ASYMPTOTICAL SOLUTIONS FOR A VIBRATIONALLY RELAXING GAS

2009 ◽  
Vol 14 (4) ◽  
pp. 423-434 ◽  
Author(s):  
Rajan Arora
Keyword(s):  
High Frequency ◽  
Small Amplitude ◽  
Symmetric Flow ◽  
Van Der Waals Equation ◽  
One Dimensional ◽  
Resonant Wave ◽  
Cylindrically Symmetric ◽  
Geometrical Acoustics ◽  
Basic Equations ◽  
Relaxing Gas

Using the weakly non‐linear geometrical acoustics theory, we obtain the small amplitude high frequency asymptotic solution to the basic equations governing one dimensional unsteady planar, spherically and cylindrically symmetric flow in a vibrationally relaxing gas with Van der Waals equation of state. The transport equations for the amplitudes of resonantly interacting waves are derived. The evolutionary behavior of non‐resonant wave modes culminating into shock waves is also studied.

scholarly journals Interaction of waves in one-dimensional dusty gas flow

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Pooja Gupta ◽  
Rahul Kumar Chaturvedi ◽  
L. P. Singh
Keyword(s):  
Shock Wave ◽  
High Frequency ◽  
Gas Flow ◽  
Ideal Gas ◽  
Transport Equations ◽  
Dust Particles ◽  
Multiple Time Scales ◽  
Dusty Gas ◽  
One Dimensional ◽  
Geometrical Acoustics

AbstractThe present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave.

Analysis of Flow in a Two-Dimensional Collapsible Channel Using Universal “Tube” Law

1994 ◽  
Vol 116 (4) ◽  
pp. 469-476 ◽  
Author(s):  
Y. Matsuzaki ◽  
T. Ikeda ◽  
T. Kitagawa ◽  
S. Sakata
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
High Frequency ◽  
Small Amplitude ◽  
Simplified Model ◽  
High Frequency Oscillation ◽  
Two Dimensional ◽  
Frequency Oscillation ◽  
One Dimensional ◽  
Wide Range

This paper presents an extension of the previous analyses on the collapsible tubeflow problem using a simplified model based on a two-dimensional channel conveying a one-dimensional flow. The main objective of the paper is to exploit the static and dynamic behavior of the model, by comparing with available experimental data and examining the accuracy of calculated results obtained for different numerical resolutions. The main revision from the previous analyses is the incorporation of a universal “tube” law that is valid for a wide range of positive and negative transmural pressure. Most of the numerical results agree qualitatively with the experimental observations. Self-excited high-frequency oscillation with very small amplitude of the membrane wall is, however, predicted to occur in a flow range where the slope of the pressure drop curve is positive. It is seen that the high-frequency oscillation is associated with the motion of the separation point of the flow.

High-frequency, "quantum" and electromechanical effects in quasi-one-dimensional charge density wave conductors

2013 ◽  
Vol 183 (1) ◽  
pp. 33-54 ◽  
Author(s):  
Vadim Ya. Pokrovskii ◽  
Sergey G. Zybtsev ◽  
Maksim V. Nikitin ◽  
Irina G. Gorlova ◽  
Venera F. Nasretdinova ◽  
...  
Keyword(s):  
Charge Density ◽  
High Frequency ◽  
Charge Density Wave ◽  
Density Wave ◽  
One Dimensional ◽  
Electromechanical Effects

scholarly journals One-Dimensional Vacuum Steady Seepage Model of Unsaturated Soil and Finite Difference Solution

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Feng Huang ◽  
Jianguo Lyu ◽  
Guihe Wang ◽  
Hongyan Liu
Keyword(s):  
Finite Difference ◽  
Unsaturated Soil ◽  
Vacuum Pressure ◽  
Vacuum Field ◽  
One Dimensional ◽  
Steady Seepage ◽  
Basic Equations ◽  
The One ◽  
Seepage Law ◽  
Relationship Of

Vacuum tube dewatering method and light well point method have been widely used in engineering dewatering and foundation treatment. However, there is little research on the calculation method of unsaturated seepage under the effect of vacuum pressure which is generated by the vacuum well. In view of this, the one-dimensional (1D) steady seepage law of unsaturated soil in vacuum field has been analyzed based on Darcy’s law, basic equations, and finite difference method. First, the gravity drainage ability is analyzed. The analysis presents that much unsaturated water can not be drained off only by gravity effect because of surface tension. Second, the unsaturated vacuum seepage equations are built up in conditions of flux boundary and waterhead boundary. Finally, two examples are analyzed based on the relationship of matric suction and permeability coefficient after boundary conditions are determined. The results show that vacuum pressure will significantly enhance the drainage ability of unsaturated water by improving the hydraulic gradient of unsaturated water.

