Instantaneous Slope Research Articles

Technical Note: General rock failure criterion

A general rock failure criterion can be represented by τ = a1(a0 + σN)β, (δτ/δσN) = tanφ where τ and σN are shear and normal stress and tanφ is the instantaneous slope of the tangent to the failure envelope at point (σN,τ). Triaxial/shear test data can be simulated at any predefined conditions. Three circles measuring the strength of the tested rock at failure characterise the envelope: the uniaxial compression, uniaxial tension and biaxial compression/tension circles. The criterion is defined through three models. The non-linear reduced regression model, is used to fit a set of N data points: σN(i), tanφi and τi to obtain the three parameters of the criterion. In uniform distributions of triaxial test data, the slope angle φ of the tangent to the envelope at an unknown point (σN,τ) is approximated by (δR/δσm) ≈ (R(i+1) - R(i))/(σm(i+1) - σm(i)) = sinφi. In uniform distributions of shear test data, the slope angle φ of the tangent to the envelope at a known point (σN,τ) is approximated by (δτ/δσN) ≈ (τ(i+1) - τ(i))/(σN(i+1) - σN(i)) = tan φi. Calculated values of tanφi, σN(i), τi for N-1 data points, they are fitted into the non-linear reduced regression model to obtain the criterion parameters. The second regression model, the variable power polynomial, takes the form R = a0 + a1σmγ + a2σm2γ, (δR/δσm) = sinφ = q. The non-uniform distributions of triaxial test data σm,Rm are firstly fitted to the polynomial for modelling irregular data. The power γ is systematically searched at order n ≤ 2. Optimal γ is reached once the condition 0 ≤ q ≤ 1 starts to be satisfied. This gives rise to a set of σN(i), τi and tanφi, which is fitted into the non-linear reduced regression model to obtain the criterion parameters. Optimal fitting can be checked graphically from the degree of conformance between the two sets of scatter plots of σ1-σ2 calculated from both the polynomial model and the criterion. The third regression model is used to linearise the non-uniform distributions of shear test data, (σN,τ) by log/log transformation and translation. The model takes the form Y = ρ0 + ρ1X + ρ2X2 where X = log(σN + τ) and Y = log τ. The associated variable t is searched systematically until ρ2 tends to zero. At this optimal condition, the three parameters of the criterion are evaluated in turn a0 = t, a1 = exp(ρ0) and β = ρ1. Experimental data are fitted to the criterion without a priori information related to the tested rock.

Long–wave forcing by the breaking of random gravity waves on a beach

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

Quasar Spectral Slope Variability in the Optical Band

We performed a new analysis of B and R light curves of a sample of PG quasars. We confirm the variability-redshift correlation and its explanation in terms of spectral variability, coupled with the increase of rest-frame observing frequency for quasars at high redshift. The analysis of the instantaneous spectral slope for the whole quasar samples indicates both an inter-QSO and intra-QSO variability-luminosity correlation. Numerical simulations show that the latter correlation cannot be entirely due to the addition of the host galaxy emission to a nuclear spectrum of variable luminosity but constant shape, implying a spectral variability of the nuclear component. Changes of accretion rate are also insufficient to explain the amount of spectral variation, while hot spots possibly caused by local disk instabilities can explain the observations.

A Viscoelasticity Index for Cheese Meltability Evaluation

A device especially designed for uniaxial creep test was used in this study. Cheddar cheeses of different fat content were used. To study the linear viscoelastic response of the cheese, temperature of 40°C and stress of 1119.5Pa were chosen. Tests were carried out at cheese ages of 1, 3, 6, and 12 wk after production date. A six-element Kelvin model was used to model the creep data. Instantaneous slope of the creep curve was defined as the viscoelasticity index. The results showed that the viscoelasticity index based on viscoelastic parameters could be used for predicting cheese meltability. From the analysis of variance test, it was evident that that the viscoelasticity index can be used to distinguish the meltability of Cheddar cheeses of different ages and fat levels.

