A modified differential scanning calorimetry for determination of cell volumetric change during the freezing process

A modified analytical and experimental method using differential scanning calorimeter (DSC) was developed to determine the cell volume change during the freezing process. Two cell types were used in the study: human platelets and erythrocytes (red blood cells). Isotonic cell suspensions with different cytocrits were prepared and used in the DSC experiments. Low cooling rates were used to avoid intracellular ice formation. Cell suspensions were cooled from room temperature to -40 degrees C. Latent heat release from the freezing of cell suspensions was shown to be a linear function of cytocrit. From slope and intercept of the linear function, cell volume change was determined based on a developed theoretical model. From experimental data and theoretical analyses, it was revealed that (a) the final volume of a human platelet at -40 degrees C was 33.7% of its isotonic volume, and 15.2% of the original (at isotonic condition) intracellular water remained unfrozen inside platelets, and (b) the final volume of human erythrocyte at -40 degrees C was 50.0% of its isotonic volume, and 30.3% of the original intracellular water was kept inside cells as residual unfrozen water.     

A numerical study of the solution of the partial eigenvalue problem

The partial eigenvalue problem that arises from the application of the finite element method is considered. A number of iterative methods are examined which consist in seeking the stationary points of the Rayleigh quotient and thus avoiding the physical assembling of the matrices involved. The computational efficiencies of the steepest descent, the conjugate gradient and the co-ordinate overrelaxation methods are compared. Several other modifications to the original conjugate gradient algorithm as well as an orthogonalization process are studied. The dependence of the convergence of the methods on the initial estimate of the eigenvectors and on different values of the relaxation parameter, in the case of the co-ordinate overrelaxation, are also examined.     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.     

A numerical solution of a nonlinear Langevin Equation

A one-dimensional Langevin Equation in which the friction term and the stochastic force term depend nonlinearly on the velocity is presented. Assuming that the Maxwell distribution is the stationary solution of the Fokker Planck Equation (which is equivalent to the nonlinear Langevin Equation) we derive a generalization of the Fluctuation Dissipation theorem. A numerical algorithm is developed which allows us to integrate the nonlinear Langevin Equation. From this numerical solution correlation functions are obtained.     

Nanocrystallization behaviour of a ternary amorphous alloy during isothermal annealing： a Monte Carlo simulation

The nanocrystallization behaviour of Zr70Cu20Ni10 metallic glass during isothermal annealing is studied by employing a Monte Carlo simulation incorporating with a modified Ising model and a Q-state Potts model. Based on the simulated microstructure and differential scanning calorimetry curves, we find that the low crystal-amorphous interface energy of Ni plays an important role in the nanocrystallization of primary Zr2Ni. It is found that when T〈T1max （where T1max is the temperature with maximum nucleation rate）, the increase of temperature results in a larger growth rate and a much finer mierostrueture for the primary Zr2Ni, which accords with the microstructure evolution in ＂flash annealing＂. Finally, the Zr2Ni/Zr2Cu interface energy σG contributes to the pinning effect of the primary nano-sized Zr2Ni grains in the later formed normal Zr2Cu grains.     

Binary and ternary oscillations in a cubic numerical scheme

We study a central difference semi-discretization of the cubic scalar conservation law. Both spatial period-2 (binary) and period-3 (ternary) oscillations are stationary solutions of this scheme, and we find where each type is linearly stable. We observe numerically the formation of ternary oscillations, to the left of Riemann shock initial data with u_r = 0, while binary oscillations form to the right of Riemann rarefaction data having u_l = 0. We derive modulation equations for both wave patterns, using them to show that binary oscillations generated by the scheme are numerical artifacts, while computing an explicit solution for the ternary modulation equations. For positive initial data, the ternary modulation equations remain hyperbolic, while the solutions enter an elliptic region for data of both signs. Conditions under which solutions of the ternary modulation equations can be inverted to yield period-3 oscillations are also discussed.     

