scholarly journals Crevasse patterns and the strain-rate tensor: a high-resolution comparison

1998 ◽  
Vol 44 (146) ◽  
pp. 68-76 ◽  
Author(s):  
J. T. Harper ◽  
N. F. Humphrey ◽  
W. T. Pfeffer
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Principal Strain ◽  
Length Scale ◽  
Strain Rate Tensor ◽  
Regional Flow ◽  
Orthogonal Grid ◽  
Valley Glacier ◽  
Longitudinal Strain Rate

AbstractValues of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2 reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate (x) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e. x > 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

scholarly journals Crevasse patterns and the strain-rate tensor: a high-resolution comparison

1998 ◽  
Vol 44 (146) ◽  
pp. 68-76 ◽  
Author(s):  
J. T. Harper ◽  
N. F. Humphrey ◽  
W. T. Pfeffer
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Principal Strain ◽  
Length Scale ◽  
Strain Rate Tensor ◽  
Regional Flow ◽  
Orthogonal Grid ◽  
Valley Glacier ◽  
Longitudinal Strain Rate

AbstractValues of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate (x) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e.x> 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

scholarly journals Early Diastolic Longitudinal Strain Rate at MRI and Outcomes in Heart Failure with Preserved Ejection Fraction

Radiology ◽  
2022 ◽  
Vol 302 (1) ◽  
pp. E5-E5
Author(s):  
Jian He ◽  
Wenjing Yang ◽  
Weichun Wu ◽  
Shuang Li ◽  
Gang Yin ◽  
...  
Keyword(s):  
Heart Failure ◽  
Ejection Fraction ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Preserved Ejection Fraction ◽  
Longitudinal Strain Rate

scholarly journals Primary Transverse Crevasses

1969 ◽  
Vol 8 (52) ◽  
pp. 107-129 ◽  
Author(s):  
G. Holdsworth
Keyword(s):  
Strain Rate ◽  
Longitudinal Strain ◽  
Critical Strain ◽  
Strain Rates ◽  
A Value ◽  
Regional Strain ◽  
Critical Strain Rate ◽  
Rate Gradient ◽  
Lines Of Evidence ◽  
Longitudinal Strain Rate

Measurements of strain-rates on a temperate glacier in a region of initial transverse fracturing indicate a critical strain-rate of 3.5±0.5 × 10−5d−1, associated with a regional strain-rate gradient of 5 × 10−8d−1m−1. At only one section of the glacier is the theoretical longitudinal strain-rate (Nye, 1959[c]) in approximate agreement with the value measured at the surface at that point. Corresponding measurements on a polar glacier (temperature −27.9°C at 10 m depth during the summer) indicate that the critical strain-rate is about 0.6±0.05 × 10−5d−1, which is associated with a gradient of strain rate of about 3 × 10−9d−1m−1. At one section there is close agreement between the theoretical and measured longitudinal strain-rate. For the temperate glacier crevasse depths ranged from 23.5 to 28 m; in the polar glacier one crevasse was 23.9±0.5 m deep, assuming a wedge form. Only an approximate agreement with the measured values of depth is obtained by using the regional strain-rate values in Nye’s crevasse-depth formula.Over a distance of 1.2 km the temperate glacier transverse crevasse spacings are very variable, ranging from 30 m to 96 m, but initially the spacings range from 55 m to 96 m, and for the first four cases the spacingsvaries from 2.7dto 3.3d, wheredis the crevasse depth. In the cold ice, crevasse spacings are far more uniform, ranging from 57 m to 66 m. A value ofs≈ 2.5dis obtained in only one case. This greater uniformity of spacing may be explained in terms of the dynamics of flow. Despite large differences in thermal, dimensional and strain-rate parameters between the two glaciers, (1) the crevasse depths are closely similar, and (2) the spacings of crevasses are similar. It has been demonstrated from two lines of evidence that the assumption that the strain on an intercrevasse block is negligible is not correct. The direction of the principal extending strain-rate is, in the most reliable cases, perpendicular to the crevasse traces within 2° to 7°.

scholarly journals Transfer of Basal Sliding Variations to the Surface of a Linearly Viscous Glacier

1985 ◽  
Vol 31 (109) ◽  
pp. 308-318 ◽  
Author(s):  
Michael J. Balise ◽  
Charles F. Raymond
Keyword(s):  
Strain Rate ◽  
Spatial Pattern ◽  
Longitudinal Strain ◽  
Surface Strain ◽  
Surface Velocity ◽  
Velocity Anomaly ◽  
Short Scale ◽  
Velocity Anomalies ◽  
The Cross ◽  
Longitudinal Strain Rate