The role of electrochemical impedance spectroscopy (EIS) in the global characterisation of the reduction kinetics of hexacyanoferrate on anodised titanium

To quantify the charge transfer ( ct) step during the reduction of hexacyanoferrate, it is studied at a galvanostatically anodised polycrystalline Ti electrode, for which a ct controlled current can be observed over a large potential domain. In particular, the present study aims the characterisation of the electrode semiconducting properties (flat band potential E fb and donor density N D), in contact with the hexacyanoferrate system. Hereto, the use of EIS is essential for the determination of the space charge capacitance ( C sc) of the TiO 2 layer, as a function of the applied potential E. A methodology is proposed to determine C sc in a convenient way. In the high frequency range of the EIS measurements, only the solid state properties are being probed, and a simple series R- C sc equivalent circuit becomes suitable. The validity of this method is checked through the analysis of different equimolar redox solutions. Finally, the values of E fb and N D are determined from the obtained non-linear Mott–Schottky plots ( C −2 sc vs E). In particular, the donor density N D is computed numerically from the instantaneous slope, by solving a finite difference equivalent of the relation for different discrete N D( E) values.

Numerical modelling of fluid oscillations caused by an instantaneous slope of the reservoir base

Numerical modelling of fluid oscillations caused by an instantaneous slope of the reservoir base

Maximal ascending and descending slopes of the T wave in men and women

To investigate possible sex differences in the dynamics of T wave generation, the maximum instantaneous slope of the ascending and descending limbs of the T wave (max dV/dt and min dV/dt, respectively), were calculated. These rate of repolarization parameters, as well as more traditional repolarization duration parameters (QT, JT, Q to T wave peak [QTm] and J to T wave peak [JTm]), were measured by computer using digitized electrocardiograms (ECGs) from the V 5 lead in 562 normal subjects (443 men and 119 women; mean age 37 years), whose heart rates (HRs) were confined to one of three narrow ranges, namely 60 ± 1, 70 ± 1, or 80 ± 1 beats/min. In both men and women, for each HR range absolute values of min dV/dt exceeded those of max dV/dt ( P < .0001). However, absolute values of both max dV/dt and min dV/dt were consistently greater in men than in women for each HR range ( P < .0001 at HR 60 ± 1; P < .02 at HR 70 ± 1, or 80 ± 1). By using correlation analysis, max dV/dt and min dV/dt were shown to be independent of the repolarization duration variables (| r| < .30). Thus, whereas in both men and women the descending limb of the T wave is steeper than the ascending limb, the maximum slope of each limb of the T wave is steeper in men than in women. These findings add to a growing body of data indicating fundamental sex differences in the physiology of cardiac repolarization and propensity to torsade de pointes.

Multiple effects of serotonin on membrane properties of trigeminal motoneurons in vitro.