A numerical solution of the Stefan problem

A two-dimensional Stefan problem is solved for a prism and a cylinder by approximating the enthalpy formulation of the problem byC ⁰ piecewise linear finite elements in space combined with a semi-implicit scheme in time. The numerical integration in space makes the scheme easy to implement.This work was partially supported by GA CR grant No. 106/93/0638.     

Equilibrium segregation in a ternary solution: A model for temper embrittlement

Whereas experimental evidence has established that temper embrittlement is due to the simultaneous intergranular segregation of some impurities I (Sb, P, As Sn, ...) and of metallic alloying elements M (Ni, Cr, Mn, ...), all the theories of this phenomenon have failed so far to rationalize the role of the alloying elements, i.e. essentially to explain why they are necessary for the segregation of the impurities to occur. The thermodynamical formalism of equilibrium segregation, when taking into account the interaction of M and I atoms in an iron base solid solution can explain this behaviour. The simplest analytical treatment of such interaction based on the regular solution model is developed. The values of the interaction coefficients between the various atoms, as evaluated from the enthalpies of mixing of the intermetallic compounds, appear consistent with the value deduced from segregation measurements. The model is shown to allow a comprehensive interpretation of the segregation behaviour of various binary and ternary solutions, in particular the iron base systems. Eventually the role of bi-dimensional compound formation in the segregation process is considered.     

Control and characterization of the nucleation process during co-expansion of ternary mixtures

In this paper, we show how the use of a third non-condensable species gives both new insight and control on the binary nucleation process during supersonic expansion of gas mixtures. We present the case of an oxygen-nitrogen mixture diluted in various proportions of helium. Using beam diagnostics, we determine the mean cluster composition and size as well as the percentage of uncondensed matter present in the beam. The presence of helium permits us to understand the cooling and clustering role played by each species during the expansion process. We discuss, in particular, its influence on the dramatic composition change observed at the nucleation onset. Received 18 April 2001     

Thermal energy storage behaviour of nanoparticle enhanced PCM during freezing and melting

The present research work aimed to investigate the melting and solidification characteristics of NPCM. The NPCM was prepared using paraffin as the PCM and high conductive MWCNT as the nanomaterial without using any dispersant. The NPCM was prepared by dispersing MWCNTs with volume fractions of 0.3%, 0.6% and 0.9% in PCM as the base PCM. SEM morphology showed the uniform dispersion of MWCNTs in the paraffin wax. The MWCNT nano-additives PCMs showed two peaks in the heating curve by DSC measurement. Lessening in melting and solidification time of 30% and 43% was attained in the case of NPCM with 0.3% and 0.9%, respectively. It is observed from the DSC analysis that the latent heat of pure paraffin during freezing and melting cycle was 139.2 J/g (at 56.61 °C) and 131.8 J/g (at 57.55 °C), respectively. Whereas, the latent heat of NPCM with 0.9% of nanofluid was 150.7 J/g (at 56.36 °C) and 148.3 J/g (58.35 °C). It is construed that a maximum change in latent heat of 7.6% and 11% was observed between pure PCM and NPCM during freezing and melting cycle. For the lesser nanoparticle concentration (0.3% and 0.6%), the percentage change in latent heat was lesser than 0.9%.     

A study of the behaviour of ampicillin in aqueous solution and thermodynamic characterization of its aggregation

The aggregation of ampicillin in water has been examined by conductivity measurements over the temperature range 288.15–313.15 K and light scattering. These measurements indicate the formation of two critical concentrations over the range 0–0.35 mol kg^?1. Aggregation number and effective aggregate charge were calculated from the static light scattering data according to the Anacker and Westwell treatment. Thermodynamic parameters of aggregate formation were obtained from a form of the mass action model applicable to systems of low aggregation number. This method was applied at both critical concentrations. A valence of one was used for the monomers present in the first equilibrium. The second equilibrium was between aggregates of two different sizes, in this case, the valence of the aggregates being the effective charge calculated from the Anacker and Westwell treatment. Experimental results show that free energies of micellization for ampicillin are higher for the first critical concentration and in the same range, but lower than for other penicillins. The enthalpies of micellization become negative when the temperature is increased, but the variation is three times greater for the first critical concentration than for the second.     

