scholarly journals The Glide Direction in Ice

1961 ◽  
Vol 3 (30) ◽  
pp. 1097-1106 ◽  
Author(s):  
W. Barclay Kamb
Keyword(s):  
Power Flow ◽  
Stress Component ◽  
Ice Crystal ◽  
Hexagonal Crystal ◽  
Plastic Properties ◽  
Axis Orientation ◽  
Cubic Metals ◽  
Non Linear ◽  
Polycrystalline Aggregates ◽  
Flow Law

AbstractThe failure to detect experimentally a glide direction in the ice crystal is satisfactorily explained by assuming that the crystal glides simultaneously in three symmetry-equivalent directions with a response to the shear stress component in each direction that is the same as that observed for the crystal as a whole or for polycrystalline aggregates—the typical non-linear, power-type flow law. A hexagonal crystal responding to stress by this type of “non-linear crystal viscosity” behaves very differently from a tetragonal one. For a tetragonal crystal, the glide directions are well defined in the response of the crystal if the power-flow-law exponent n exceeds n ~ 1·5, whereas for a hexagonal crystal a well-defined glide direction can be observed only if n > c. 5. The response of a hexagonal crystal is entirely independent of a-axis orientation if n = 3 exactly. For 3 < n < c. 5 the true glide direction should be weakly apparent, whereas for 1 < n < 3 the crystal should show a response weakly suggestive of preferred glide in a direction perpendicular to the true glide direction. In the observed range of n values for ice, 2 < n < 4, the expected response to simultaneous glide differs so slightly from the hitherto-postulated a-axis-independent, “non-crystallographic” glide as to be practically undetectable experimentally. This circumstance makes it possible to identify <>as the glide direction, from structural considerations alone, and to accommodate the plastic properties of the ice crystal into the modern concepts of crystal plasticity. It may be expected that hexagonal close packed and face-centred cubic metals at high temperatures, in steady state creep, will show translation gliding without well-defined glide directions.

scholarly journals The Glide Direction in Ice

1961 ◽  
Vol 3 (30) ◽  
pp. 1097-1106 ◽  
Author(s):  
W. Barclay Kamb
Keyword(s):  
Power Flow ◽  
Stress Component ◽  
Ice Crystal ◽  
Hexagonal Crystal ◽  
Plastic Properties ◽  
Axis Orientation ◽  
Cubic Metals ◽  
Non Linear ◽  
Polycrystalline Aggregates ◽  
Flow Law

AbstractThe failure to detect experimentally a glide direction in the ice crystal is satisfactorily explained by assuming that the crystal glides simultaneously in three symmetry-equivalent directions with a response to the shear stress component in each direction that is the same as that observed for the crystal as a whole or for polycrystalline aggregates—the typical non-linear, power-type flow law. A hexagonal crystal responding to stress by this type of “non-linear crystal viscosity” behaves very differently from a tetragonal one. For a tetragonal crystal, the glide directions are well defined in the response of the crystal if the power-flow-law exponent n exceedsn~ 1·5, whereas for a hexagonal crystal a well-defined glide direction can be observed only ifn&gt;c. 5. The response of a hexagonal crystal is entirely independent ofa-axis orientation ifn= 3 exactly. For 3 &lt;n&lt;c. 5 the true glide direction should be weakly apparent, whereas for 1 &lt;n&lt; 3 the crystal should show a response weakly suggestive of preferred glide in a direction perpendicular to the true glide direction. In the observed range ofnvalues for ice, 2 &lt;n&lt; 4, the expected response to simultaneous glide differs so slightly from the hitherto-postulateda-axis-independent, “non-crystallographic” glide as to be practically undetectable experimentally. This circumstance makes it possible to identify &lt;&gt;as the glide direction, from structural considerations alone, and to accommodate the plastic properties of the ice crystal into the modern concepts of crystal plasticity. It may be expected that hexagonal close packed and face-centred cubic metals at high temperatures, in steady state creep, will show translation gliding without well-defined glide directions.

Passivity-based control of islanded microgrids with unknown power loads

2020 ◽  
Vol 37 (4) ◽  
pp. 1548-1573
Author(s):  
Sofía Avila-Becerril ◽  
Gerardo Espinosa-Pérez ◽  
Oscar Danilo Montoya ◽  
Alejandro Garces
Keyword(s):  
Power Flow ◽  
Voltage Regulation ◽  
Algebraic Equations ◽  
Linear Dynamical Systems ◽  
Linear Algebraic Equations ◽  
Control Scheme ◽  
Non Linear ◽  
Local Measurements ◽  
Islanded Mode ◽  
Passivity Based Control