Intracellular recordings from guinea pig trigeminal motoneurons (TMNs) in brain stem slices were used to determine the underlying ionic mechanisms responsible for our previously demonstrated enhancement of TMN excitability during jaw movements by serotonin (5-HT). 5-HT (0.5-100 microM) depolarized motoneurons and increased input resistance in the majority of neurons tested. Additionally, 5-HT reduced the amplitude of the postspike medium-duration afterhyperpolarization, decreased the current threshold for maintained spike discharge, and increased the maximum slope of the steady-state spike frequency-current relationship. Under voltage clamp, from holding potentials close to resting potential, 5-HT produced an inward current and a decrease in instantaneous slope conductance, suggesting a reduction in a resting K+ leak conductance (I(leak)). The instantaneous current-voltage (I-V) relationship for the inward 5-HT current (I(5-HT)) was linear throughout most of the voltage range tested. However, the steady-state I-V relationship showed some degree of inward rectification at potentials starting around -70 mV. The mean reversal potential for the instantaneous I(5-HT) was -86.2 +/- 4.5 (SE) mV (n = 9), a value slightly negative to the predicted potassium equilibrium potential of -82 mV in these neurons. In the presence of 2 mM Ba2+, 5-HT application did not produce a further reduction in input conductance, but did expose a Ba2+-insensitive residual inward current that was resistant to Cs+ application. The instantaneous I-V relationship during 5-HT application in the presence of Ba2+ was shifted downward and parallel to control, suggesting that Ba2+ and 5-HT block the same resting I(leak). The residual Ba2+- and Cs+-insensitive component of the total inward I(5-HT) was voltage independent and was blocked when the extracellular Na+ was replaced by choline, suggesting that the predominant charge carrier for this residual current is Na+. 5-HT enhanced a hyperpolarization-activated cationic current, I(h). In the presence of Ba2+, the time course of I(5-HT) resembled that of I(h) and showed a similar voltage dependence that was blocked by extracellular Cs+ (1-3 mM). The effects of 5-HT on membrane potential, input resistance, and I(h) were partially mimicked by 5-HT2 agonists and suppressed by 5-HT2 antagonists. It is concluded that 5-HT enhances TMN membrane excitability through modulation of multiple intrinsic membrane conductances. This provides for a mechanism(s) to fine tune the input-output discharge properties of these neurons, thus providing them with greater flexibility in output in response to time-varying synaptic inputs during various movements of the jaw.

Unloaded shortening of skinned mammalian skeletal muscle fibres: effects of the experimental approach and passive force.

In rabbit, rat and human skinned skeletal muscle fibres the length-time relationship of isotonic releases was determined after maximal Ca2+ activation. Slack test experiments provided information about unloaded conditions. Force clamp experiments of different load were extrapolated for zero load and compared with the slack test data. The course length-time relationship for unloaded conditions was similar using both approaches. However, slack test data showed a triphasic shape which could be fitted by three straight lines (phase I, II, III), whereas the data of force clamp experiments exhibited a steady curved shape. Consequently, the instantaneous slopes differed in the two relationships, but the distance which was shortened during the time interval of phase II was similar in both approaches. The ratio between these unloaded shortening velocities resulting from force clamp and slack test experiments was 1.01 +/- 0.05 (SD) (n = 25). The effects of passive force on the velocity of fibre shortening was investigated in skinned rabbit muscle fibres using slack test experiments. A significant increase in the unloaded shortening velocity was observed when the sarcomere length of the fibres was increased to values which exhibited considerable amounts of passive force. The high reproducibility of the isotonic releases required in this study was achieved by improving some methodological details. Using these improved techniques an identity between the relative fibre and sarcomere shortening was observed during the isotonic releases.

Sensitivity and reproducibility of the instantaneous hyperemic flow versus pressure slope index compared to coronary flow reserve for the assessment of stenosis severity

The objective of this study was to compare the reproducibility and sensitivity of the instantaneous hyperemic flow versus pressure slope index (i-HFVP) and coronary flow reserve (CFR). The i-HFVP is the slope of the relationship between diastolic hyperemic coronary flow and diastolic aortic pressure, normalized for bed weight. In contrast to CFR (the ratio of hyperemic to basal coronary flow), the i-HFVP has been shown to be independent of changes in aortic pressure, heart rate, contractility, and preload. To compare reproducibility, i-HFVP and CFR were measured three times in eight dogs instrumented with high-fidelity micromanometers and flow probes, allowing for full hemodynamic recovery between phases (15 to 40 minutes). Maximum hyperemia was induced with intravenous adenosine. The sensitivity of i-HFVP and CFR was assessed in 16 instrumented dogs. Measurements were performed for one basal state and for five subcritical incremental stenoses created with a screw occluder during hyperemia. Intraclass variability correlation coefficients were 0.96 for i-HFVP but only 0.56 for CFR. Both i-HFVP and CFR showed significant decrements with each increasing stenosis. However, the percentage reductions at each level were significantly greater for the i-HFVP. The difference in percentage reduction favoring increased sensitivity of the i-HFVP ranged from 11% to 23%. It was concluded that the i-HFVP is more reproducible and more sensitive to the presence of stenoses than CFR.

