Slab Avalanche Modeling

2020 ◽  
pp. 36-44
Author(s):  
Francois Louchet
Keyword(s):  
Cellular Automaton ◽  
Shear Strain ◽  
Size Distribution ◽  
Power Law ◽  
Crack Opening ◽  
Strain Rates ◽  
Opposite Case ◽  
Successive Initiation

The chapter starts with a review of a few unfounded arguments sometimes used to account for snow slab instability, and often resulting from the application of mechanical laws that are invalid in a granular, brittle, and healable material like snow. Statistical aspects are investigated using a two-threshold cellular automaton, one for basal instability, and the second one for crown crack opening. The results reproduce the power-law size distribution of starting zone sizes mentioned in chapter 4, and validate a “4-step” triggering scheme made of successive initiation and expansion events for both the basal crack and the crown crack. The possible sintering of collapsed weak layers is then analyzed. It is shown to flow as a slurry for shear strain rates less than a predetermined threshold, or to sinter in the opposite case, which provides a “joker” to any successful “4-step” scheme, turning an incipient avalanche into a simple “whumpf”.

scholarly journals Developing and Evaluating Ice Cloud Parameterizations for Forward Modeling of Radar Moments Using in situ Aircraft Observations

2015 ◽  
Vol 32 (5) ◽  
pp. 880-903 ◽  
Author(s):  
Maximilian Maahn ◽  
Ulrich Löhnert ◽  
Pavlos Kollias ◽  
Robert C. Jackson ◽  
Greg M. McFarquhar
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Particle Mass ◽  
Maximum Diameter ◽  
Doppler Spectrum ◽  
Doppler Velocity ◽  
Radar Observations ◽  
Size Relation ◽  
Particle Area

AbstractObserving ice clouds using zenith pointing millimeter cloud radars is challenging because the transfer functions relating the observables to meteorological quantities are not uniquely defined. Here, the authors use a spectral radar simulator to develop a consistent dataset containing particle mass, area, and size distribution as functions of size. This is an essential prerequisite for radar sensitivity studies and retrieval development. The data are obtained from aircraft in situ and ground-based radar observations during the Indirect and Semi-Direct Aerosol Campaign (ISDAC) campaign in Alaska. The two main results of this study are as follows: 1) An improved method to estimate the particle mass–size relation as a function of temperature is developed and successfully evaluated by combining aircraft in situ and radar observations. The method relies on a functional relation between reflectivity and Doppler velocity. 2) The impact on the Doppler spectrum by replacing measurements of particle area and size distribution by recent analytical expressions is investigated. For this, higher-order moments such as skewness and kurtosis as well as the slopes of the Doppler spectrum are also used as a proxy for the Doppler spectrum. For the area–size relation, it is found that a power law is not sufficient to describe particle area and small deviations from a power law are essential for obtaining consistent higher moments. For particle size distributions, the normalization approach for the gamma distribution of Testud et al., adapted to maximum diameter as size descriptor, is preferred.

Strength and deformation of frozen saturated sand at −30 °C

1982 ◽  
Vol 19 (1) ◽  
pp. 104-107 ◽  
Author(s):  
V. R. Parameswaran ◽  
M. Roy
Keyword(s):  
Strain Rate ◽  
Power Law ◽  
Quartz Sand ◽  
Peak Strength ◽  
Strain Rates ◽  
Saturated Sand ◽  
Ideal Plastic ◽  
Strength And Deformation ◽  
Power Law Equation

Frozen saturated quartz sand containing 20% moisture by weight, when deformed at −30 °C at various strain rates, showed various modes of behaviour such as visco-plastic, almost ideal plastic, and brittle with little plasticity with increasing order of strain rate. The values of peak strength observed for strain rates between 5 × 10−7 and 6 × 10−3 s−1 were in the range 15–42 MPa, stress being related to strain rate by a power-law equation.

Stress-Strain Curves for Oxygen-Free High Conductivity Copper at Shear Strain Rates of up to 103s-1

1970 ◽  
Vol 185 (1) ◽  
pp. 1149-1158 ◽  
Author(s):  
K. Bitans ◽  
P. W. Whitton
Keyword(s):  
Shear Strain ◽  
Testing Machine ◽  
Shear Bands ◽  
Strain Curve ◽  
Strain Rates ◽  
Adiabatic Shear Bands ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
The Given ◽  
Tubular Specimens

Shear stress-shear strain curves for o.f.h.c. copper at room temperature have been obtained at constant shear strain rates in the range 1 to 103s-1, using thin walled tubular specimens in a flywheel type torsion testing machine. Results show that, for a given value of strain, the stress decreases when the rate of strain is increased. Moreover, the elastic portion of the stress-strain curve tends to disappear as the rate of strain is increased. It is postulated that these effects are due to the formation of adiabatic shear bands in the material when the given rate of strain is impressed rapidly enough. A special feature of the design of the testing machine used is the rapid application of the chosen strain rate.

