlling phononic crystals: realization of acoustic Boolean logic gates

A phononic crystal (PC) consisting of a square array of cylindrical polyvinylchloride inclusions in air is used to construct a variety of acoustic logic gates. In a certain range of operating frequencies, the PC band structure shows square-like equi-frequency contours centered off the gamma point. This attribute allows for the realization of non-collinear wave and group velocity vectors in the PC wave vector space. This feature can be utilized to control with great precision, the relative phase between propagating acoustic waves in the PC. By altering the incidence angle of the impinging acoustic beams or varying the PC thickness, interferences occur between acoustic wave pairs. It is recognized that information can be encoded with this mechanism (e.g., wave amplitudes/interference patterns) and accordingly to construct a series of logic gates emulating Boolean functions. The NAND, XOR, and NOT gates are demonstrated with finite-difference time-domain simulations of acoustic waves impinging upon the PC.     

Convective heat loss of water in a circular pipe cooled at constant rate

A numerical study is made of the heat loss by natural convection of water within a horizontal circular cylinder with wall temperature decreasing at a constant rate. The particular situation of water with maximum density at 4 °C is formulated in dimensionless relations based on a linear relationship between the water thermal expansion coefficient and the temperature. Such an approach leads to an exhaustive solution in terms of a non linear Rayleigh number. The link is also established with the standard situation where the hypothesis of a linear relationship between density and temperature is applicable. In particular it is shown that the quasi steady state results obtained for a standard situation become equilibrium curves to which the system tends with increasing difference between the temperature of the boundary and 4 °C. A complete numerical solution is obtained for non linear Rayleigh numbers ranging between 0 and 10⁷. Previous numerical and experimental results on the horizontal circular cylinder are also discussed and recast in terms of the present dimensional approach.     

Assessment of the Full Compatibility of Copper(I)-Catalyzed Alkyne-Azide Cycloaddition and Oxime Click Reactions for bis-Labelling of Oligonucleotides

The conjugation of oligonucleotides with reporters is of great interest for improving their intrinsic properties or endowing new ones. In this context, we report herein a new procedure for the bis-labelling of oligonucleotides through oxime ligation (Click-O) and copper(I)-catalyzed alkyne–azide cycloaddition (Click-H). 5′-Azido and 3′-aldehyde precursors were incorporated into oligonucleotides, and subsequent coupling reactions through Click-O and Click-H (or vice versa) were successfully achieved. In particular, we exhaustively investigated the full compatibility of each required step for both tethering strategies. The results demonstrate that click Huisgen and click oxime reactions are fully compatible. However, whilst both approaches can deliver the targeted doubly conjugated oligonucleotide, the route involving click oxime ligation prior to click Huisgen is significantly more successful. Thus the reactions investigated here can be considered to be key elements of the chemical toolbox for the synthesis of highly sophisticated bioconjugates.     

Effect of the character of high-angle grain boundaries on segregation: An elastic model

We introduce a model for high-angle grain boundaries in the form of a two-dimensional array of compressive forces. Segregation profiles driven by the stress field around the boundary are calculated for several levels of translational order. We find an enhancement of segregation with increasing degree of translational disorder, in agreement with experimental observations.     

Glass Formation Ability and Kinetics of the Gd55A120Ni25 Bulk Metallic Glass

We report a new bulk glass-forming alloy GdssA12oNi25. The bulk sample of the alloy is prepared in the shape of rods in diameter 2ram by suction casting. The rod exhibits typical amorphous characteristics in the x-ray diffraction pattern, paramagnetic property at 30OK, distinct glass transition and multi-step crystallization behaviour in differential scanning calorimetry traces. The gJass formation ability of the alloy is investigated by using the reduced glass transition temperature Trg and the parameter γ- Kinetics of glass transition and primary crystallization is also studied. The fragility parameter m obtained from the Vogel-Fulcher-Tammann dependence of glass transition temperature Tg on In φ （φ is the heating rate） classifies the bulk metallic glasses into the intermediate category according to Angell＇s classification.     

Coulomb blockade without potential barriers

We study transport through a strongly correlated quantum dot and show that Coulomb blockade can appear even in the presence of perfect contacts. This conclusion arises from numerical calculations of the conductance for a microscopic model of spinless fermions in an interacting chain connected to each lead via a completely open channel. The dependence of the conductance on the gate voltage shows well defined Coulomb blockade peaks which are sharpened as the interaction strength is increased. Our numerics is based on the embedding method and the DMRG algorithm. We explain the emergence of Coulomb blockade with perfect contacts by a reduction of the effective coupling matrix elements between many-body states corresponding to successive particle numbers in the interacting region. A perturbative approach, valid in the strong interaction limit, yields an analytic expression for the interaction-induced suppression of the conductance in the Coulomb blockade regime.