Experimental Evidence of Velocity-Weakening Friction during Ice Slip over Frozen Till: Implications for Basal Seismicity in Fast Moving, Soft-Bed Glaciers and Ice Streams

2021 ◽  
Author(s):  
Seth Saltiel ◽  
Christine McCarthy ◽  
Timothy T. Creyts ◽  
Heather M. Savage
Keyword(s):  
Melting Point ◽  
Linear Time ◽  
Ice Streams ◽  
Strong Constraint ◽  
Slow Slip Events ◽  
Spatial And Temporal Scales ◽  
Frictional Strength ◽  
Rate And State Friction ◽  
The Stability ◽  
Friction Parameters

Abstract Observations of glacier slip over till beds, across a range of spatial and temporal scales, show abundant seismicity ranging from Mw∼−2 microearthquakes and tremor (submeter asperities and millisecond duration) to Mw∼7 slow-slip events (∼50  km rupture lengths and ∼30  min durations). A complete understanding of the mechanisms capable of producing seismic signals in these environments represents a strong constraint on bed conditions. In particular, there is a lack of experimental confirmation of velocity-weakening behavior of ice slipping on till, where friction decreases with increasing velocity—a necessity for nucleating seismic slip. To measure the frictional strength and stability of ice sliding against till, we performed a series of double-direct-shear experiments at controlled temperatures slightly above and below the ice melting point. Our results confirm velocity-strengthening ice–till slip at melting temperatures, as has been found in the few previous studies. We provide best-fit rate-and-state friction parameters and their standard deviations from averaging 13 experiments at equivalent conditions. We find evidence of similar velocity-strengthening behavior with 50% by volume debris-laden ice slid against till under the same conditions. In contrast, velocity-weakening and linear time-dependent healing of ice–till slip is present at temperatures slightly below the melting point, providing an experimentally supported mechanism for subglacial seismicity on soft-beds. The stability parameter (a−b) decreases with slip velocity, and evolution occurs over large (mm scale) displacements, suggesting that shear heating and melt buildup is responsible for the weakening. These measurements provide insight into subglacial stiffness in which seismicity of this type might be expected. We discuss glaciological circumstances pointing to potential field targets in which to test this frozen seismic asperity hypothesis.

scholarly journals Ice sheet flow with thermally activated sliding. Part 1: the role of advection

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190410 ◽  
Author(s):  
E. Mantelli ◽  
M. Haseloff ◽  
C. Schoof
Keyword(s):  
Melting Point ◽  
Ice Sheet ◽  
Companion Paper ◽  
Ice Streams ◽  
Thermally Activated ◽  
Bed Temperature ◽  
Basal Sliding ◽  
Fast Motion ◽  
The Stability

Flow organization into systems of fast-moving ice streams is a well-known feature of ice sheets. Fast motion is frequently the result of sliding at the base of the ice sheet. Here, we consider how this basal sliding is first initiated as the result of changes in bed temperature. We show that an abrupt sliding onset at the melting point, with no sliding possible below that temperature, leads to rapid drawdown of cold ice and refreezing as the result of the increased temperature gradient within the ice, and demonstrate that this result holds regardless of the mechanical model used to describe the flow of ice. Using this as a motivation, we then consider the possibility of a region of ‘subtemperate sliding’ in which sliding at reduced velocities occurs in a narrow range of temperatures just below the melting point. We confirm that this prevents the rapid drawdown of ice and refreezing of the bed, and construct a simple numerical method for computing steady-state ice sheet profiles that include a subtemperate region. The stability of such an ice sheet is analysed in a companion paper.

A Geographical Information System (GIS) study of Triassic vertebrate biochronology

2005 ◽  
Vol 142 (4) ◽  
pp. 327-354 ◽  
Author(s):  
E. J. RAYFIELD ◽  
P. M. BARRETT ◽  
R. A. McDONNELL ◽  
K. J. WILLIS
Keyword(s):  
Spatial Data ◽  
Geographical Information Systems ◽  
Western Europe ◽  
Temporal Distribution ◽  
Geographical Information ◽  
Late Triassic ◽  
Spatial And Temporal Scales ◽  
Potential Index ◽  
The Stability ◽  
Land Vertebrate