AbstractThe transfer of basal velocity anomalies to the surface of a glacier is investigated using a model of a planar parallel-sided slab (thicknessH) of linear viscous rheology. Surface velocity parallel (us) and normal (vs) to the surface is calculated for various spatial distributions of basal velocity anomalies with components parallel (ub) and normal (vb) to the surface. Four scales of differing behavior can be identified depending on the spatial lengthLof the basal anomalies. At very short scales (L≤ 1H) there is essentially no response at the surface. At short scales (1H≤L≤ 5H), a basal anomalyubinduces a response in bothusandvs. The spatial pattern ofusis such that velocity peaks inuscan be shifted from peaks inub, and may differ in number. The amplitude ofusis up to about 0.3|ub|. The amplitude of the cross-component effectvsmay be greater than the amplitude ofus. A basal anomalyvbinduces a response in bothvsandus. The pattern ofvsis the same as the pattern ofvb, and the amplitude ofvsis up to about 0.7 |vb|. The amplitude of the cross-component effectusis less than the amplitude ofvs. At intermediate scales (5H≤L≤ 10H), results differ from the short scale in two respects; velocity peaks inuscorrespond with peaks inub; and surface amplitudes are increased, except for cross-component effects for which surface amplitudes are of the same order as at the short scale. These cross-component effects at the short and intermediate scales show in particular that substantial anomalous surface-normal motions can be induced by deformation, even though the basal velocity anomaly is parallel to the surface. At long scales (10H≤L), the velocity anomaly at the surface is essentially the same as the anomaly at the bed. For all scales, the longitudinal strain-rate averaged over depth is larger in magnitude than the longitudinal strain-rate at the surface and, at the short scale, it may differ in sign, so thatvscannot be easily estimated from surface strain-rate. Although the simplifications of the model do not allow its rigorous quantitative application to field measurements, the results indicate the need for caution in interpreting surface-velocity variations in terms of basal velocity anomalies. It is important to establish the spatial pattern of surface motions for any chance of a confident interpretation in terms of basal motions.

Abstract 2570: Effects Of Exercise On Left Ventricular Diastolic Function Depend On Homogenous Increase In Diastolic Strain Rates

Circulation ◽  
2007 ◽  
Vol 116 (suppl_16) ◽  
Author(s):  
Teck Hwa Goh ◽  
Zoran B Popovic ◽  
Adisai Buakhamsri ◽  
Neil Greenberg ◽  
James D Thomas
Keyword(s):  
Strain Rate ◽  
Longitudinal Strain ◽  
Stress Testing ◽  
Color Doppler ◽  
Left Ventricular Diastolic Function ◽  
Left Ventricular ◽  
Strain Rates ◽  
The Difference ◽  
The Relationship ◽  
Longitudinal Strain Rate

Objectives: It has been speculated that early diastolic left ventricular (LV) suction depends on LV apex relaxing more promptly than LV base, and that these relationships are accentuated during exercise. In this study, we sought to determine impact of exercise on the relationship between parameters of LV diastolic mechanics (peak early longitudinal (E SrL), circumferential (E SrC) and radial (E SrR) strain rate, and peak LV untwisting velocity) and intraventricular pressure gradient (IVPG) as marker of diastolic suction. Methods: We studied 23 healthy volunteers (age 38 ± 10 years, 13 females) by Vivid 7 ultrasound machine (GE) during supine bicycle stress. Segmental diastolic strain rates and untwisting velocity were obtained by speckle tracking software (EchoPac, GE Medical) while IVPG was measured by applying the Euler equation to the transmitral color Doppler M mode of the LV inflow. Segmental diastolic strain rates were averaged over basal, mid, and apical levels. Results: Absolute values of E SrL, E SrC and E SrR homogenously increased during exercise (P<0.001 for all) by the same degree at all LV three levels (p=NS for the difference between levels). (see table ) Untwisting velocity during exercise increased from -1.54 ± 0.69 to -3.40 ± 1.54 rad/s while IVPG increased from 1.41 ± 0.67 to 3.90 ± 1.69 mmHg (p<0.001 for both). Out of strain parameters, average E SrL increase during exercise showed strongest correlation with IVPG (r=0.64, p<0.001) and untwisting velocity (r=0.62, p<0.001). Higher untwisting velocity was associated with the greater IVPG (r=0.70, p<0.001). Conclusions: Increase of suction during exercise is related to homogeneous augmentation of relaxation throughout left ventricle. Longitudinal strain rate was the best predictor of the increase of untwisting velocity and IVPG. These data could serve as a reference for diastolic stress testing.