Abstract In this paper, the control problem of microgrids (MGs)operating in islanded mode is approached from a passivity-based control perspective. A control scheme is proposed that, relying only on local measurements for the power converters included in the network representation, achieves both voltage regulation and power balance in the network through the generation of grid-forming and grid-following nodes. From the mathematical perspective, the importance of the contribution lies in the feature that, exploiting a port-controlled Hamiltonian representation of the MG, the closed-loop system’s stability properties are formally proved using arguments from the theory of non-linear dynamical systems. Fundamental for this achievement is the decomposition of the system into subsystems that require a control law and another whose variables can evolve in a free way. From the practical viewpoint, the advantage of the proposed controller lies in the feature that the power demanded by the loads is satisfied without neither computing its specific value nor solving the non-linear algebraic equations given by the power flow, avoiding the computational burden associated with this task. The usefulness of the scheme is illustrated via a numerical simulation that includes practical considerations.

scholarly journals Study of an ice core to the bedrock in the accumulation zone of an Alpine glacier

1976 ◽  
Vol 17 (75) ◽  
pp. 13-28 ◽  
Author(s):  
M. Vallon ◽  
J.-R. Petit ◽  
B. Fabre
Keyword(s):  
Water Content ◽  
Ice Core ◽  
Ice Crystal ◽  
Vertical Orientation ◽  
Axis Orientation ◽  
Alpine Glacier ◽  
Small Crystals ◽  
Average Water ◽  
Intermediate Size ◽  
Average Size

AbstractA water table appearing every summer where the ice begins, at a gerpth of approximately 30 m, accelerates the transformation of firn into ice during the summer (80% of the ice formed every year appears in less than 2 months). The ice formed in this way contains from 0 to 0.6% water. The average water content increases gradually with the gerpth because of the heat of gerformation. But, near bedrock, between 180 and 187 m, the permeability of the blue ice is such that the water content drops (0.3% as compared to 1.3% between 160 and 180 m).From a gerpth of 33 m, a foliation of sedimentary origin gradually gervelops in the ice. Its dip increases regularly to a gerpth of 145 m. At 145 m it jumps sudgernly freom 20° to 40°, then at 170 m freom 40° to 65°, which can be explained by old modifications in the bergschrund. This foliation disappears near bedrock (180-187 m), where there are no bubbles in the ice.The average size of an ice crystal increases slowly in the firn, shows seasonal fluctuations between 30 and 50 m, then jumps freom a diameter of 1 or 2 mm to 10 or 20 mm between 50 and 80 m. Between 180 and 187 m, the ice is mager of large crystals (3-10 cm diameter; the figure, however, is probably inexact due to a recrystallization of the samples).The very strong sub-vertical orientation of the optic axes of the firn crystals disappears quickly, and freom 66 m on, in ice with large crystals, a fabric of multiple maxima appears (generally, 3 or 4 directions, forming a triangle or a rhombus). On the other hand, in the small crystals that form bands parallel to the plane of foliation, only one direction of preferential orientation can be seen, or two close to one another. Crystals of intermediate size (10 to 50 mm) generally have two directions of preferred orientation at an angle of approximately 50° to one another. No matter how big the crystals are, the angle between the most commonc-axis orientation and the vertical does not change freom 60 to 170 m gerpth.

An Approximate Method for Non -Darcy Radial Gas Flow

1964 ◽  
Vol 4 (02) ◽  
pp. 96-114 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Linear Equation ◽  
Flow Rate ◽  
Analytical Solutions ◽  
Gas Flow ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Non Linear Equation ◽  
Approximate Analytical Solutions ◽  
Non Linear ◽  
Flow Law

Abstract Approximate analytical solutions for non-Darcy radial gas flow are derived for bounded and infinite reservoirs producing at either constant rate or constant pressure. These analytical solutions are compared with published results for non-Darcy flow obtained on digital and analogue computers, and the agreement is shown to be very good. Some observations on the interpretation of gas well tests are made. Introduction The flow of gases in porous media is a problem that has been the subject of much study in recent years, and many methods have been proposed for solving the non-linear equations associated with it. The assumption that the flow satisfies Darcy's Law (1) leads to a non-linear equation of the form (2) in a homogeneous medium, assuming an equation of state(3) It has been observed, however, that the linear relationship between the flow rate and pressure gradient is only approximately valid even at low flow rates, and that as the flow rate increases the deviations from linearity also increase. It has been suggested by a number of authors that Darcy's Law should be replaced by a quadratic flow law of the form (4) This form of equation was first suggested by Forchheimer and, later, Katz and Cornell, and Irmay, developed a similar equation. Houpeurt derived this form of equation using the concept of an idealized pore system in which each channel consists of sequences of truncated cones giving rise to successive restrictive orifices along the channel. This type of representation leads to a quadratic flow law of type, for all fluids, but it is found that the quadratic term is only significant in the case of gas flow. The methods of Houpeurt for solving gas flow problems will be discussed further in another section of this paper. Solutions of the non-linear equation for Darcy gas flow may be classified as either computer (digital and analogue), or approximate analytical ones. The former include the well-known solutions of Bruce et al., and Aronofsky and Jenkins, but the latter solutions, apart from the simple linearization of equation [2] to yield a diffusion equation in p2, are not so well-known. SPEJ P. 96ˆ

scholarly journals Mass–Balance and Ice–Flow–Law Parameters for East Antarctica

1985 ◽  
Vol 31 (109) ◽  
pp. 334-339 ◽  
Author(s):  
T.C Hamley ◽  
I.N. Smith ◽  
N.W. Young
Keyword(s):  
Power Flow ◽  
Grid Point ◽  
Ice Sheet ◽  
Field Measurements ◽  
East Antarctica ◽  
Surface Velocity ◽  
Shear Strain Rate ◽  
Polar Research Institute ◽  
Flow Law ◽  
Basal Shear

