A nonlinear least squares program, MULTI(FILT), based on fast inverse Laplace transform for microcomputers

A nonlinear curve fitting program MULTI(FILT) into which the fast inverse Laplace transform (FILT) is incorporated was developed on a microcomputer. FILT is an algorithm for the numerical inversion of Laplace-transformed equations (image equations) to generate the corresponding real time courses. The pharmacokinetic models can be defined in the form of Laplace-transformed equations as a subroutine in MULTI(FILT). MULTI(FILT) achieves the numerical inversion of the defined image equations according to FILT and the subsequent curve-fitting of the inverse-transformed time courses to the experimental data points to estimate the pharmacokinetic parameters by the nonlinear least-squares method. MULTI(FILT) has a function to impose constraints on the pharmacokinetic parameters. In order to verify the reliability of MULTI(FILT), the pharmacokinetic parameters estimated by MULTI(FILT) were compared with those by MULTI using 100 time courses which were artificially generated according to the Monte Carlo method, based on data for theophylline and bishydroxycoumarin. The estimated pharmacokinetic parameters by MULTI(FILT) agreed with those by MULTI. Thus, it is suggested that FILT, developed in the field of electronic technology, is also useful in the pharmacokinetic field.     

A NEW APPROACH TO IMPROVE THE NUMERICAL WEATHER PREDICTION

For certain particular initial values, the results of numerical weather prediction are extremely sensitive to the errors in some parameters of the models, which probably is one of the reasons to bring about serious failures to the forecast. In this paper, this speculation is shown by an example of numerical experiments, and it is suggested that the parameters in the models be modified with the information provided by observational data of the recent atmospheric evolution to avoid failures of the forecast. The numerical simulation tests with a simple quasi-geostrophic barotropic model have obtained satisfying results.     

TITFIT, a comprehensive program for numerical treatment of potentiometric data by using analytical derivatives and automatically optimized subroutines with the Newton-Gauss-Marquardt algorithm

TITFIT, a computer program written in HP-enhanced BASIC is able to fit potentiometric titration curves with up to 400 points by using the Newton-Gauss-Marquardt technique supplemented by the use of analytical derivatives. The program contains a part which writes an optimized subroutine as needed by the model. The program also has additional facilities such as visual interactive adjustment of parameters and a plotting subroutine for graphical presentation of the final results. Data can be entered either manually through the keyboard or automatically through an RS-232 serial interface. The performance of the program is discussed for the well studied Ni(2+) glycine system; the results are similar to those already published in the literature.     

Multistep reaction analysis. A numerical approach based on relaxation theory

A general numerical method and program for simulation of the kinetics of multistep reactions is described, with details for collation of data, construction of a mechanistic model, and simulation of reciprocal relaxation times and calculation of individual rate constants. The working scheme of the program includes an initial approximate simulation by adjustment of the rate constants followed by their optimization with a Powell minimization subroutine. The procedure is applied to aromatic nucleophilic addition.     

Ident--a radioisotope-identification subroutine for use with the gamma-ray spectrum analysis program sampo

A radioisotope-identification and mass-determination subroutine has been added to the gamma-ray spectrum analysis program SAMPO. The subroutine IDENT contains a nuclear data library of 750 gamma-rays that are likely to be encountered in thermal-neutron activation analysis. Peaks found by SAMPO are compared with the library peaks and possible isotope identifications are made. To maximize the degree of confidence in the isotope identification, the subroutine carries out a half-life check and also confirms that the most prominent gamma-ray of the isotope concerned is present. Using the library data, together with information on the neutron flux, duration of the irradiation, subsequent decay time, and gamma-detection efficiency, the subroutine calculates the masses of elements identified in the sample, and can handle spectra acquired during either simple or cyclic irradiation. As well as the calculated masses the output contains information on identifications rejected by certain criteria. The nuclear data library used by the subroutine is presented in this paper in a simplified tabular form, and, as such, may be used for direct isotope identification and elemental mass determination.     

