MODELING OF GOLD DISPERSION IN GLASSY POLYMERS BY SMOLUCHOWSKI EQUATION

2002 ◽  
Vol 13 (09) ◽  
pp. 1301-1312 ◽  
Author(s):  
ZBIGNIEW J. GRZYWNA ◽  
JACEK STOLARCZYK
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Partial Differential Equation ◽  
Smoluchowski Equation ◽  
Glassy Polymers ◽  
Time Dependent ◽  
Acetone Vapor ◽  
Induced Stress ◽  
Theoretical Predictions ◽  
Good Agreement

A unidimensional diffusion in a potential field of induced stress is considered. The way from random walk (RW) to limiting partial differential equation (Smoluchowski equation) for standard and time dependent RW is shown. A technologically important case of gold dispersion in crystallizing polymer swollen by acetone vapor is analyzed. Theoretical predictions based on Smoluchowski equation with time dependent coefficients are found to be in very good agreement with experimental data.

scholarly journals Energy Dependence of Total Cross Sections for Reactions with 4, 6he, 6, 7, 9li Nuclei

KnE Energy ◽  
2018 ◽  
Vol 3 (1) ◽  
pp. 21
Author(s):  
Yu Penionzhkevich ◽  
Yu Sobolev ◽  
V Samarin ◽  
M Naumenko
Keyword(s):  
Experimental Data ◽  
Energy Range ◽  
Numerical Solution ◽  
Energy Dependence ◽  
Cross Sections ◽  
Beam Energy ◽  
Microscopic Analysis ◽  
Time Dependent ◽  
Total Cross Sections ◽  
Good Agreement

The paper presents the results of measurement of the total cross sections for reactions 4,6He + Si and 6,7,9Li + Si in the beam energy range 5−50 A⋅MeV. The enhancements of the total cross sections for reaction 6He + Si compared with reaction 4He + Si, and 9Li + Si compared with reactions 6,7Li + Si have been observed. The performed microscopic analysis of total cross sections for reactions 6He + Si and 9Li + Si based on numerical solution of the time-dependent Schrödinger equation for external neutrons of projectile nuclei 6He and 9Li yielded good agreement with experimental data.

Measurement of Residual Strains As a Parameter of Matrix Cracking in CFRP Laminates

2020 ◽  
Author(s):  
M. J. Mohammad Fikry ◽  
Shinji Ogihara ◽  
Vladimir Vinogradov
Keyword(s):  
Viscoelastic Behavior ◽  
Matrix Cracking ◽  
Time Dependent ◽  
Strain Gauges ◽  
Recovery Test ◽  
Cfrp Laminates ◽  
Matrix Cracks ◽  
Theoretical Predictions ◽  
Residual Strains ◽  
Good Agreement

Abstract Matrix cracking in CFRP laminates results in degradation of mechanical properties of the material and appearance of residual strains. In this study, the residual strains investigated are experimentally and analytically for CFRP [0/756]s laminates. The strain gauges were used in this study to measure the strains. Due to very small residual strains at the unloading condition, the residual strains were also measured at different stress levels for laminates with different crack densities and are compared with theoretical predictions. Time-dependent viscoelastic behavior of the material is also considered to accurately measure the residual strains due to the occurrence of matrix cracks. This was done by using the strain recovery test when the loads were stopped for 1–1.5 hours during unloading and the strain changes during these times were recorded. The experimental results of the residual strains are in reasonably good agreement with the theoretical predictions. The fiber non-linearity properties of the laminates may cause some experimental data to shift above the analytical line.

scholarly journals Fractional-Derivative Approximation of Relaxation in Complex Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Kin M. Li ◽  
Mihir Sen ◽  
Arturo Pacheco-Vega
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
System Identification ◽  
Complex Systems ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Initial Conditions ◽  
Time Dependent ◽  
Fractional Order Differential Equation

In this paper, we present a system identification (SI) procedure that enables building linear time-dependent fractional-order differential equation (FDE) models able to accurately describe time-dependent behavior of complex systems. The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo definition of the fractional derivative, and the Mittag-Leffler function, is used to obtain the corresponding solutions. Since the set of parameters for the model and its initial conditions are nonunique, and there are small but significant differences in the predictions from the possible models thus obtained, the SI operation is carried out via global regression of an error-cost function by a simulated annealing optimization algorithm. The SI approach is assessed by considering previously published experimental data from a shell-and-tube heat exchanger and a recently constructed multiroom building test bed. The results show that the proposed model is reliable within the interpolation domain but cannot be used with confidence for predictions outside this region. However, the proposed system identification methodology is robust and can be used to derive accurate and compact models from experimental data. In addition, given a functional form of a fractional-order differential equation model, as new data become available, the SI technique can be used to expand the region of reliability of the resulting model.