AbstractA comprehensive set of ice-velocity and thickness data from traverses within the IAGP study area (bounded by long. 90°E. and 135°E., and north of lat. 80°S.) is compared with steady-state mass-flux calculations based on Scott Polar Research Institute (SPRI) map compilations.The results of previous regional mass-budget estimates are reviewed and followed by a description of the new field measurements and the basis upon which a computer “grid–point” program is used to calculate balance fluxes.A comparison of measured and balance fluxes indicates that the ice sheet in this region of East Antarctica is unlikely to be significantly out of balance.The ratio of average column to surface velocity is discussed and calculated to be 0.89.An analysis of the mean shear strain-rate (VS/Z), versus down-slope basal shear stress (τb=ρgᾱZ), suggests that power flow-law parameters ofn= 3.21 andk= 0.023 bar−nm−1are appropriate for the effective basal shear zone in this region of the Antarctic ice sheet.

scholarly journals Crystal Size and Orientation Patterns in the Wisconsin-Age Ice from Dye 3, Greenland

1988 ◽  
Vol 10 ◽  
pp. 109-115 ◽  
Author(s):  
C.C. Langway ◽  
H. Shoji ◽  
N. Azuma
Keyword(s):  
Crystal Size ◽  
Ice Core ◽  
Ice Crystal ◽  
Axis Orientation ◽  
Measuring Device ◽  
Thin Sections ◽  
Core Samples ◽  
Physical Measurements ◽  
Ice Crystal Size ◽  
Velocity Measuring

Crystal size and c-axis orientation patterns were measured on the Dye 3, Greenland, deep ice core in order to investigate time-dependent changes or alterations in the physical character of the core as a function of time after recovery. The physical measurements were expanded to include depth intervals not previously studied in the field. The recent study focused on core samples located between 1786 m and the bottom of the ice sheet at 2037 m.Manual c-axis measurements were made on 23 new thin sections using a Rigsby-type universal stage. A new semi-automatic ultrasonic wave-velocity measuring device was developed in order to compare the results with the earlier manual measurements and to study an additional 114 ice-core samples in the Wisconsin-age ice. Crystal-size measurements were made on specimen surfaces by inducing evaporation grooves at crystal boundaries and measuring linear intercepts. The ultrasonically measured test samples were subsequently cleaned and analyzed by ion chromatography in order to measure impurity concentration levels of Cl−, NO3− and SO42− and study their effects on crystal growth and c-axis orientation.

scholarly journals A Novel Three-Phase Harmonic Power Flow Algorithm for Unbalanced Radial Distribution Networks with the Presence of D-STATCOM Devices

Electronics ◽  
2021 ◽  
Vol 10 (21) ◽  
pp. 2663
Author(s):  
Raavi Satish ◽  
Kanchapogu Vaisakh ◽  
Almoataz Y. Abdelaziz ◽  
Adel El-Shahat
Keyword(s):  
Radial Distribution ◽  
Power Flow ◽  
Distribution Networks ◽  
Flow Solution ◽  
Three Phase ◽  
Harmonic Pollution ◽  
Flow Algorithm ◽  
Non Linear ◽  
Radial Distribution Networks ◽  
Harmonic Power

Due to the rapid advancement in power electronic devices in recent years, there is a fast growth of non-linear loads in distribution networks (DNs). These non-linear loads can cause harmonic pollution in the networks. The harmonic pollution is low, and the resonance problem is absent in distribution static synchronous compensators (D-STATCOM), which is the not case in traditional compensating devices such as capacitors. The power quality issue can be enhanced in DNs with the interfacing of D-STATCOM devices. A novel three-phase harmonic power flow algorithm (HPFA) for unbalanced radial distribution networks (URDN) with the existence of linear and non-linear loads and the integration of a D-STATCOM device is presented in this paper. The bus number matrix (BNM) and branch number matrix (BRNM) are developed in this paper by exploiting the radial topology in DNs. These matrices make the development of HPFA simple. Without D-STATCOM integration, the accuracy of the fundamental power flow solution and harmonic power flow solution are tested on IEEE−13 bus URDN, and the results are found to be precise with the existing work. Test studies are conducted on the IEEE−13 bus and the IEEE−34 bus URDN with interfacing D-STATCOM devices, and the results show that the fundamental r.m.s voltage profile is improved and the fundamental harmonic power loss and total harmonic distortion (THD) are reduced.

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