An Elongating String Under the Action of a Transverse Force

1957 ◽  
Vol 24 (4) ◽  
pp. 609-616
Author(s):  
Werner Goldsmith
Keyword(s):  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Transverse Force ◽  
Transverse Displacement ◽  
Fixed Frequency ◽  
Constant Acceleration ◽  
Forcing Function ◽  
Subsonic Regime ◽  
Arbitrary Amplitude ◽  
Analytical Expressions

Abstract The motion of a uniform undamped flexible string whose length increases with time has been investigated when an arbitrary time-dependent force acts transversely at the free end. The method of characteristics has been employed to derive analytical expressions for the transverse displacement in the subsonic regime. Cases are considered when the free end of the wire moves either at constant velocity or at constant acceleration. Numerical solutions are presented in dimensionless form for a sinusoidal forcing function of arbitrary amplitude and fixed frequency. The possibility of the existence of resonances in the string has been examined.

On the Dynamic Expansion of a Circular Hole in an Infinite Plate of Rate-Sensitive Plastic Material

1978 ◽  
Vol 45 (1) ◽  
pp. 67-72 ◽  
Author(s):  
P. C. Upadhyay ◽  
V. K. Stokes
Keyword(s):  
Circular Hole ◽  
Exponential Type ◽  
Material Properties ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Infinite Plate ◽  
Constant Acceleration ◽  
Plastic Materials ◽  
Wide Range

The dynamic expansion of a circular hole in an infinite plate has been considered for rate-sensitive plastic materials by using an elastic-visco-perfertly plastic model of the exponential type. Numerical solutions have been obtained, by the method of characteristics, for the case when the hole is subjected to a constant acceleration. Solutions have been presented in the form of nondimensional plots covering a wide range of material properties and accelerations.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals Wave Ogives

1986 ◽  
Vol 32 (112) ◽  
pp. 325-334 ◽  
Author(s):  
E.D. Waddington
Keyword(s):  
Mass Balance ◽  
Method Of Characteristics ◽  
Wave Pattern ◽  
Wave Excitation ◽  
Ice Flow ◽  
Forcing Function ◽  
Excitation Potential ◽  
Ice Velocity ◽  
Balance Functions ◽  
Velocity Channel

AbstractWave ogives arise in a solution of the continuity equation by the method of characteristics. Steady ice flow is assumed. Ice velocity, channel width, and mass-balance functions combine to form a wave-excitation potential that yields the forcing function for wave ogives. This linear-systems formulation extends the ogive theory of Nye. Convolution of the temporal cumulative mass balance and spatial forcing functions gives the total wave pattern below an ice fall. Many ice falls do not generate ogives because the wave amplitude is modulated by a factor related to ice-fall length. The wave ogives at Austerdalsbreen, Norway, are due almost entirely to ice acceleration at the top of the ice-fall, i.e. the same zone that King and Lewis showed was responsible for forming Forbes bands.

Kinetics of protein binding determine rates of uptake of drugs by brain

1986 ◽  
Vol 251 (6) ◽  
pp. R1212-R1220 ◽  
Author(s):  
P. J. Robinson ◽  
S. I. Rapoport
Keyword(s):  
Protein Binding ◽  
Rate Constants ◽  
Plasma Proteins ◽  
Numerical Solutions ◽  
Free Drug ◽  
Arterial Blood ◽  
Drug Concentrations ◽  
Analytical Expressions ◽  
Kinetics Of ◽  
The Brain

A mathematical model describing the kinetics of binding and release of substances by plasma proteins is presented. The effects of protein binding on the uptake of substances such as drugs from the capillary network of the brain are discussed. The model assumes equilibration between bound and free forms of drug in arterial blood and incorporates the on-off rate constants for the drug-protein complex and rate constants for passage of free drug across the blood-brain barrier and for drug metabolism in the brain. Regional cerebral blood flow and the related capillary transit time are important parameters in the model. Analytical expressions for bound and free drug concentrations and for the net extraction of drug are derived where practicable, and numerical solutions also are presented. Effects of changes in the total drug and protein concentrations in the plasma are discussed with special reference to the uptake of bilirubin by the brain.