Tachycardia, contractility and volume loading alter conventional indexes of coronary flow reserve, but not the instantaneous hyperemic flow versus pressure slope index

Objectives and Background. Because measurements of flow reserve are often made in the selling of fluctuating hemodynamic variables that cause alterations in basal or hyperemic coronary blood Row, traditional flow reserve indexes may be difficult to Interpret. Prior work in this laboratory has suggested that the instantaneous hyperemic flow versus pressure slope indexis a more hemodynamlcally stable alternative to measures of flow reserve. Although this index has no hemodynamic dependence on changes in aortic pressure, the extent to which it is affected by other factors that alter myocardial work is unknown. Therefore, the purpose of this investigation was to analyze the effects of tachycardia (induced by atrial pacing at 10 beats/min above the basal heart rate), dobutamine infusion (10 μg/kg per min) and saline solution volume loading (500 ml) on measurements of traditional coronary flow reserve, the resistance reserve ratio and the instantaneous hyperemic flow versus pressure slope index.Methods. Twenty-nine open chest anesthetized dogs were studied in four sequential stages: baseline, tachycardia, dobutamine infusion and saline solution volume loading. Traditional coronary flow reserve was defined as the ratio of hyperemic coronary blood flow to basal coronary Mood flow, the resistance reserve ratio as the ratio of basal coronary resistance to hyperemic coronary resistance and the instantaneous hyperemic flow versus pressure slope index as the slope of the instantaneous relation between diastolic hyperemic coronary Wood flaw and diasiolic aortic pressure normalized by perfusion bed weight. Hyperemia was induced by intravenous adenosine infusion (1 mg/kg per min). Mean aortic pressure was kept nearly constant daring the interventions by manipulation of an sortic clamp or a vena caval snare.Results. The final study group comprised 18 open chest dogs. Coronary flow reserve was significantly decreased by tachycardia (3.7 ± 1.2 to 3.0 ± 1.2, p < 0.0001), decreased by saline solution volume loading (3.2 ± 1.3 vs. 2.7 ± 0.8, p = 0.06) and significantly increased by dobatamine infusion (3.2 ± 1.3 to 4.3 ± 1.5, p < 0.0005). In contrast, the instantaneous hyperanic flow versos pressure slope index was not affected by the three inter-ventions (7.4 ± 3.1 vs. 7.3 ± 3.3, 7.4 ± 3.2 vs. 7.4 ± 3.4 and 7.5 ± 3.1 vs. 7.3 ± 3.4, respectively, all p = NS). The changes observed in the resistance reserve ratio were of similar or greater magnitude and significance to the changes in coronary flow reserve.Conclusions. The instantaneous hyperemic flow versus pressure slope index offers a hemodynamically stable alternative to measures of vascular reserve because it is indepeadent of moderate changes in heart rate, contractility and volume loading that may occur commonly in clinical situations.

Comparative responses of coronary flow reserve and the new instantaneous hyperemic flow versus pressure slope index to tachycardia, increased contractility, and volume loading

Comparative responses of coronary flow reserve and the new instantaneous hyperemic flow versus pressure slope index to tachycardia, increased contractility, and volume loading

Instantaneous hyperemic flow versus pressure slope index: Validation of a new measure of vascular reserve

Instantaneous hyperemic flow versus pressure slope index: Validation of a new measure of vascular reserve

The power function as a simple stem profile examination tool

Formulae are presented for calculating the volume, surface area, centre of gravity, centre of mass, form, taper, and instantaneous slope of the power function. A profile plotting technique is also used that allows visual comparisons between average stem profiles independent of the size and taper of individual stems. The technique is used to demonstrate that the position near 30% of the height from the base of the stem is a position of form stability for volume estimation. Using the paracone profile model (a power function midway between a paraboloid and a cone) with the diameter at the 30% position and the total stem height, individual stem volume estimates within 10% of the true volume (95% confidence) are obtained once again using a sample of 50 yearling aspen (Populustremuloides Michx.). The plotting technique is then applied to the aspen sample, and the average profiles support the hypothesis that juvenile stems may begin life as paraboloids. The average centre of gravity, the average centre of mass, the sectional form, the average form, and the taper of the stems are also examined and are shown to be quantitative indicators of the plotted profile characteristics.

