Ranges of projectiles in amorphous materials

1968 ◽  
Vol 46 (6) ◽  
pp. 455-465 ◽  
Author(s):  
J. B. Sanders
Keyword(s):  
Distribution Function ◽  
Kinetic Energy ◽  
Power Law ◽  
Interaction Potential ◽  
Amorphous Materials ◽  
Initial Kinetic Energy ◽  
Initial Direction ◽  
Average Value ◽  
Inverse Power Law ◽  
The Moment

By using an inverse power-law approximation for the interaction potential between a fast-moving projectile and the atoms of an amorphous target into which it penetrates, it is possible to calculate moments of any order of different combinations of range quantities as functions of the initial kinetic energy of the projectile. By the moment of order n of a statistically distributed quantity X we mean the average value of Xn. The quantities concerned are the projection of the total distance from its point of entrance, reached by the projectile on its initial direction of motion, and the projection on the plane, perpendicular to this direction. From these moments, a distribution function of the penetration depth can be constructed. This calculation has been performed for 85Kr ions entering amorphous Al2O3 with different energies. The result is compared with measurements made by Domeij et al.

scholarly journals Impact Fracture of Composite and Homogeneous Nanoagglomerates

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
Author(s):  
S. J. Antony ◽  
R. Moreno-Atanasio ◽  
J. Musadaidzwa ◽  
R. A. Williams
Keyword(s):  
Kinetic Energy ◽  
Impact Loading ◽  
Fracture Behaviour ◽  
Time Lag ◽  
Impact Fracture ◽  
Initial Kinetic Energy ◽  
Normal Impact ◽  
Fracture Characteristics ◽  
Hard Shell ◽  
The Moment

It is not yet clear on whether the fracture characteristics of structured composite capsules and homogeneous nanoagglomerates differ significantly under impact loading conditions. Experimental measurement of impact fracture properties of such small agglomerates is difficult, due to the length and time scales associated with this problem. Using computer simulations, here we show that nanoagglomerates are subjected to normal impact loading fracture within a few nanoseconds in a brittle manner. The restitution coefficient of the nanoagglomerates varies nonlinearly with initial kinetic energy. The fracture of nanoagglomerates does not always happen at the moment when they experience the maximum wall force, but occurs after a time lag of a few nanoseconds as characterised by impact survival time (IST) and IST index. IST is dependant on the initial kinetic energy, mechanical and geometric properties of the nanoagglomerates. For identical geometries of the capsules, IST index is higher for capsules with a soft shell than for these with a hard shell, an indication of the enhanced ability of the soft nanocapsules to dissipate impact energy. The DEM simulations reported here based on theories of contact mechanics provide fundamental insights on the fracture behaviour of agglomerates—at nanoscale, the structure of the agglomerates significantly influences their breakage behaviour.

Inverse Power Law Behavior in a Memory Scanning Experiment

2006 ◽  
Author(s):  
Gerardo Ramirez ◽  
Sonia Perez ◽  
John G. Holden
Keyword(s):  
Power Law ◽  
Inverse Power ◽  
Memory Scanning ◽  
Inverse Power Law

Scaling

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Distribution Function ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Power Law ◽  
Scaling Laws ◽  
Power Laws ◽  
Distribution Functions ◽  
Temporal Process ◽  
Approximate Power

Scaling appears practically everywhere in science; it basically quantifies how the properties or shapes of an object change with the scale of the object. Scaling laws are always associated with power laws. The scaling object can be a function, a structure, a physical law, or a distribution function that describes the statistics of a system or a temporal process. We focus on scaling laws that appear in the statistical description of stochastic complex systems, where scaling appears in the distribution functions of observable quantities of dynamical systems or processes. The distribution functions exhibit power laws, approximate power laws, or fat-tailed distributions. Understanding their origin and how power law exponents can be related to the particular nature of a system, is one of the aims of the book.We comment on fitting power laws.

scholarly journals Rotational broadening and conservation of angular momentum in post-extreme horizontal branch stars

2018 ◽  
Vol 613 ◽  
pp. A66
Author(s):  
G. Fontaine ◽  
M. Latour
Keyword(s):  
Angular Momentum ◽  
Rotation Speed ◽  
Momentum Conservation ◽  
Evolutionary Models ◽  
Horizontal Branch ◽  
Natural Consequence ◽  
Average Value ◽  
Horizontal Branch Stars ◽  
The Moment ◽  
Ehb Stars

We show that the recent realization that isolated post-extreme horizontal branch (post-EHB) stars are generally characterized by rotational broadening with values of V rot sini between 25 and 30 km s−1 can be explained as a natural consequence of the conservation of angular momentum from the previous He-core burning phase on the EHB. The progenitors of these evolved objects, the EHB stars, are known to be slow rotators with an average value of V rot sini of ~7.7 km s−1. This implies significant spin-up between the EHB and post-EHB phases. Using representative evolutionary models of hot subdwarf stars, we demonstrate that angular momentum conservation in uniformly rotating structures (rigid-body rotation) boosts that value of the projected equatorial rotation speed by a factor ~3.6 by the time the model has reached the region of the surface gravity-effective temperature plane where the newly-studied post-EHB objects are found. This is exactly what is needed to account for their observed atmospheric broadening. We note that the decrease of the moment of inertia causing the spin-up is mostly due to the redistribution of matter that produces more centrally-condensed structures in the post-EHB phase of evolution, not to the decrease of the radius per se.