Macro/Meso/Micro Elastic-Viscoplastic Analysis of Plain-Woven Laminates Using Homogenization Theory

2014 ◽  
Vol 626 ◽  
pp. 365-371 ◽  
Author(s):  
Kohei Oide ◽  
Tetsuya Matsuda
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Glass Fiber ◽  
Present Method ◽  
Time Dependent ◽  
Homogenization Theory ◽  
Fiber Bundles ◽  
Woven Glass Fiber ◽  
Good Agreement

In this study, macro/meso/micro elastic-viscoplastic analysis of plain-woven laminates is conducted based on a homogenization theory for nonlinear time-dependent composites. For this, a plain-woven laminate is modeled with respect to three scales by considering the laminate as a macrostructure, fiber bundles (yarns) and a matrix in the laminate as a mesostructure, and fibers and a matrix in the yarns as a microstructure. Then, an elastic-viscoplastic constitutive equation of the laminate is derived by dually applying the homogenization theory for nonlinear time-dependent composites to not only the meso/micro but also the macro/meso scales. Using the present method, the elastic-viscoplastic analysis of a plain-woven glass fiber/epoxy laminate subjected to on-and off-axis loading is performed. It is shown that the present method successfully takes into account the effects of viscoplasticity of the epoxy in yarns on the elastic-viscoplastic behavior of the plain-woven GFRP laminate. It is also shown that the results of analysis are in good agreement with experimental data.

Calculation of Elastic Induced Stress of Surrounding Rocks

2012 ◽  
Vol 170-173 ◽  
pp. 37-40
Author(s):  
Bo Qian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Superposition Principle ◽  
Compatibility Conditions ◽  
Partial Differential ◽  
Induced Stress ◽  
Stress Functions ◽  
Round Section

In accordance with equilibrium differential equations and compatibility conditions of deformation, the partial differential equation of induced stress is achieved for elastic surrounding rocks of tunnels and chambers of round section. By method of the superposition principle, elastic analytical solutions of induced stress of surrounding rocks is derived from the partial differential equation, which is based on stress functions and boundary conditions.

scholarly journals New test of the dynamic theory of neutron diffraction by a moving grating

2018 ◽  
Vol 177 ◽  
pp. 03005
Author(s):  
Maxim Zakharov ◽  
Alexander Frank ◽  
German Kulin ◽  
Semyon Goryunov
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Neutron Diffraction ◽  
Dynamic Theory ◽  
Time Of Flight ◽  
Dynamical Theory ◽  
Zero Order ◽  
Significant Suppression ◽  
Theoretical Predictions ◽  
Good Agreement

Recently, multiwave dynamical theory of neutron diffraction by a moving grating was developed. The theory predicts that at a certain height of the grating profile a significant suppression of the zero-order diffraction may occur. The experiment to confirm predictions of this theory was performed. The resulting diffracted UCNs spectra were measured using time-of-flight Fourier diffractometer. The experimental data were compared with the results of numerical simulation and were found in a good agreement with theoretical predictions.

A Simple, Accurate Integral Solution for Accelerating Turbulent Boundary Layers With Transpiration

1995 ◽  
Vol 117 (3) ◽  
pp. 535-538 ◽  
Author(s):  
James Sucec
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Skin Friction ◽  
Boundary Layers ◽  
Integral Form ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Integral Solution ◽  
Good Agreement

The inner law for transpired turbulent boundary layers is used as the velocity profile in the integral form of the x momentum equation. The resulting ordinary differential equation is solved numerically for the skin friction coefficient, as well as boundary layer thicknesses, as a function of position along the surface. Predicted skin friction coefficients are compared to experimental data and exhibit reasonably good agreement with the data for a variety of different cases. These include blowing and suction, with constant blowing fractions F for both mild and severe acceleration. Results are also presented for more complicated cases where F varies with x along the surface.

Thermal Behavior and Friction in Journal Bearings

1970 ◽  
Vol 92 (3) ◽  
pp. 373-380 ◽  
Author(s):  
Al. Nica
Keyword(s):  
Experimental Data ◽  
Thermal Behavior ◽  
Heat Dissipation ◽  
Journal Bearings ◽  
Friction Torque ◽  
Operating Characteristics ◽  
Lubricant Flow ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Good Agreement

This paper deals with friction and the field of temperature in the lubricant film of journal bearings. Theoretical results regarding the thermal behavior are checked with experimental data and good agreement is found. Emphasis is put on the variation of temperature and lubricant flow with the operating characteristics of the bearing and it is seen that theoretical predictions for minima of friction torque are backed by temperature measurements. Further on, the friction torque and the mechanism of heat dissipation in bearings are dealt with, in order to verify the assumptions used in the calculation schemes. The means of efficiently cooling the bearing are also discussed, as well as the part played by the divergent zone in this process.

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