Estimation of adsorption isotherm parameters with inverse method--possible problems

In recent years the inverse method (IM) has been frequently applied to estimate of isotherm parameters. The IM has been used for adsorption process modeling for one, two and even three component chromatography. This method requires only a few injections with various sample concentrations, so the solute consumption and time requirements are very modest. The successful estimation of isotherm parameters with IM depends on applied chromatography column model and a numerical method used to solve the model. For HPLC column the classical equilibrium-dispersive (ED) model can be used. This model is solved frequently with very fast Rouchon finite difference method. However, the accuracy of computations with Rouchon method is decreasing with increase of the number of analyzed components. The aim of this work is the comparison of the results obtained with inverse method when ED model was solved with Rouchon or orthogonal collocation on finite element (OCFE) scheme. Assuming that solution of ED model with OCFE method can be regarded as real a solution, it was found that the Rouchon scheme may not give satisfactory results even for column with 10,000 theoretical plates for three component chromatography. Moreover, the optimal conditions for separation, calculated with Rouchon method, can be remarkably different from that obtained with the OCFE method. The next aim of this work is the presentation of Craig method application to estimation of model parameters with IM.     

Effect of radiation absorption modes on ignition time of translucent polymers subjected to time-dependent heat flux

Majority of previous solid ignition models, including numerical and analytical ones, considered only surface absorption of incident heat flux for simplification. However, the influence of in-depth absorption on pyrolysis and subsequent ignition cannot be ignored for infrared translucent polymers. This work addresses this problem and focuses on time-dependent heat flux to establish an analytical model for ignition behaviors prediction by means of theoretical analysis. Ignition temperature was utilized as the ignition criterion, and both surface and in-depth absorption scenarios were considered. Thermally thick polymethyl methacrylate and polyamide 6 were selected as reference materials to verify the reliability and applicability of the proposed model by comparing the analysis results with experimental data as well as numerical simulations. A method for determining the approximation parameters of the theoretical analysis was presented to derive the relationship between ignition time and the coefficients in heat flux expressions. The results show that the higher surface temperature owing to surface absorption accelerates the pyrolysis rate and results in a shorter ignition time, while in-depth absorption affects the ignition time inversely. The effect of surface heat loss was also evaluated quantitatively through both analytical and numerical models. The uncertainty of the proposed model is mainly caused by the selection of the approximation parameters. Nevertheless, it provides an alternative approach to estimate the ignition time of translucent polymers besides numerical simulation.

     

Practical conversion from torsion space to Cartesian space for in silico protein synthesis

Many applications require a method for translating a large list of bond angles and bond lengths to precise atomic Cartesian coordinates. This simple but computationally consuming task occurs ubiquitously in modeling proteins, DNA, and other polymers as well as in many other fields such as robotics. To find an optimal method, algorithms can be compared by a number of operations, speed, intrinsic numerical stability, and parallelization. We discuss five established methods for growing a protein backbone by serial chain extension from bond angles and bond lengths. We introduce the Natural Extension Reference Frame (NeRF) method developed for Rosetta's chain extension subroutine, as well as an improved implementation. In comparison to traditional two-step rotations, vector algebra, or Quaternion product algorithms, the NeRF algorithm is superior for this application: it requires 47% fewer floating point operations, demonstrates the best intrinsic numerical stability, and offers prospects for parallel processor acceleration. The NeRF formalism factors the mathematical operations of chain extension into two independent terms with orthogonal subsets of the dependent variables; the apparent irreducibility of these factors hint that the minimal operation set may have been identified. Benchmarks are made on Intel Pentium and Motorola PowerPC CPUs.     

Voronoi binding site models: Calculation of binding modes and influence of drug binding data accuracy

A new and accurate method for calculating the geometrically allowed modes of binding of a ligand molecule to a Voronoi site model is reported. It is shown that the feasibility of the binding of a group of atoms to a Voronoi site reduces to a simple set of linear and quadratic inequalities and quadratic equalities which can be solved by minimization of a simple function. Newton's numerical method of solution coupled to a line search proved to be successful. Moreover, we have developed efficient molecular and site data bases to discard quickly infeasible binding modes without time-consuming numerical calculation. The method is tested with a data set consisting of the binding constants for a series of biphenyls binding to prealbumin. After determination of the conformation space of the molecules and proposal of a Voronoi site geometry, the geometrically feasible modes are calculated and the energy interaction parameters determined to fit the observed binding energies to the site within experimental error ranges. We actually allowed these ranges to vary in order to study the influence of their broadness on the site geometry and found that as they increase, one can first model the receptor as a three-region site then as a single region site, but never as a two-region site.     