scholarly journals Inverse-power-law behavior of cellular motility reveals stromal–epithelial cell interactions in 3D co-culture by OCT fluctuation spectroscopy

Optica ◽  
2015 ◽  
Vol 2 (10) ◽  
pp. 877 ◽  
Author(s):  
Amy L. Oldenburg ◽  
Xiao Yu ◽  
Thomas Gilliss ◽  
Oluwafemi Alabi ◽  
Russell M. Taylor ◽  
...  
Keyword(s):  
Epithelial Cell ◽  
Power Law ◽  
Cell Interactions ◽  
Inverse Power ◽  
Cellular Motility ◽  
Inverse Power Law

Anomalies in Strongly Coupled Harmonic Quantum Brownian Motion

2013 ◽  
Vol 20 (01) ◽  
pp. 1350002 ◽  
Author(s):  
F. Giraldi ◽  
F. Petruccione
Keyword(s):  
Time Evolution ◽  
Power Law ◽  
Weak Coupling ◽  
Inverse Power ◽  
Strong Coupling Regime ◽  
Weak Coupling Regime ◽  
Spectral Densities ◽  
Inverse Power Law ◽  
Critical Configurations ◽  
Long Time

The exact dynamics of a quantum damped harmonic oscillator coupled to a reservoir of boson modes has been formally described in terms of the coupling function, both in weak and strong coupling regime. In this scenario, we provide a further description of the exact dynamics through integral transforms. We focus on a special class of spectral densities, sub-ohmic at low frequencies, and including integrable divergencies referred to as photonic band gaps. The Drude form of the spectral densities is recovered as upper limit. Starting from special distributions of coherent states as external reservoir, the exact time evolution, described through Fox H-functions, shows long time inverse power law decays, departing from the exponential-like relaxations obtained for the Drude model. Different from the weak coupling regime, in the sub-ohmic condition, undamped oscillations plus inverse power law relaxations appear in the long time evolution of the observables position and momentum. Under the same condition, the number of excitations shows trapping of the population of the excited levels and oscillations enveloped in inverse power law relaxations. Similarly to the weak coupling regime, critical configurations give arbitrarily slow relaxations useful for the control of the dynamics. If compared to the value obtained in weak coupling condition, for strong couplings the critical frequency is enhanced by a factor 4.

scholarly journals SCALE-FREE UNIVERSAL SPECTRUM FOR ATMOSPHERIC AEROSOL SIZE DISTRIBUTION FOR DAVOS, MAUNA LOA AND IZANA

2013 ◽  
Vol 23 (02) ◽  
pp. 1350028 ◽  
Author(s):  
A. M. SELVAM
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Aerosol Size Distribution ◽  
Scale Free ◽  
Mauna Loa ◽  
Atmospheric Particulates ◽  
Inverse Power Law ◽  
Universal Scale ◽  
Radius Size ◽  
Fractal Fluctuations

Atmospheric flows exhibit fractal fluctuations and inverse power law for power spectra indicates an eddy continuum structure for the self-similar fluctuations. A general systems theory for aerosol size distribution based on fractal fluctuations is proposed. The model predicts universal (scale-free) inverse power law for fractal fluctuations expressed in terms of the golden mean. Atmospheric particulates are held in suspension in the fractal fluctuations of vertical wind velocity. The mass or radius (size) distribution for homogeneous suspended atmospheric particulates is expressed as a universal scale-independent function of the golden mean, the total number concentration and the mean volume radius. Model predicted spectrum is compared with the total averaged radius size spectra for the AERONET (aerosol inversions) stations Davos and Mauna Loa for the year 2010 and Izana for the year 2009. There is close agreement between the model predicted and the observed aerosol spectra. The proposed model for universal aerosol size spectrum will have applications in computations of radiation balance of earth–atmosphere system in climate models.

Some measurements of the flux of infra-red radiation in the atmosphere

1956 ◽  
Vol 236 (1205) ◽  
pp. 175-186 ◽  
Keyword(s):  
Kinetic Energy ◽  
Lower Stratosphere ◽  
Atmospheric Radiation ◽  
Radiative Cooling ◽  
Classical View ◽  
Upper Troposphere ◽  
Infra Red ◽  
The Moment ◽  
Effective Radiation ◽  
Red Radiation

For the continual development of the kinetic energy of the winds, it is necessary for the upper troposphere to be cooled by radiation. Results are reported of nine aircraft ascents on which the upward and downward flows of infra-red radiation were measured and com­pared with values calculated using the radiation charts of Elsasser and Yamamoto. The divergence of radiative flux deduced from these measurements clearly shows that the cooling in the troposphere is not very different from that calculated from radiation charts. The importance of clouds on the radiative pattern is demonstrated; at the moment, incom­plete knowledge of cloud structure will be the chief factor limiting the value of calculations of atmospheric radiation. The measurements are of very limited value in the stratosphere, since, for the very small quantities of water there, the effective radiation is in the rotation band of water vapour ( λ between 30 and 70 μ ) and the radiometer used was not sensitive to these wavelengths. If the use of radiation charts is extrapolated to these conditions they indicate that the radiative cooling continues in the lower stratosphere. This is in contrast with the ‘classical’ view that the stratosphere is in radiative equilibrium.

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