Cross-Coupled Control of Biaxial Feed Drive Servomechanisms

A cross-coupled controller, designed to improve high-speed contouring accuracy independently of tracking accuracy in biaxial machine tool feed drive servomechanisms, is presented here. The controller parameters depend on the instantaneous slope of the desired contour and hence vary with time for curved contours, resulting in a time-varying controller. An approximate stability analysis of the controller is presented. The proposed controller is evaluated experimentally on a microcomputer controlled two-axis positioning table and compared to a more traditional uncoupled controller. Controller performance is evaluated for straight line, cornering and circular contours at feed rates varying from 2.25 m/min to 7.2 m/min. The experimental results show that the proposed controller reduces contouring error as compared to the uncoupled controller and leaves the tracking error practically unchanged. The cross-coupled controller is simple to implement and is practical.

A non-linear finite element model of a spinal segment

Lumbar intervertebral joints play an important role in the etiology of low-back pain. An understanding of its mechanical response is essential both from the point of its normal function as well as injury prognosis. Since purely experimental investigations cannot provide complete information, mathematical models to supplement experimental records are necessary. In this study a finite element model of a lumbar intervertebral segment is developed to analyze the stress distributions and strain energy absorbing capacities. Experiments were conducted to obtain the geometry and load-deflection data. The nonlinear sigmoidal load-deflection behavior was divided into five distinct phases based on the variation of stiffness, defined by the instantaneous slope of the load-deflection diagram. The threshold of trauma was defined at the point at which the structure exhibited softening characteristics (this corresponds with the first drop of stiffness). Load at this level was termed as the micro failure of softening load. At the point of ultimate load, the specimen had zero stiffness. The non-linear axisymmetric (geometrical and material) model incorporated the cartilagenious and cortical bone, the endplates, and the disc. The nucleus pulposus was modeled using isoparametric quadrilateral fluid elements. The model was validated with experimental axial load-deflection data. To exercise the model, homogeneous, isotropic, and loading path independent material parameters were used for all the components of the spinal segment with the exception of the annulus. The Young's modulus of annulus was estimated as a function of load level using the method of steepest descent. The disc absorbed about 84% of the total strain energy in the initial loading phase (ambient range), and at the threshold of failure, it gradually decreased to about 65%. The bony elements absorbed about 15% at the threshold. The nucleus pressure increased to about 11MPa at the threshold of trauma.

Dynorphin A decreases voltage‐dependent calcium conductance of mouse dorsal root ganglion neurones.

The actions of the opioid peptides dynorphin A and (Leu)enkephalin were assessed on calcium-dependent action potentials and inward calcium currents recorded from somata of mouse dorsal root ganglion (d.r.g.) neurones grown in primary dissociated cell culture. Dynorphin A and (Leu)enkephalin decreased the duration of somatic calcium-dependent action potentials in a portion of d.r.g. neurones impaled with potassium acetate-filled micropipettes. When substantial potassium conductance was blocked by intracellular injection of caesium acetate, d.r.g. neurones continued to respond to dynorphin A but responses to (Leu)enkephalin were abolished. In voltage-clamp experiments, dynorphin A but not (Leu)enkephalin reduced the magnitude of inward calcium currents. Dynorphin A responses were blocked by the opiate antagonist naloxone. The dynorphin A effect was due to reduction of voltage-dependent calcium conductance since dynorphin A reduced depolarization-evoked inward currents but did not alter membrane conductance following blockade of calcium channels by cadmium, and because dynorphin A reduced the instantaneous current-voltage slope (chord conductance) during step commands that produced maximal activation of voltage-dependent calcium conductance. Dynorphin A binds with high affinity to kappa-opioid receptors. (Leu)enkephalin, which has affinity for both mu- and delta-receptors but not for kappa-opioid receptors, was without effect on calcium conductance. Therefore, we suggest that kappa-receptors are coupled to voltage-dependent calcium-channels and that binding of dynorphin A produces a decrease of calcium current.

