scholarly journals ABLATIVE PRESSURE PULSE

2021 ◽  
Author(s):  
Jan Grzesik
Keyword(s):  
Pressure Pulse ◽  
Unit Area ◽  
Rate Of Change ◽  
Space Distribution ◽  
Gas Temperature ◽  
Time Rate ◽  
Formula One ◽  
Phase Space Distribution ◽  
Universal Formula ◽  
Per Se

<div> We examine herein a simple model for the evolution in time of the pressure which a suddenly vaporized, ablating layer exerts upon the subjacent body. The model invokes a plausible construct of surface material instantaneously thrust into a gaseous regime governed by a Maxwell-Boltzmann phase space distribution. The surface pressure <i>per se</i> is gotten by computing the time rate of change of the momentum per unit area which the retrograde molecules, and only those, transfer through impact/reflection to the unvaporized body below. An explicit pressure formula, one alluding to the variable gas temperature within the vaporized layer, is obtained as a single quadrature requiring numerical integra- tion at finite times past the onset of impact. Limiting, null pressure values, both close-in and in pulse aftermath, can nevertheless be extracted in analytic terms, confirming in particular the indispensable asymptotic evanescence. A universal formula in dimensionless variables is given for pressure versus time, both suitably normalized.</div>

scholarly journals ABLATIVE PRESSURE PULSE

2021 ◽  
Author(s):  
Jan Grzesik
Keyword(s):  
Pressure Pulse ◽  
Unit Area ◽  
Rate Of Change ◽  
Space Distribution ◽  
Gas Temperature ◽  
Time Rate ◽  
Formula One ◽  
Phase Space Distribution ◽  
Universal Formula ◽  
Per Se

<div> We examine herein a simple model for the evolution in time of the pressure which a suddenly vaporized, ablating layer exerts upon the subjacent body. The model invokes a plausible construct of surface material instantaneously thrust into a gaseous regime governed by a Maxwell-Boltzmann phase space distribution. The surface pressure <i>per se</i> is gotten by computing the time rate of change of the momentum per unit area which the retrograde molecules, and only those, transfer through impact/reflection to the unvaporized body below. An explicit pressure formula, one alluding to the variable gas temperature within the vaporized layer, is obtained as a single quadrature requiring numerical integra- tion at finite times past the onset of impact. Limiting, null pressure values, both close-in and in pulse aftermath, can nevertheless be extracted in analytic terms, confirming in particular the indispensable asymptotic evanescence. A universal formula in dimensionless variables is given for pressure versus time, both suitably normalized.</div>

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

A New Mass Modelling Trick

2006 ◽  
Vol 2 (S235) ◽  
pp. 88-89
Author(s):  
Dalia Chakrabarty
Keyword(s):  
Distribution Function ◽  
Velocity Dispersion ◽  
Type Systems ◽  
Elliptical Galaxies ◽  
Space Distribution ◽  
Early Type ◽  
Phase Space Distribution ◽  
Mass Distributions ◽  
Kinematic Information ◽  
System Geometry

The estimation of the distribution of the total (luminous and dark) mass in early type systems is hard! Even for the lucky few systems for which kinematic information is available, its implementation is mired in problems, given uncertainties about the assumptions that enter the calculations; the most critical of such assumptions involve considerations of the system geometry and the shape of its velocity ellipsoid. This work offers an independent means of getting to the mass distributions of early type galaxies, without relying directly on the phase space distribution function. The methodology is based upon the well established idea that in elliptical galaxies, the largest variations in normalised velocity dispersion profiles occur typically at R < 0.5Re (Re≡ half-light radius) and at R ≥ 2Re.

STUDY OF PHASE PROPAGATION IN SUPERCONDUCTING ALUMINUM BY ULTRASONIC ATTENUATION MEASUREMENTS

1959 ◽  
Vol 37 (5) ◽  
pp. 614-618 ◽  
Author(s):  
K. L. Chopra ◽  
T. S. Hutchison
Keyword(s):  
Magnetic Field ◽  
Eddy Current ◽  
Ultrasonic Attenuation ◽  
Cylindrical Specimen ◽  
Current Theory ◽  
Superconducting Phase ◽  
Rate Of Change ◽  
Time Rate ◽  
Phase Propagation ◽  
The Magnetic Field

The phase propagation in superconducting aluminum has been studied by measuring the time rate of change of ultrasonic attenuation. The time taken for the destruction of the superconducting phase in a cylindrical specimen, by means of a magnetic field, H, greater than the critical field, Hc, is approximately proportional to{H/(H–Hc)} in agreement with eddy-current theory. In the converse case, where the superconducting phase is restored by switching off the magnetic field H (>Hc), the total time taken is nearly independent of the temperature (or Hc) as well as H. The superconducting phase grows at a non-uniform volume rate which is considerably less than the uniform rate of collapse.

Simulation study of Landau damping near the persisting to arrested transition

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Alexander J. Klimas ◽  
Adolfo F. Viñas ◽  
Jaime A. Araneda
Keyword(s):  
Phase Space ◽  
Simulation Study ◽  
High Speed ◽  
Space Distribution ◽  
Landau Damping ◽  
Field Mode ◽  
Low Speed ◽  
Phase Space Distribution ◽  
Saturation Stage ◽  
First Time

A one-dimensional electrostatic filtered Vlasov–Poisson simulation study is discussed. The transition from persisting to arrested Landau damping that is produced by increasing the strength of a sinusoidal perturbation on a background Vlasov–Poisson equilibrium is explored. Emphasis is placed on observed features of the electron phase-space distribution when the perturbation strength is near the transition value. A single ubiquitous waveform is found perturbing the space-averaged phase-space distribution at almost any time in all of the simulations; the sole exception is the saturation stage that can occur at the end of the arrested damping scenario. This waveform contains relatively strong, very narrow structures in velocity bracketing $\pm v_{\text{res}}$ – the velocities at which electrons must move to traverse the dominant field mode wavelength in one of its oscillation periods – and propagating with $\pm v_{\text{res}}$ respectively. Local streams of electrons are found in these structures crossing the resonant velocities from low speed to high speed during Landau damping and from high speed to low speed during Landau growth. At the arrest time, when the field strength is briefly constant, these streams vanish. It is conjectured that the expected transfer of energy between electrons and field during Landau growth or damping has been visualized for the first time. No evidence is found in the phase-space distribution to support recent well-established discoveries of a second-order phase transition in the electric field evolution. While trapping is known to play a role for larger perturbation strengths, it is shown that trapping plays no role at any time in any of the simulations near the transition perturbation strength.

Cosmic-Ray Energy Changes

1974 ◽  
Vol 2 (5) ◽  
pp. 297-299 ◽  
Author(s):  
L. J. Gleeson ◽  
G. M. Webb
Keyword(s):  
Cosmic Rays ◽  
Current Density ◽  
Cosmic Ray ◽  
Rate Of Change ◽  
Time Rate ◽  
Differential Current

The purpose of this paper is to provide a new expression for < ṗ > the average time-rate-of-change of momentum of cosmic-ray particles propagating in the interplanetary region. The expression derived replaces the previously used adiabatic deceleration formula and it is arrived at by a rearrangement and reinterpretation of the well known equation of transport for cosmic-rays. Thus, although we provide a new expression for < ṗ > we maintain the equation of transport and do not render invalid results for differential intensity and differential current density of cosmic-ray particles obtained by its solution (Jokipii 1971; Gleeson 1972).

Sign in / Sign up

Export Citation Format

Share Document