On capillary waves in the gradient theory of interfaces

1985 ◽  
Vol 63 (2) ◽  
pp. 131-134 ◽  
Author(s):  
Luis de Sobrino ◽  
Jože Peternelj
Keyword(s):  
Dispersion Relation ◽  
Thermal Effects ◽  
Equations Of Motion ◽  
Capillary Waves ◽  
Gradient Theory ◽  
Two Phase ◽  
Long Wavelength ◽  
Phase Solution

We have solved the equations of motion for an inhomogeneous, nondissipative fluid linearized about a two-phase solution in order to determine the dispersion relation for capillary waves of long wavelength. The solution is reasonably rigorous in that no physical assumptions have been introduced. We find that, in accordance with the results of Turski and Langer and contrary to other workers' claims, the dispersion relation agrees with classical capillary theory only if thermal effects are included.

Note on capillary waves in the gradient theory of interfaces

1985 ◽  
Vol 63 (8) ◽  
pp. 1132-1133 ◽  
Author(s):  
Luis De Sobrino
Keyword(s):  
Free Energy ◽  
Dispersion Relation ◽  
Classical Theory ◽  
Capillary Waves ◽  
Gradient Theory ◽  
Gradient Term

The calculation of the dispersion relation for capillary waves in the gradient theory of interfaces has been generalized to the case in which the gradient term in the free energy depends on temperature. The dispersion relation is found to agree with the classical theory.

Analysis of Single- and Two-Phase Flows in Turbopump Inducers

1967 ◽  
Vol 89 (4) ◽  
pp. 577-586 ◽  
Author(s):  
P. Cooper
Keyword(s):  
Equation Of State ◽  
Flow Field ◽  
Thermal Effects ◽  
Single Phase ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Recent Theory ◽  
Two Phase ◽  
Overall Efficiency

A model is developed for analytically determining pump inducer performance in both the single-phase and cavitating flow regimes. An equation of state for vaporizing flow is used in an approximate, three-dimensional analysis of the flow field. The method accounts for losses and yields internal distributions of fluid pressure, velocity, and density together with the resulting overall efficiency and pressure rise. The results of calculated performance of two sample inducers are presented. Comparison with recent theory for fluid thermal effects on suction head requirements is made with the aid of a resulting dimensionless vaporization parameter.

Free nonlinear vibration analysis of nano-truncated conical shells based on modified strain gradient theory

2021 ◽  
pp. 146442072110419
Author(s):  
Alireza Sheykhi ◽  
Shahrokh Hosseini-Hashemi ◽  
Adel Maghsoudpour ◽  
Shahram E Haghighi
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Couple Stress ◽  
Equations Of Motion ◽  
Differential Quadrature ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Modified Strain Gradient Theory ◽  
Conical Shells ◽  
Modified Couple Stress

In this study, the nonlinear free vibrations behaviour of nano-truncated conical shells was analysed, using the first-order shear deformable shell model. The analysis took into account the structure size through modified strain gradient theory, and differential quadrature and Fréchet derivative methods in von Kármán-Donnell-type approach to kinematic nonlinearity. The governing equations were obtained, utilizing Hamilton's principle. Partial differential equations plus the non-classical and classical boundary conditions were used to obtain the shells’ equations of motion. Discretizing the boundary conditions and equations of motion were performed based on a generalized differential quadrature analogy. The eigenvalue system was considered based on the harmonic balance technique. The Galerkin and Fréchet derivative approaches were used to determine the nonlinear free vibration behaviour of the carbon nano-cone, which was modelled in the simply- and clamped-supported boundary conditions. Comparisons were made between the findings from the new model versus the couple and classical stress theories, indicating that the classical and modified couple stress theories are distinct representations of modified strain gradient theory. The results also revealed that the degree of hardening of nano-truncated conical shells in the modified strain gradient theory is less than that of modified couple stress and classical theories. This led to a rise in the non-dimensional amplitude and frequency ratios. This study investigated the effect of size on free nonlinear vibrations of nano-truncated conical shells for various apex angles and lengths. Finally, we evaluated and compared our findings versus those reported by previous studies, which confirmed the precision and accuracy of our results.

LPE Growth of GaInAsP on (100)GaAs by a Two-Phase-Solution Technique

1984 ◽  
Vol 23 (Part 2, No. 1) ◽  
pp. L52-L54 ◽  
Author(s):  
Hideo Kawanishi ◽  
Takeshi Suzuki
Keyword(s):  
Solution Technique ◽  
Two Phase ◽  
Phase Solution

A nonlocal strain gradient theory for rotating thermo-mechanical characteristics on magnetically actuated viscoelastic functionally graded nanoshell

2020 ◽  
Vol 31 (12) ◽  
pp. 1511-1523
Author(s):  
Mohammad Mahinzare ◽  
Hossein Akhavan ◽  
Majid Ghadiri
Keyword(s):  
Boundary Conditions ◽  
Strain Gradient ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Smart Structure ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Nonlocal Strain Gradient Theory ◽  
Nonlocal Strain Gradient

In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.

Magnetic Superlattice: Localized Magnetostatic Waves and Magnetic Polaritons

2003 ◽  
Vol 17 (15) ◽  
pp. 829-839
Author(s):  
R. T. Tagiyeva ◽  
M. Saglam
Keyword(s):  
Magnetic Material ◽  
Electromagnetic Wave ◽  
Dispersion Relation ◽  
Wave Theory ◽  
Frequency Region ◽  
Long Wavelength ◽  
Magnetostatic Waves ◽  
General Dispersion ◽  
Magnetic Polaritons ◽  
Magnetic Superlattice

Localized magnetostatic waves and magnetic polaritons at the junction of the magnetic material and magnetic superlattice composed of the alternating ferromagnetic or ferromagnetic and nonmagnetic layers are investigated in the framework of the electromagnetic wave theory in Voigt geometry. The general dispersion relation for localized magnetic polaritons and magnetostatic waves (MW) are derived in the long-wavelength limit. The dispersion curves and frequency region of the exsistence of the localized MW and magnetic polaritons are calculated numerically.

scholarly journals A two-phase solution approach for a manufacturing-distribution problem with rework, outsourcing, and multi-shipment policy

2020 ◽  
Vol 18 (4) ◽  
pp. 505-509
Author(s):  
Chiu Peter ◽  
Peng-Cheng Sung ◽  
Victoria Chiu
Keyword(s):  
Cost Minimization ◽  
Algebraic Approach ◽  
Solution Procedure ◽  
Batch Size ◽  
Real Problem ◽  
Two Phase ◽  
Solution Approach ◽  
Straightforward Solution ◽  
The Cost ◽  
Phase Solution

In a recent study, a manufacturing batch-size and end-product shipment problem with outsourcing, multi-shipment, and rework was investigated using mathematical modeling and derivatives in its solution procedure. This study demonstrates that a simplified two-phase algebraic approach can also solve the problem and decide the cost-minimization policies for batch-size and end-product shipments. Our proposed straightforward solution approach enables the practitioners in the production planning and controlling filed to comprehend and efficiently solve the best replenishing batch-size and shipment policies of this real problem.

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