Search results for "Numerical"
showing 10 items of 2002 documents
Numerical models for long-term performance assessment of lightweight insulating assemblies
2019
Abstract This paper presents the results of numerical modelling of hygrothermal processes in test buildings situated in the Botanical garden of the University of Latvia. Long-term performance of wall, floor and ceiling insulating assemblies for five different buildings was simulated using WUFI Pro 6.3. On the experimental side, measurements of temperature and relative humidity at key points of assembles have been accumulated over a period of roughly six years and material samples were taken from building envelope materials for biological analysis. We found that our models rather successfully reproduce the experientially observed temperature and relative humidity dynamics. In the process, we…
Global extrapolation with a parallel splitting method
1992
Extrapolation with a parallel splitting method is discussed. The parallel splitting method reduces a multidimensional problem into independent one-dimensional problems and can improve the convergence order of space variables to an order as high as the regularity of the solution permits. Therefore, in order to match the convergence order of the space variables, a high order method should also be used for the time integration. Second and third order extrapolation methods are used to improve the time convergence and it was found that the higher order extrapolation method can produce a more accurate solution than the lower order extrapolation method, but the convergence order of high order extr…
Benefits of solvent concentration pulses in retention time modelling of liquid chromatography
2019
The advantages and disadvantages of the use of isocratic experimental designs including transient increments of organic solvent (i.e., pulses) in the mobile phase(s) of lowest elution strength are explored with modelling purposes. For retained solutes, this type of mixed design offers similar or better predictive capability than gradient designs, shorter measurement time than pure isocratic designs, and retention model parameters that agree with those derived from pure isocratic experiments, with similar uncertainties. The predicted retention times are comparable to those offered by models adjusted from pure isocratic designs, and the solvent waste is appreciably lower. Under a practical st…
Stiffness-Adaptive Taylor method for the integration of non-stiff and stiff kinetic models
1992
A systematic derivation procedure that greatly facilitates the application of the Taylor method to the integration of kinetic models is developed. In addition, an algorithm that gives the integration step as a function of the required level of accuracy is proposed. Using the Taylor method, application of this algorithm is immediate and largely reduces the integration time. In addition, a new method of integration of kinetic models, whose most important feature is the self-adaptability to the stiffness of the system along the integration process, is developed. This “stiffness-adaptive” Taylor method (SAT method) makes use of several algorithms, combining them to meet the particular requireme…
Fractional visco-elastic Timoshenko beam deflection via single equation
2015
SUMMARY This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letni…
Fractional viscoelastic beam under torsion
2017
Abstract This paper introduces a study on twisted viscoelastic beams, having considered fractional calculus to capture the viscoelastic behaviour. Further another novelty of this paper is extending a recent numerical approach, labelled line elementless method (LEM), to viscoelastic beams. The latter does not require any discretization neither in the domain nor in the boundary. Some numerical applications have been reported to demonstrate the efficiency and accuracy of the method.
LEM for twisted re-entrant angle sections
2014
In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any…
Clarkson-McCarthy inequalities with unitary and isometry orbits
2020
Abstract A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten p-classes for p > 2 is proved: if A , B are two n-by-n matrices, then there exists some pair of n-by-n unitary matrices U , V such that U | A + B 2 | p U ⁎ + V | A − B 2 | p V ⁎ ≤ | A | p + | B | p 2 . A similar statement holds for compact Hilbert space operators. Another improvement of McCarthy's inequality is given via the new operator parallelogramm law, | A + B | 2 ⊕ | A − B | 2 = U 0 ( | A | 2 + | B | 2 ) U 0 ⁎ + V 0 ( | A | 2 + | B | 2 ) V 0 ⁎ for some pair of 2n-by-n isometry matrices U 0 , V 0 .
Estimation of significant solvent concentration ranges and its application to the enhancement of the accuracy of gradient predictions.
2004
Abstract The solvent concentration range actually useful for gradient predictions is significantly narrower than the total range scanned in a gradient run. This range, called “solvent informative range” (SIR), if known with the highest accuracy, allows to predict gradient retention times ( t g ) with minimal error. The small size of the SIR supports the application of the linear solvent strength theory (LSST). Furthermore, LSST allows a closed-form solution to the integral required to predict gradient retention times, which eliminates numerical integration, needed with other retention models. A methodology that calculates the SIR by applying error analysis, and uses it to improve the accura…
Multilayer neural networks: an experimental evaluation of on-line training methods
2004
Artificial neural networks (ANN) are inspired by the structure of biological neural networks and their ability to integrate knowledge and learning. In ANN training, the objective is to minimize the error over the training set. The most popular method for training these networks is back propagation, a gradient descent technique. Other non-linear optimization methods such as conjugate directions set or conjugate gradient have also been used for this purpose. Recently, metaheuristics such as simulated annealing, genetic algorithms or tabu search have been also adapted to this context.There are situations in which the necessary training data are being generated in real time and, an extensive tr…