Dynamics of crystal size distributions with size-dependent rates

The growth and dissolution dynamics of nonequilibrium crystal size distributions (CSDs) can be determined by solving the governing population balance equations (PBEs) representing reversible addition or dissociation. New PBEs are considered that intrinsically incorporate growth dispersion and yield complete CSDs. We present two approaches to solving the PBEs, a moment method and a numerical scheme. The results of the numerical scheme agree with the moment technique, which can be solved exactly when powers on mass-dependent growth and dissolution rate coefficients are either zero or one. The numerical scheme is more general and can be applied when the powers of the rate coefficients are non-integers or greater than unity. The influence of the size dependent rates on the time variation of the CSDs indicates that as equilibrium is approached, the CSDs become narrow when the exponent on the growth rate is less than the exponent on the dissolution rate. If the exponent on the growth rate is greater than the exponent on the dissolution rate, then the polydispersity continues to broaden. The computation method applies for crystals large enough that interfacial stability issues, such as ripening, can be neglected. (C) 2002 Elsevier Science B.V. All rights reserved.

Biphasic composite of Tricalcium phosphate reinforced with Hydroxyapatite Whiskers

Biphasic calcium phosphates have received considerable attention due to their optimum dissolution rate in the human body after implantation. These materials are composed of hydroxyapatite (HA) and resorbable tricalcium phosphate (TCP). In the present investigation, HA whiskers are reinforced into TCP to enhance the mechanical properties of this biphasic composite. Various amounts (30-50 wt%) HA whiskers are reinforced in TCP matrix. Microstructural characterization has been carried out using field-emission scanning electron microscope. Mechanical properties have been investigated by microindentation in a universal testing machine (UTM). As TCP is resorbable, it will dissolve in body fluid and there is a strong possibility for the faceted HA whiskers to interact with functional groups present in the body fluid surroundings.

Measurement of the corrosion rate of aluminium in sodium hydroxide using holographic interferometry

The application of holographic interferometry to the measurement of the corrosion rate of aluminium in sodium hydroxide is investigated. Details of the fabrication of the corrosion cell and the experimental procedure are given. Thickness loss of aluminium was found for different dissolution times and compared with the conventional weight-loss method using a microbalance.

Free Energy Gap Dependence of the Electron-Transfer Rate from the Inverted to the Normal Region

numerical study of the free energy gap (FEG) dependence of the electron-transfer rate in polar solvents is presented. This study is based on the generalized multidimensional hybrid model, which not only includes the solvent polarization and the molecular vibration modes, but also the biphasic polar response of the solvent. The free energy gap dependence is found to be sensitive to several factors, including the solvent relaxation rate, the electronic coupling between the surfaces, the frequency of the high-frequency quantum vibrational mode, and the magnitude of the solvent reorganization energy. It is shown that in some cases solvent relaxation can play an important role even in the Marcus normal regime. The minimal hybrid model involves a large number of parameters, giving rise to a diverse non-Marcus FEG behavior which is often determined collectively by these parameters. The model gives the linear free energy gap dependence of the logarithmic rate over a substantial range of FEG, spanning from the normal to the inverted regime. However, even for favorable values of the relevant parameters, a linear free energy gap dependence of the rate could be obtained only over a range of 5000-6000 cm(-1) (compared to the experimentally observed range of 10000 cm(-1) reported by Benniston et al.). The present work suggests several extensions/generalizations of the hybrid model which might be necessary to fully understand the observed free energy gap dependence.

Optimal barrier subdivision for Kramers' escape rate

We examine the effect of subdividing the potential barrier along the reaction coordinate on Kramers' escape rate for a model potential. Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate.

Oxygen transfer and energy dissipation rate in surface aerator

The dissipation rate of turbulent kinetic energy (epsilon) is a key parameter for mixing in surface aerators. In particular, determination epsilon across the impeller stream, where the most intensive mixing takes place, is essential to ascertain that an appropriate degree of mixing is achieved. Present work by using commercial software VisiMix (R) calculates the energy dissipation rate in geometrically similar unbaffled surface aeration systems in order to scale-up the oxygen transfer process. It is found that in geometrically similar system, oxygen transfer rate is uniquely correlated with dissipation rate of energy. Simulation or scale-up equation governing oxygen transfer rate and dissipation rate of energy has been developed in the present work.

Oxygen transfer and energy dissipation rate in surface aerator

The dissipation rate of turbulent kinetic energy(e)is a key parameter for mixing in surface aerators. In particular, determination e across the impeller stream, where the most intensive mixing takes place, is essential to ascertain that an appropriate degree of mixing is achieved. Present work by using commercial software VisiMix calculates the energy dissipation rate in geometrically similar unbaffled surface aeration systems in order to scale-up the oxygen transfer process. It is found that in geometrically similar system,oxygen transfer rate is uniquely correlated with dissipation rate of energy. Simulation or scale-up equation governing oxygen transfer rate and dissipation rate of energy has been developed in the present work.

Synergy between tribo-oxidation and strain rate response on governing the dry sliding wear behavior of titanium.