Propagation of a blast wave in uniform or non-uniform media: a uniformly valid analytic solution

1972 ◽  
Vol 52 (2) ◽  
pp. 369-378 ◽  
Author(s):  
P. L. Sachdev
Keyword(s):  
Analytic Solution ◽  
Numerical Solutions ◽  
Blast Waves ◽  
Shock Propagation ◽  
Point Explosion ◽  
Propagation Theory ◽  
Constant Acceleration ◽  
Weak Regime ◽  
Spherical Shock ◽  
Good Agreement

The shock propagation theory of Brinkley & Kirkwood (1947) is extended to provide a uniformly valid analytic solution of point-explosion problems both when the undisturbed medium is uniform and when it is stratified. This is achieved mainly by selecting the parameter expressing a similarity restraint in this theory such that initially it gives precisely the Taylor–Sedov solution, while asymptotically, in the weak regime, still retaining the well-known Landau–Whitham–Sedov form of the solution for shock overpressure. The shock overpressure, as calculated by the present method for spherical and cylindrical blast waves in the entire regime from the point of explosion to where they have become very weak, shows excellent agreement with that from the exact numerical solutions of Lutzky & Lehto (1968) and Plooster (1970). The solution for a spherical shock propagating in an exponential atmosphere stratified by a constant acceleration due to gravity also shows a good agreement with the exact numerical solution of Lutzky & Lehto.

Unsteady Convection Flow of Some Nanofluids Past a Moving Vertical Flat Plate With Heat Transfer

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
M. Turkyilmazoglu
Keyword(s):  
Flat Plate ◽  
Radiation Effect ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Nanofluid Flow ◽  
Flow Problems ◽  
Temperature Boundary ◽  
Analytical Expressions ◽  
Thermal Radiation Effect

This paper is devoted to the study of heat and mass transfer characteristics of some nanofluid flows past an infinite flat plate moving vertically. Some water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina (Al2O3), and titanium oxide (TiO2) are analytically analyzed taking into consideration the thermal radiation effect for two types of temperature boundary conditions. The physically significant properties like skin friction coefficient and Nusselt number are easy to conceive from the derived exact analytical expressions for the velocity and temperature profiles. Results are believed to constitute a tool to verify the validity of numerical solutions for more complicated transient free/forced convection nanofluid flow problems.

scholarly journals Accelerated self-constricted electron streams in plasma

1959 ◽  
Vol 249 (1258) ◽  
pp. 318-334 ◽  
Keyword(s):  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Electron Flow ◽  
Electron Stream ◽  
Ion Collisions ◽  
Two Fluid Model ◽  
Analytical Expressions ◽  
Positive Ion ◽  
Two Fluid

The mechanism is described of radial oscillations in a neutralized cylindrical electron stream in an accelerating electric field. The analysis is based on the two-fluid model of plasma. Analytical expressions for small amplitude oscillations and numerical solutions for large amplitudes are derived. It is found, when electron-positive ion collisions are taken into account, that for dense streams in low electric fields the radial oscillations (pinch oscillations) can destroy the streaming character of the electron flow and thus prevent its acceleration.

Patterns of Airflow in Circular Tubes Caused by a Corona Jet With Concentric and Eccentric Wire Electrodes

2010 ◽  
Vol 132 (8) ◽  
Author(s):  
Reza Baghaei Lakeh ◽  
Majid Molki
Keyword(s):  
Corona Discharge ◽  
Secondary Flow ◽  
Cross Section ◽  
Cross Sections ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Flow Patterns ◽  
Circular Tubes ◽  
The Method Of Characteristics ◽  
The Cross

A computational investigation is conducted to study the patterns of airflow induced by corona discharge in the cross section of a circular tube. The secondary flow induced by corona wind in various flow passages has been the subject of numerous investigations. The flow patterns are often identified by multiple recirculation bubbles. Such flow patterns have also been anticipated for circular cross sections where the corona discharge is activated by an electrode situated at the center of the cross section. In this investigation, it is shown that, contrary to public perception, a symmetric corona discharge does not generate a secondary flow in circular cross sections. This investigation then proceeds to demonstrate that the flow responsible for thermal enhancements in circular tubes often reported in the published literature is induced only when there is a slight asymmetry in the position of the electrode. The present computations are performed in two parts. In part one, the electric field equations are solved using the method of characteristics. In part two, the flow equations are solved using a finite-volume method. It is shown that the method of characteristics effectively eliminates the dispersion errors observed in other numerical solutions. The present computations show that the flow in the eccentric configuration is characterized by a corona jet that is oriented along the eccentricity direction and two recirculation zones situated on either sides of the jet. In addition to the computational approach, a number of analytical solutions are presented and compared with the computational results.

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