Choice of Model for Estimation of Adsorption Isotherm Parameters in Gradient Elution Preparative Liquid Chromatography

The inverse method is a numerical method for fast estimation of adsorption isotherm parameters directly from a few overloaded elution profiles and it was recently extended to adsorption isotherm acquisition in gradient elution conditions. However, the inverse method in gradient elution is cumbersome due to the complex adsorption isotherm models found in gradient elution. In this case, physicochemically correct adsorption models have very long calculation times. The aim of this study is to investigate the possibility of using a less complex adsorption isotherm model, with fewer adjustable parameters, but with preserved/acceptable predictive abilities. We found that equal or better agreement between experimental and predicted elution profiles could be achieved with less complex models. By being able to select a model with fewer adjustable parameters, the calculation times can be reduced by at least a factor of 10.

     

Kinetics of Diffusion-Controlled Adsorption of Colloid Particles and Proteins

A theoretical model was developed for describing localized adsorption kinetics of proteins and colloid particles at solid/liquid interfaces. In contrast to previous approaches the adsorption and desorption rate constants as well as the surface blocking function were evaluated explicitly without using empirical parameters. It was also predicted that irreversible adsorption kinetics can unequivocally be characterized in terms of the adsorption rate constant k(a) and the maximum (jamming) coverage Theta(mx) known for various particle shapes from previous Monte-Carlo simulations. The dimensionless constant k(a) was shown to be inversely proportional to the concentration of particles which is usually very low for protein and colloid adsorption measurements. From the theoretical model it was also deduced that in this case the asymptotic adsorption law for large dimensionless time tau can be expressed as Theta(mx)-Theta approximately 1/tau(1/(n-1)) (where n=3 for spheres, n=4 for side-on adsorption of spheroids, n=5 for randomly oriented spheroid adsorption). It was also shown that this limiting adsorption regime occurs for proteins at surface coverage Theta(l) very close to the jamming value Theta(mx), becoming therefore difficult to detect due to limited experimental accuracy. These analytical predictions were found to be in agreement with numerical calculations performed by using the finite-difference scheme, valid for an arbitrary range of adsorption time. Moreover, it was demonstrated that these numerical results adequately reflected the experimental results of Johnson and Lenhoff who determined the kinetics of colloid particle adsorption using atomic force microscopy. Previously used approaches assuming that particle adsorption flux is reduced by the factor B(Theta) were found to be inadequate. It was also demonstrated that due to the similarity of underlying parameters the results obtained for colloid systems can be exploited as well-defined reference data for estimating the adsorption kinetics of proteins. Copyright 2000 Academic Press.     

Thermodynamical approach to sympathetic cooling of neutral particles

We present a "toy" classical model for sympathetic cooling of the neutral Brownian particle in the frame of robust thermodynamical approach. The cooling time is expressed with the parameters of the Brownian particle and the particles from the cooling reservoir. Qualitative and numerical estimations of the model confirm that the sympathetic cooling can be efficient for heavy neutral molecules and clusters.     

Automated parameter optimization in modeling absorption spectra and resonance Raman excitation profiles

An automated method is described for optimizing the molecular parameters in simultaneous modeling of optical absorption spectra and resonance Raman excitation profiles. The method utilizes a previously developed Fortran routine that calculates absorption spectra and Raman excitation profiles for polyatomic molecules in solution from a model for the potential energy surfaces and spectral broadening mechanisms. It is combined here with an optimization routine from the commercial MATLAB package that iteratively adjusts the parameters of the molecular model to minimize the least-squared error between calculated and experimental spectra. Optimizations that typically require days to weeks of human time when performed interactively can be accomplished automatically in less than an hour of computer time. The method can handle large molecules (we show results for as many as 23 Raman-active modes) and mixtures of spectral broadening mechanisms (lifetime, Brownian oscillator, and inhomogeneous), and is robust toward noise or missing data points.     