The present work provides an insight into the dry sliding wear behavior of titanium based on synergy between tribo-oxidation and strain rate response. Pin-on-disc tribometer was used to characterize the friction and wear behavior of titanium pin in sliding contact with polycrystalline alumina disk under ambient and vacuum condition. The sliding speed was varied from 0.01 to 1.4 ms(-1), normal load was varied from 15.3 to 76 N and with a sliding distance of 1500 m. It was seen that dry sliding wear behavior of titanium was governed by combination of tribo-oxidation and strain rate response in near surface region of titanium. Strain rate response of titanium was recorded by conducting uni-axial compression tests at constant true strain rate of 100 s(-1) in the temperature range from 298 to 873 K. Coefficient of friction and wear rate were reduced with increased sliding speed from 0.01 to 1.0 ms(-1). This is attributed to the formation of in situ self lubricating oxide film (TiO) and reduction in the intensity of adiabatic shear band cracking in the near surface region. This trend was confirmed by performing series of dry sliding tests under vacuum condition of 2 x 10(-4) Torr. Characterization tools such as optical microscopy, scanning electron microscopy, and X-ray diffractometer provided evidence of such processes. These experimental findings can be applied to enhance the dry sliding wear behavior of titanium with proper choice of operating conditions such as sliding speed, normal load, and environment.

Conformational transitions in a Pro-Pro peptide on dissolution of single crystals

The peptide t-butyloxycarbonyl-α-aminoisobutyryl-L-prolyl-L-prolyl-N-methylamide has been shown to adopt an extended structure in the solid state. The Pro-Pro segment occurs in the poly-proline II conformation. On dissolution of single crystals at not, vert, similar 233°K, a single species corresponding to the all Image peptide backbone is observed by 270 MHz 1H NMR. On warming, Image to Image isomerization about the Pro-Pro bond is facilitated. Both Image (ψ not, vert, similar−50°) and Image (ψ not, vert, similar 130°) rotamers about the Pro3 Cα---CO bond are detectable in the Pro-Pro Image conformer, at low temperature. These observations demonstrate unambiguously the large differences in the solid state and solution conformations of a Pro-Pro sequence.

Influence of clofibrate administration on the rate of synthesis of macromolecules in regenerating rat liver

Administration of the antihypercholesterolaemic drug clofibrate stimulates the rates of synthesis of nucleic acids and proteins in rat liver. The biosynthesis of mitochondrial proteins also is enhanced by the drug. In drug-fed animals, the rates of incorporation in vivo of radioactive precursors into DNA, RNA and proteins are stimulated even when the liver undergoes regeneration following partial hepatectomy. The rate of synthesis of mitochondrial proteins in the regenerative phase is higher in clofibrate-fed animals. These effects are consistent with the hepatomegalic and mitochondria-proliferating property of the drug.

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ ε ⋅dσ from the constitutive equation relating the strain rate (ε) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

Systematic Construction of Linear Transform Based Full-Diversity, Rate-One Space-Time Frequency Codes

In this paper, we generalize the existing rate-one space frequency (SF) and space-time frequency (STF) code constructions. The objective of this exercise is to provide a systematic design of full-diversity STF codes with high coding gain. Under this generalization, STF codes are formulated as linear transformations of data. Conditions on these linear transforms are then derived so that the resulting STF codes achieve full diversity and high coding gain with a moderate decoding complexity. Many of these conditions involve channel parameters like delay profile (DP) and temporal correlation. When these quantities are not available at the transmitter, design of codes that exploit full diversity on channels with arbitrary DIP and temporal correlation is considered. Complete characterization of a class of such robust codes is provided and their bit error rate (BER) performance is evaluated. On the other hand, when channel DIP and temporal correlation are available at the transmitter, linear transforms are optimized to maximize the coding gain of full-diversity STF codes. BER performance of such optimized codes is shown to be better than those of existing codes.

High-Rate, Multisymbol-Decodable STBCs From Clifford Algebras

It is well known that space-time block codes (STBCs) obtained from orthogonal designs (ODs) are single-symbol decodable (SSD) and from quasi-orthogonal designs (QODs) are double-symbol decodable (DSD). However, there are SSD codes that are not obtainable from ODs and DSD codes that are not obtainable from QODs. In this paper, a method of constructing g-symbol decodable (g-SD) STBCs using representations of Clifford algebras are presented which when specialized to g = 1, 2 gives SSD and DSD codes, respectively. For the number of transmit antennas 2(a) the rate (in complex symbols per channel use) of the g-SD codes presented in this paper is a+1-g/2(a-9). The maximum rate of the DSD STBCs from QODs reported in the literature is a/2(a-1) which is smaller than the rate a-1/2(a-2) of the DSD codes of this paper, for 2(a) transmit antennas. In particular, the reported DSD codes for 8 and 16 transmit antennas offer rates 1 and 3/4, respectively, whereas the known STBCs from QODs offer only 3/4 and 1/2, respectively. The construction of this paper is applicable for any number of transmit antennas. The diversity sum and diversity product of the new DSD codes are studied. It is shown that the diversity sum is larger than that of all known QODs and hence the new codes perform better than the comparable QODs at low signal-to-noise ratios (SNRs) for identical spectral efficiency. Simulation results for DSD codes at variousspectral efficiencies are provided.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Penetration Rate Effect on Miniature Cone Tip Resistance for Different Cohesionless Materials

Cone penetrometer tests were carried out in a 140 mm diameter triaxial chamber by using a miniature cone of diameter 19.5 mm. The rate of cone penetration was varied from 0.01 mm/s to 0.1 mm/s. Tests were performed in (i) clean sand, (ii) silty sand, and (iii) sand added with fly ash. Two different effective vertical pressures (sigma(nu)), 100 kPa and 300 kPa, were employed. It was noted that for clean and silty sand, the effect of penetration rate on the ultimate tip resistance (q(cu)) of the cone was found to remain only marginal. On the other hand, for sand added with 30% fly ash, the variation in q(cu) values with penetration rate was found to become quite significant. The effect of penetratio rate on q(cu) in all the cases was found to increase with a decrease in the rate of cone penetration. It was noted that with an increase in sigma(nu), the effect of penetration rate on q(cu) was found to become smaller. The effect of the cone penetration rate on q(cu) generally reduces with an increase in the relative density of the material.