Abstract 4246: Dobutamine-induced Reserve of the Two-dimensional Longitudinal Strain Rate Predicts Clinical and Neurohumoral Improvement After Levosimendan Treatment in Acutely Decompensated Chronic Heart Failure

Circulation ◽  
2008 ◽  
Vol 118 (suppl_18) ◽  
Author(s):  
Vasiliki Bistola ◽  
Ioannis Paraskevaidis ◽  
Ignatios Ikonomidis ◽  
Ioannis Parissis ◽  
Gerasimos Filippatos ◽  
...  
Keyword(s):  
Strain Rate ◽  
Speckle Tracking ◽  
Longitudinal Strain ◽  
Nyha Class ◽  
Radial Strain ◽  
Left Ventricular ◽  
Contractile Reserve ◽  
Systolic Strain ◽  
Strain And Strain Rate ◽  
Longitudinal Strain Rate

Objective: Levosimendan improves symptoms and the hemodynamic profile in patients with acutely decompensated chronic heart failure (ADCHF). We aimed to investigate: the association of low dose dobutamine (DSE)-induced changes of two-dimensional strain parameters with the corresponding changes of left ventricular ejection fraction (LVEF) and left ventricular outflow tract velocity time integral (LVOT VTI) in patients with ADCHF, and whether left ventricular contractile reserve assessed by both conventional and speckle tracking echocardiography is associated with clinical and neurohumoral improvement after levosimendan treatment. Methods: Thirty one consecutive patients with ADCHF (mean age 65 ± 10 years, NYHA class 3.6 ± 0.3, LVEF 22 ± 6%) were studied by DSE (peak dose 20 μg/kg/min) prior to 24-hour infusion of levosimendan (0.01 μg/kg/min, without bolus). The LVEF, LVOT VTI, mean longitudinal, circumferential and radial strain and strain rate using speckle tracking imaging were measured. Results: Twenty-three patients (74%) had evidence of contractile reserve (increase of LVEF > 10% and LVOT VTI > 20% after peak dobutamine dose, CR+), and 8 (26%) showed no reserve (CR−). CR+ versus CR- patients demonstrated greater improvement of NYHA class (mean NYHA change: −1.0±0.5 vs −0.5±0.3 NYHA class, p=0.01), and reduction of b-type natriuretic peptide levels (− 34±30 vs + 4±31%, p <0.01) 48 hours after completion of treatment. By multivariate analysis, mean longitudinal systolic strain rate reserve (resting - peak longitudinal strain rate ΔLSR (%)) was the best predictor of improvement of NYHA class (p= 0.039) and BNP (p= 0.042) after levosimendan administration among the reserve of: LV FS, EF, LVOT VTI, longitudinal strain, circumferential and radial strain and strain rate. Conclusion: Dobutamine-induced reserve of 2-dimentional speckle tracking longitudinal systolic strain rate is associated with clinical and neurohumoral improvement after treatment with levosimendan in patients with ADCHF.

scholarly journals A Method of Determining the Strain-Rate Tensor at the Surface of a Glacier

1959 ◽  
Vol 3 (25) ◽  
pp. 409-419 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Strain Rate ◽  
Least Squares Method ◽  
Strain Tensor ◽  
Rate Of Change ◽  
Principal Strain ◽  
Strain Rate Tensor ◽  
Strain Rates ◽  
Principal Stresses ◽  
Independent Components ◽  
Good Agreement

AbstractThe rate of strain tensor at a point on the surface of a glacier may be determined by setting up a number of stakes in a pattern and measuring the rate of change of the distances between them. A suitable pattern consists of four stakes at the corners of a square with one stake at the center. Five such patterns were used on Austerdalsbreen, Norway, in August 1956. The problem is to deduce the best values of the 3 independent components of the strain-rate tensor from the 8 measured quantities, and, for this purpose, a least-squares method, invented by Bond for the analogous problem in crystal physics, is used. The principal strain-rates are found to within about ±0.005 yr.−1and their directions relative to the stake system to within about ±0.5°. The directions and magnitudes of the principal stresses are then deduced from Glen’s flow law and a suitable general theory. The directions of the principal strain-rates are in good agreement with the directions of the crevasses, but the experiment is inconclusive on the question of the magnitude of the stress needed to form a crevasse.

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