Geographical Information Systems (GIS) have been applied extensively to analyse spatial data relating to varied environmental issues, but have not so far been used to address biostratigraphical or macroevolutionary questions over extended spatial and temporal scales. Here, we use GIS techniques to test the stability, validity and utility of proposed Middle and Late Triassic ‘Land Vertebrate Faunachrons’ (LVFs), a global biostratigraphical framework based upon terrestrial/freshwater tetrapod occurrences. A database of tetrapod and megafloral localities was constructed for North America and Western Europe that also incorporated information on relevant palaeoenvironmental variables. This database was subjected to various spatial analysis techniques. Our GIS analysis found support at a global level for Eocyclotosaurus as an Anisian index taxon and probably Aetosaurus as a Norian indicator. Other tetrapod taxa are useful biostratigraphical/biochronological markers on a regional basis, such as Longosuchus and Doswellia for Late Carnian time. Other potential index fossils are hampered, however, by taxonomic instability (Mastodonsaurus, Metoposaurus, Typothorax, Paleorhinus, Pseudopalatus, Redondasaurus, Redondasuchus) and/or are not clearly restricted in temporal distribution (Paleorhinus, Angistorhinus, Stagonolepis, Metoposaurus and Rutiodon). This leads to instability in LVF diagnosis. We found only in the western Northern Hemisphere is there some evidence for an Anisian–Ladinian biochronological unit amalgamating the Perovkan and Berdyankian LVFs, and a possible late Carnian unit integrating the Otischalkian and Adamanian.Megaplants are generally not useful for biostratigraphical correlation in the Middle and Upper Triassic of the study area, but there is some evidence for a Carnian-age floral assemblage that corresponds to the combined Otischalkian and Adamanian LVFs. Environmental biases do not appear to strongly affect the spatial distribution of either the tetrapods or megaplants that have been proposed as index taxa in biostratigraphical schemes, though several examples of apparent environmental bias were detected by the analysis. Consequently, we argue that further revision and refinement of Middle and Late Triassic LVFs is needed before they can be used to support global or multi-regional biostratigraphical correlations. Caution should therefore be exercised when using the current scheme as a platform for macroevolutionary or palaeoecological hypotheses. Finally, this study demonstrates the potential of GIS as a powerful tool for tackling palaeontological questions over extended timescales.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Kernel and Offspring Concepts for the Stability Robustness of Multiple Time Delayed Systems (MTDS)

2006 ◽  
Vol 129 (3) ◽  
pp. 245-251 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Characteristic Root ◽  
Invariance Property ◽  
Multiple Time ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Robustness ◽  
The Stability

A novel treatment for the stability of linear time invariant (LTI) systems with rationally independent multiple time delays is presented in this paper. The independence of delays makes the problem much more challenging compared to systems with commensurate time delays (where the delays have rational relations). We uncover some wonderful features for such systems. For instance, all the imaginary characteristic roots of these systems can be found exhaustively along a set of surfaces in the domain of the delays. They are called the “kernel” surfaces (curves for two-delay cases), and it is proven that the number of the kernel surfaces is manageably small and bounded. All possible time delay combinations, which yield an imaginary characteristic root, lie either on this kernel or its infinitely many “offspring” surfaces. Another hidden feature is that the root tendencies along these surfaces exhibit an invariance property. From these outstanding characteristics an efficient, exact, and exhaustive methodology results for the stability assessment. As an added uniqueness of this method, the systems under consideration do not have to be stable for zero delays. Several example case studies are presented, which are prohibitively difficult, if not impossible to solve using any other peer methodology known to the authors.

scholarly journals Creep Instability of Ice Sheets

1976 ◽  
Vol 16 (74) ◽  
pp. 278-279
Author(s):  
Garry K.C. Clarke
Keyword(s):  
Melting Point ◽  
Ambient Temperature ◽  
Finite Thickness ◽  
Wave Number ◽  
Slab Thickness ◽  
Perturbation Equation ◽  
Rate Of Increase ◽  
The Stability ◽  
Image Position ◽  
Advection Velocity

Abstract The equation governing the growth or decay of a temperature perturbation T’ in an ice slab under shear stress σ xy is where K and k are respectively the thermal conductivity and diffusivity of ice, KB-v is the advection velocity normal to the bed and is the rate of increase of strain heating with temperature assuming a power law for flow. For a slab of infinite thickness under constant stress and at constant ambient temperature, T Fourier analysis gives -k2+a/k < o as the condition for stability where k is the wave number of a sinusoidal perturbation. When the slab has finite thickness the stability depends on the sign of the eigenvalues λm of the perturbation equation and on the boundary condition at the ice-rock interface. In general the eigenfunctions and eigenvalues must be found by approximate methods such as the Rayleigh-Ritz procedure but in the case where the stress and ambient temperature are constant over the slab thickness and there is no advection the eigenfunctions are either sines or cosines depending on the boundary conditions. In this special case the stability condition is if the bed is frozen and if it is at the melting point. The eigenvalue associated with the smallest value of m is the least stable so the maximum stable thickness is thus h = ½ π(a/K)1/2 if the bed is frozen or h = π (a/K)1/2 if it is at the melting point. For typical flow-law parameters these depths are around 250 m and 500 m respectively. The eigenvalues are related in a simple way to the growth or decay rates of the eigenfunctions: (K λm)–1 is the time constant for the mth eigenfunction. Depth-dependent stress, temperature, and advection have a marked effect on stability. A slab in which stress and temperature increase to values B and T B at the bed is considerably more stable than a slab held at constant stressσB and a constant temperature T B. Advection normal to the bed also has a major influence on stability. If the advection velocity is taken to vary linearly with depth and the bed is frozen, the effect of upward advection is to decrease stability and of downward advection to increase it. When the bed is temperate the effect of advection is more complex: downward advection increases stability but upward advection may increase or decrease it depending on the magnitude of the advection velocity.

scholarly journals Ice sheet flow with thermally activated sliding. Part 2: the stability of subtemperate regions