Subwavelength focusing of a cylindrically symmetric plano-concave lens based on a one-dimensional Thue–Morse photonic quasicrystal

2018 ◽  
Vol 11 (9) ◽  
pp. 092002 ◽  
Author(s):  
Wei Tan ◽  
Exian Liu ◽  
Bei Yan ◽  
Jianlan Xie ◽  
Rui Ge ◽  
...  
Keyword(s):  
One Dimensional ◽  
Cylindrically Symmetric ◽  
Concave Lens ◽  
Photonic Quasicrystal

A One Dimensional, Time Dependent Inlet / Engine Numerical Simulation for Aircraft Propulsion Systems

1997 ◽  
Author(s):  
Doug Garrard ◽  
Milt Davis ◽  
Steve Wehofer ◽  
Gary Cole
Keyword(s):  
Numerical Simulation ◽  
Gas Turbine ◽  
High Frequency ◽  
Gas Turbine Engine ◽  
Simulation System ◽  
Time Dependent ◽  
Propulsion Systems ◽  
Turbine Engine ◽  
One Dimensional ◽  
Supersonic Inlet

The NASA Lewis Research Center (LeRC) and the Arnold Engineering Development Center (AEDC) have developed a closely coupled computer simulation system that provides a one dimensional, high frequency inlet / engine numerical simulation for aircraft propulsion systems. The simulation system, operating under the LeRC-developed Application Portable Parallel Library (APPL), closely coupled a supersonic inlet with a gas turbine engine. The supersonic inlet was modeled using the Large Perturbation Inlet (LAPIN) computer code, and the gas turbine engine was modeled using the Aerodynamic Turbine Engine Code (ATEC). Both LAPIN and ATEC provide a one dimensional, compressible, time dependent flow solution by solving the one dimensional Euler equations for the conservation of mass, momentum, and energy. Source terms are used to model features such as bleed flows, turbomachinery component characteristics, and inlet subsonic spillage while unstarted. High frequency events, such as compressor surge and inlet unstart, can be simulated with a high degree of fidelity. The simulation system was exercised using a supersonic inlet with sixty percent of the supersonic area contraction occurring internally, and a GE J85-13 turbojet engine.

The effects of pH on force and stiffness development in mouse muscles

1987 ◽  
Vol 65 (8) ◽  
pp. 1798-1801 ◽  
Author(s):  
J. M. Renaud ◽  
R. B. Stein ◽  
T. Gordon
Keyword(s):  
High Frequency ◽  
Small Amplitude ◽  
Force Production ◽  
Muscle Length ◽  
Low Ph ◽  
Muscle Stiffness ◽  
Average Force ◽  
Cross Bridge ◽  
Effects Of Ph ◽  
Cross Bridges

Changes in force and stiffness during contractions of mouse extensor digitorum longus and soleus muscles were measured over a range of extracellular pH from 6.4 to 7.4. Muscle stiffness was measured using small amplitude (<0.1% of muscle length), high frequency (1.5 kHz) oscillations in length. Twitch force was not significantly affected by changes in pH, but the peak force during repetitive stimulation (2, 3, and 20 pulses) was decreased significantly as the pH was reduced. Changes in muscle stiffness with pH were in the same direction, but smaller in extent. If the number of attached cross-bridges in the muscle can be determined from the measurement of small amplitude, high frequency muscle stiffness, then these findings suggest that (a) the number of cross-bridges between thick and thin filaments declines in low pH and (b) the average force per cross-bridge also declines in low pH. The decline in force per cross-bridge could arise from a reduction in the ability of cross-bridges to generate force during their state of active force production and (or) in an increased percentage of bonds in a low force, "rigor" state.

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