Adenosine agonists reduce voltage‐dependent calcium conductance of mouse sensory neurones in cell culture.

Adenosine and several of its analogues produced a concentration-dependent shortening of calcium-dependent action potential (c.a.p.) duration of mouse dorsal root ganglion (d.r.g.) neurones in dissociated cell culture. The following rank order of potency was obtained: N6-(L-phenylisopropyl)adenosine greater than N6-(D-phenylisopropyl)adenosine greater than N6-cyclohexyladenosine greater than 2-chloroadenosine much greater than 1-methylisoguanosine greater than adenosine. Effects of adenosine agonists on c.a.p. duration were blocked by methylxanthine adenosine antagonists. Adenosine monophosphate (AMP) and cyclic AMP shortened c.a.p.s in d.r.g. neurones, while ATP also depolarized cells. Voltage-clamp analysis revealed that the effect arose from reduction of a voltage-dependent calcium conductance. Adenosine agonists reduced depolarization-evoked inward currents but did not alter membrane conductance following blockade of calcium channels by cadmium. Additionally, adenosine reduced the instantaneous current-voltage slope (chord conductance) during step commands that produced maximal activation of voltage-dependent calcium conductance. If effects of adenosine on neuronal somata and synaptic terminals are similar, adenosine agonists may inhibit neurotransmitter release in the central nervous system by inhibiting a voltage-dependent calcium conductance. Since effects of adenosine agonists did not correspond with their relative potencies as modulators of adenylate cyclase activity or inhibitors of neurotransmitter release in peripheral tissues, a novel adenosine receptor may be involved in regulation of this conductance.

Comparing the effectiveness of fertilizers

The effectiveness of different sources of the same nutrient should be compared using plots of yield versus fertilizer applied to find how much more of the less-effective source is needed to provide the same yield. This gives the same result as measuring the relative response to the two fertilizers — provided response is defined as the instantaneous slope of the yield-fertilizer curve rather than the yield produced by a given amount of fertilizer. In most cases, and especially for immobile nutrients, the relative effectiveness, measured as suggested, will not be affected by the level of application. It is reasonable to assume this simple case until this assumption can be disproved — rather than assuming a more complicated case in the first instance.

The traveltime equation, tau‐p mapping, and inversion of common midpoint data

Seismic traveltime data can be described in terms of instantaneous slope (dT/dX) and intercept time (τ). With this parameterization, the most general form of the traveltime equation is developed and found to be valid for reflections and refractions, all source‐receiver offsets, and all commonly used experimental geometries. For common source‐receiver experiments, the instantaneous slope of the traveltime data represents the true horizontal ray parameter p, and the intercept time is the sum along the ray of thickness‐vertical slowness products referenced to the fixed surface station. For common midpoint (CMP) experiments, we show that the instantaneous slope is the average slowness of upgoing and downgoing rays at the surface, and the intercept time is again the sum of thickness‐vertical slowness products, but referenced to the common midpoint. This inherent averaging immediately explains the superiority of the CMP experiment in the presence of dip. In addition to providing a general traveltime equation, we find that τ-p parameterization reorganizes traveltime data in a way which greatly facilitates interpretation. For reflections, the τ-p trajectories are sums of ellipses and all turning rays (whether refracted or postcritically reflected) combine to form a well defined and easily identified trajectory. We present a method for deriving a velocity‐depth function from this trajectory which is applicable to both refracted and reflected arrivals.