硅橡胶硫化反应场的数值模拟

以化学反应动力学原理为基础,实验确定了硅氢加成反应的动力学模型;引入 了硫化率增量的概念,获得了全量硫化率和硫化率增量的数值计算式;根据统计理 论,获得了起始分子无规分布时的交联结构参数的数值计算式;介绍了非稳态硫化 反应场的有限元模拟步骤。在此基础上,设计了硅橡胶硫化反应过程的有限元模拟 软件;应用该软件,根据输入的初边值条件,可计算任一空间点在任一时刻的交联 反应参数和交联结构参数,进而可预测制品性能、优化反应参数,或优化设计高分 子材料。最后给出了一个典型算例,并实验验证了该模拟理论及算法的合理性。     

Numerical simulations of phase separation dynamics in a water-oil-surfactant system

We have studied numerically the dynamics of the microphase separation of a water-oil-surfactant system. We developed an efficient and accurate numerical method for solving the two-dimensional time-dependent Ginzburg-Landau model with two order parameters. The numerical method is based on a conservative, second-order accurate, and implicit finite-difference scheme. The nonlinear discrete equations were solved by using a nonlinear multigrid method. There is, at most, a first-order time step constraint for stability. We demonstrated numerically the convergence of our scheme and presented simulations of phase separation to show the efficiency and accuracy of the new algorithm.     

Review of time lag permeation technique as a method for characterisation of porous media and membranes

The time lag permeation technique has proven to bean effective method for characterisation. Because of the simple nature of the permeation experiment, transport parameters can be directly obtained from experimental data hence avoiding the intensive mathematical treatment required by other techniques. The method has historically been applied to diffusion and adsorption in porous membranes and diffusion in polymer membranes. Since its origins in 1920, interest in the time lag method has expanded because of its value in characterising simple permeation processes and also complex systems of diffusion with simultaneous adsorption and surface diffusion. This review focuses on presenting the asymptotic solution of the mass balance diffusion equations and includes applications of time lag analysis, in order to give a critical and broad perspective of this method as a tool for characterisation. It includes much of the previously published literature in order to show that for most cases the asymptotic solution of the transport equations is simple, and for more complex cases that an analytical solution is possible hence avoiding cumbersome numerical techniques.     

气相色谱运动过程仿真

通过对组分在色谱柱内运动过程的仿真,指出平均归一化线速与实际过程的当地线速的区别及其对保留时间模拟准确度的影响。     

A modified program for computation of formation constants of synergetic extraction complexes with two-phase titrations by using the Marquardt-Fletcher algorithm

A modified computer program SCTPT for the computation of formation constants of extraction complexes with two-phase pH titration data by using the Marquardt-Fletcher algorithm is described. It can be used to deal with extraction systems which consist of a metal, an acidic extractant and a neutral synergistic reagent with no need of new subroutine. It has been applied successfully to the Pb-PMBP(1-phenyl-3-methyl-4-benzoyl-pyrazolone-5)-TBP (tributyl phosphate) system. The results obtained are in agreement with those published in the literature.     

Global dynamic optimization for parameter estimation in chemical kinetics

We present the first method guaranteed to find the best possible least-squares (chi2) fit of experimental data by a nonlinear kinetic model. Several important advantages of knowing with certainty the best possible fit rather than a locally optimum fit are discussed and demonstrated using data from the recent literature. This is particularly important when the model and the data appear to be inconsistent. With the new method, one can rigorously demonstrate that a nonlinear kinetic model with several adjustable rate parameters is inconsistent with measured experimental data. The numerical method presented is a valuable tool in evaluating the validity of a complex kinetics model.     

A theoretical form of the Martin-Hou equation of state

A new equation of state is derived from the Barker-Henderson hard-sphere perturbation theory. It has the form similar to the Martin-Hou equation of state. The numerical values of the characteristic constants in the equation can be calculated by the method of Martin and Hou. The equation can be used to predict P-V-T properties accurately for fluids when the critical parameters (T_c, P_c and V_c) and one point on the vapor pressure cure are given. By using the functional relationships between the characteristic constants and the microscopic parameters, the molecular microscopic parameters of the substance can be obtained.