scholarly journals Global variability of phytoplankton functional types from space: assessment via the particle size distribution

2010 ◽  
Vol 7 (3) ◽  
pp. 4295-4340 ◽  
Author(s):  
T. S. Kostadinov ◽  
D. A. Siegel ◽  
S. Maritorena
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Power Law ◽  
Seasonal Succession ◽  
Remote Sensing Data ◽  
Good Correspondence ◽  
Size Classes ◽  
Functional Types ◽  
Phytoplankton Size

Abstract. A new method of retrieving the parameters of a power-law particle size distribution (PSD) from ocean color remote sensing data was used to assess the global distribution and dynamics of phytoplankton functional types (PFT's). The method retrieves the power-law slope, ξ, and the abundance at a reference diameter, N0, based upon the shape and magnitude of the particulate backscattering coefficient spectrum. Relating the PSD to PFT's on global scales assumes that the open ocean particulate assemblage is biogenic. The retrieved PSD's can be integrated to define three size-based PFT's by the percent volume concentration contribution of three phytoplankton size classes – picoplankton (0.5–2 μm in equivalent spherical diameter), nanoplankton (2–20 μm) and microplankton (20–50 μm). Validation with in-situ HPLC diagnostic pigments results in satisfactory match-ups for the pico- and micro-phytoplankton size classes. Global climatologies derived from SeaWiFS monthly data reveal PFT and particle abundance spatial patterns that are consistent with current understanding. Oligotrophic gyres are characterized by lower particle abundance and higher contribution by picoplankton-sized particles than transitional or eutrophic regions. Seasonal succession patterns for size-based PFT's reveal good correspondence between increasing chl and percent contribution by microplankton, as well as increasing particle abundance. Long-term trends in particle abundances are generally inconclusive yet are well correlated with the MEI index indicating increased oligotrophy (i.e. lower particle abundance and increased contribution of picoplankton-sized particles) during the warm phase of an El Niño event. This work demonstrates the utility and future potential of assessing phytoplankton functional types using remote characterization of the particle size distribution.

scholarly journals Estimating The Sea Ice Floe Size Distribution Using Satellite Altimetry: Theory, Climatology, and Model Comparison

2019 ◽  
Author(s):  
Christopher Horvat ◽  
Lettie Roach ◽  
Rachel Tilling ◽  
Cecilia Bitz ◽  
Baylor Fox-Kemper ◽  
...  
Keyword(s):  
Sea Ice ◽  
Size Distribution ◽  
Power Law ◽  
Model Comparison ◽  
Climate Model ◽  
Thickness Distribution ◽  
Wave Model ◽  
Polar Regions ◽  
Scaling Exponent ◽  
Ocean Surface Waves

Abstract. In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are spare – traditionally taken via a pain-staking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and globally is largely unknown. Frequently, measured FSDs are assessed using a single number, the scaling exponent of the closest power law fit to the observed floe size data, although in the absence of adequate datasets there have been limited tests of this power-law hypothesis. Here we derive and explain a mathematical technique for deriving statistics of the sea ice FSD from polar-orbiting altimeters, satellites with sub-daily return times to polar regions with high along-track resolutions. Applied to the CryoSat-2 radio altimetric record, covering the period from 2010–2018, and incorporating 11 million individual floe samples, we produce the first climatology and seasonal cycle of sea ice floe size statistics. We then perform the first pan-Arctic test of the power law hypothesis, finding limited support in the range of floe sizes typically analyzed in photographic observational studies. We compare the seasonal variability in observed floe size to fully coupled climate model simulations including a prognostic floe size and thickness distribution and coupled wave model, finding good agreement in regions where modeled ocean surface waves cause sea ice fracture.

NEW UNIVERSALITY CLASS OF IMPACT FRAGMENTATION

Fractals ◽  
2003 ◽  
Vol 11 (04) ◽  
pp. 369-376 ◽  
Author(s):  
HAJIME INAOKA ◽  
MAREKAZU OHNO
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Fragment Size ◽  
Universality Class ◽  
Fragment Size Distribution ◽  
Space Filling ◽  
Impact Fragmentation

We conducted a set of experiments of impact fragmentation of samples with voids, such as pumice stones and bricks. We discovered that the fragment size distribution follows a power law, but that the exponent of the distribution is different from that of the distribution by the fragmentation of a space-filling sample like a gypsum ball. The value of the exponent is about 0.9. And the value seems universal for samples with voids.

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.

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