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Improving the Quality of Lyophilized Animal Vaccines: A Review of Optimization Strategies for Freeze-Drying Processes. [PDF]
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2021
In multiple scale method, the independent variable will be replaced by several variables, each with a scaled down speed of variation. Replacing the independent variable, makes a nonlinear ordinary differential equation to be transformed to a series of linear partial differential equations. Combination of the solutions of the linear partial differential
Reza N. Jazar
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In multiple scale method, the independent variable will be replaced by several variables, each with a scaled down speed of variation. Replacing the independent variable, makes a nonlinear ordinary differential equation to be transformed to a series of linear partial differential equations. Combination of the solutions of the linear partial differential
Reza N. Jazar
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1999
Abstract In this chapter we apply the multiple-scale method to the study of problem (6.1). The method is presented in Section 7.1 and a formal asymptotic expansion for u ε is obtained. The goal of Section 7.2 is to prove the error estimate stated in Theorem 6.3.
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Abstract In this chapter we apply the multiple-scale method to the study of problem (6.1). The method is presented in Section 7.1 and a formal asymptotic expansion for u ε is obtained. The goal of Section 7.2 is to prove the error estimate stated in Theorem 6.3.
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Solitons in Superlattices: Multiple Scales Method
International Journal of Theoretical Physics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tian, Qiang, Zhang, Qiyi, Zhou, Hui
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A HIGHER ORDER METHOD OF MULTIPLE SCALES
Journal of Sound and Vibration, 1997Summary: Perturbation methods are often applied in the analysis of weakly nonlinear dynamic systems. The method of multiple scales, for instance, is a common choice. \textit{Z. Rahman} and \textit{T. D. Burton} [ibid. 133, No. 3, 369--379 (1989; Zbl 1235.70099)] proposed a version of the method of multiple scales which can be used to determine the ...
Lee, C. L., Lee, C.-T.
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On the Reconstitution Problem in the Multiple Time-Scale Method
Nonlinear Dynamics, 1999The authors consider general systems of the form \(\ddot q+F(q, \dot q,t;\mu)=0\), where \(\mu\) is a vector containing small physical quantities, or small deviations from the critical values of other parameters. A perturbation parameter \(\varepsilon\) is introduced by the equation \(\mu= \varepsilon \widehat\mu\), \(\widehat\mu= O(1)\), then the ...
LUONGO, Angelo, Paolone A.
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An Alternative Example of the Method of Multiple Scales
SIAM Review, 2000Summary: An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable.
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The Sitnikov Problem Investigation with the Method of Multiple Scales
Iranian Journal of Science and Technology, Transactions A: Science, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manshadi, Ali Dehghan +1 more
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Multiple scale finite element methods
International Journal for Numerical Methods in Engineering, 1991AbstractNew temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems.
Liu, Wing Kam +2 more
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