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190411
Author(s):  
E. Mantelli ◽  
C. Schoof
Keyword(s):  
Melting Point ◽  
Large Scale ◽  
Thermal Structure ◽  
Ice Sheet ◽  
Temperature Dependent ◽  
Length Scales ◽  
Thermally Activated ◽  
Potential Alternative ◽  
The Stability ◽  
Alternative Structure

The onset of sliding in ice sheets may not take the form of a sharp boundary between regions at the melting point, in which sliding is permitted, and regions below that temperature, in which there is no slip. Such a hard switch leads to the paradox of the bed naturally wanting to refreeze as soon as sliding has commenced. A potential alternative structure is a region of subtemperate sliding. Here temperatures are marginally below the melting point and sliding velocities slower than they would if the bed was fully temperate. Rather than being controlled by a standard sliding law, sliding velocities are then constrained by the need to maintain energy balance. This thermal structure arises in temperature-dependent sliding laws in the limit of strong sensitivity to temperature. Here, we analyse the stability of such subtemperate regions, showing that they are subject to a set of instabilities that occur at all length scales between ice thickness and ice sheet length. The fate of these instabilities is to cause the formation of patches of frozen bed, raising the possibility of highly complicated cold-to-temperate transitions with spatial structures at short length scales that cannot be resolved in large-scale ice sheet simulation codes.

Aqueous nonelectrolyte solutions — Part XX: Formula of structure I methane hydrate, congruent dissociation melting point, and formula of the metastable hydrate

2003 ◽  
Vol 81 (12) ◽  
pp. 1443-1450 ◽  
Author(s):  
David N Glew
Keyword(s):  
Melting Point ◽  
Equilibrium Constant ◽  
Methane Hydrate ◽  
Equilibrium Constants ◽  
Stability Range ◽  
Congruent Melting Point ◽  
Quadruple Point ◽  
Dissociation Equilibrium ◽  
Metastable Structure ◽  
The Stability

Sixteen new measurements of high precision for structure I methane hydrate with water between 31.93 and 47.39 °C are shown to be metastable and exhibit higher methane pressures than found by earlier workers. Comparison of earlier measurements between 26.7 and 47.2 °C permit positive identification of the structure II and the structure I hydrates. Forty-nine equilibrium constants Kp(h1[Formula: see text]l1g) for dissociation of structure I methane hydrate into water and methane, 32 between –0.29 and 26.7 °C for the stable hydrate and 17 between 31.93 and 47.39 °C for the metastable hydrate, are best represented by a three-parameter thermodynamic equation, which indicates a standard error (SE) of 0.63% on a single Kp(h1[Formula: see text]l1g) determination. The congruent dissociation melting point C(h1l1gxm) of metastable structure I methane hydrate is at 47.41 °C with SE 0.02 °C and at pressure 505 MPa. The congruent equilibrium constant Kp(h1[Formula: see text]l1g) is 102.3 MPa with SE 0.2 MPa. ΔH°t(h1[Formula: see text]l1g) is 62 281 J mol–1 with SE 184 J mol–1, and the congruent formula is CH4·5.750H2O with SE 0.059H2O. At the congruent point, ΔV(h1[Formula: see text]l1g) is zero within experimental precision, and its estimate is 1.3 with SE 1.6 cm3 mol–1. The stability range of structure I methane hydrate with water extends from quadruple point Q(s1h1l1g) at –0.29 °C up to quadruple point Q(h1h2l1g) at 26.7 °C, and its metastability range with water extends from 26.7 °C up to the congruent dissociation melting point C(h1l1gxm) at 47.41 °C. Key words: methane hydrate, clathrate structure I, metastability range, dissociation equilibrium constant, formula, congruent melting point, metastability of structure I hydrate.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

scholarly journals Torsion Discriminance for Stability of Linear Time-Invariant Systems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 386
Author(s):  
Yuxin Wang ◽  
Huafei Sun ◽  
Yueqi Cao ◽  
Shiqiang Zhang
Keyword(s):  
Lebesgue Measure ◽  
Linear Time ◽  
Zero Solution ◽  
Positive Lebesgue Measure ◽  
Asymptotically Stable ◽  
Linear Time Invariant ◽  
Measurable Set ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

This paper extends the former approaches to describe the stability of n-dimensional linear time-invariant systems via the torsion τ ( t ) of the state trajectory. For a system r ˙ ( t ) = A r ( t ) where A is invertible, we show that (1) if there exists a measurable set E 1 with positive Lebesgue measure, such that r ( 0 ) ∈ E 1 implies that lim t → + ∞ τ ( t ) ≠ 0 or lim t → + ∞ τ ( t ) does not exist, then the zero solution of the system is stable; (2) if there exists a measurable set E 2 with positive Lebesgue measure, such that r ( 0 ) ∈ E 2 implies that lim t → + ∞ τ ( t ) = + ∞ , then the zero solution of the system is asymptotically stable. Furthermore, we establish a relationship between the ith curvature ( i = 1 , 2 , ⋯ ) of the trajectory and the stability of the zero solution when A is similar to a real diagonal matrix.

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