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Thomas-Fermi model can be applied to describe state of electrons for mixtures. A method to solve the mixture Thomas-Fermi equation is proposed. With the proper initial test solution and step length, this method searches the solution in a way that reduces the steps by half, which can get solutions with various densities and temperatures fast.     

A numerical algorithm for the solution of a phase-field model of polycrystalline materials

We describe an algorithm for the numerical solution of a phase-field model (PFM) of microstructure evolution in polycrystalline materials. The PFM system of equations includes a local order parameter, a quaternion representation of local orientation and a species composition parameter. The algorithm is based on the implicit integration of a semidiscretization of the PFM system using a backward difference formula (BDF) temporal discretization combined with a Newton–Krylov algorithm to solve the nonlinear system at each time step. The BDF algorithm is combined with a coordinate-projection method to maintain quaternion unit length, which is related to an important solution invariant. A key element of the Newton–Krylov algorithm is the selection of a preconditioner to accelerate the convergence of the Generalized Minimum Residual algorithm used to solve the Jacobian linear system in each Newton step. Results are presented for the application of the algorithm to 2D and 3D examples.     

On the two-component Benard problem a numerical solution

A numerical solution for the two-component Bénard problem is presented, taking into account the contribution of thermal diffusion to the total density gradient. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. The results calculated by the two methods are in agreement when the Soret coefficient is not too large. But when the gradients become important, the exact numerical solution presented here shows a small divergence from the variational method.The critical Rayleigh number is also compared with the one extrapolated from the analytical solution obtained for free boundary conditions.     

A numerical solution of the layer-to-layer transition problem as a waveguide diffraction problem

Application of net-point methods to the solution of the layer-to-layer transition problem leads to the necessity to restrict the domain and formulate artificial boundary conditions. In the present work the introduction of an artificial coaxial for reducing the original problem to a waveguide diffraction problem is applied. The test results of the finite-element program that we developed, which demonstrate the high accuracy of the method, are considered. The investigated dependence of the solution on the artificial boundary location shows the rapid convergence of the method.     

Adsorption behaviour of NaCl solution on the surface of MgO: a molecular dynamics study

Magnesium alloy is one of the most promising biomaterials in vascular clogging and bone injury. But it still has some defects to overcome and the key task is to control the degradation velocity. In this study, the reaction between NaCl solution and MgO is simplified as the first stage of the degradation of magnesium alloy stent, and the adsorption properties of NaCl solution on the MgO surface are investigated by MD simulation. The distribution of each component of the solution perpendicular to the MgO surface is analysed and the diffusion coefficient is calculated. Besides, a parameterised analysis is carried out. The results show that there is a solution layer formed at the surface of the MgO, and the existence of metal oxide restricts the diffusion of the solution. The adsorption capacity and the diffuse rate have an opposite variation tendency with the change of temperature, concentration and velocity. The self-diffusion coefficient of the solution increases with the increase in temperature as well as velocity, inversely adsorption capacity decreases with the increase in velocity. Besides, the influence of temperature on the adsorption capacity is small. What is more, the diffusion coefficient decreases while the adsorption capacity increases with the increase in concentration.     

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Rashba coupling in three-electron-quantum dot: A numerical solution

We present a numerical solution of a Schrödinger equation for three electrons in a quantum dot with hard-wall confining potential in the presence Spin-Orbit coupling. After separation of the problem by some hyperspherical technique, we have solved the resulting equations by using a novel finite difference method. Then a study of the wave functions, eigen-energies and accuracy of the method is done.