Larger Annulus Research Articles

The time course of contrast masking reveals two distinct mechanisms of human surround suppression

We explored the time course of surround suppression and found clear evidence for two distinct mechanisms: one strong, transient, and largely monocular, the other weaker, sustained, and binocular. We measured detection thresholds for a Gabor target at 8 deg eccentricity surrounded by a large annulus of matching spatial frequency and orientation. At short stimulus durations surround suppression was very strong, but the suppression strength decreased precipitously for durations longer than approximately 100 msec. The strong transient component did not transfer between the eyes and occurred almost instantaneously (<1 frame delay, 12 msec) irrespective of the separation between target and surround. Both suppression components were tightly tuned to orientation, peaking at target orientation, but neither was tuned to target spatial phase. These results are in good agreement with surround suppression properties measured in macaque V1 neurons. The absence of interocular transfer, the strong orientation selectivity, and the high propagation speed incommensurate with slow horizontal connections in V1 suggest that the transient component of suppression originates between input layers and the subsequent layers in V1.

Multidiameter Tools Deliver Lower Cost Per Foot

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 112785, "Multi-Diameter String Tools Deliver Lower Cost- Per-Foot in Demanding Rotary-Steerable Applications," by Steve Barton, SPE, Wayne Jones, SPE, and Rick Young, ReedHycalog, and Helge Rorvik, SPE, Halliburton, originally prepared for the 2008 IADC/SPE Drilling Conference, Orlando, Florida, 4-6 March. The paper has not been peer reviewed. Use of hole-opening tools in conjunction with rotary-steerable systems (RSSs) has increased dramatically in the past few years. Although excellent performance has been delivered with the mainstream commercial tools, alternative options have been developed to enable an RSS to drill the pilot hole in conjunction with a string tool to open the hole in a single run. The most popular current option involves a weight- or hydraulic-actuated under-reamer. However, fixed-blade, multidiameter reaming tools have been developed recently for use within rotary-steerable (RS) assemblies. Introduction Hole-opening tools fall into two main categories: eccentric and concentric. Eccentric reamers are fixed reamers that are dominated by bicenter drill bits or "wing-like" string reamer tools using polycrystalline-diamond-compact (PDC) cutters. They are developed for applications where hole enlargement is required but where the tool has to pass through a smaller-diameter restriction than that of the final hole size. The concentric tools are more diverse and range from fixed designs such as concentric drill bits and string tools (that could be either PDC or roller-cone cutting structures) to more-complex tools that open on demand by either mechanical or hydraulic control. The growth in the use of hole-opening devices over the last few years was driven predominantly by the growth of deepwater drilling. The lessons learned from innovations in the deep water have extended those applications to shallower waters and even to selected land wells. Hole-opening-while-drilling devices have enabled operators to set larger strings of casing deeper in holes where hole stability, lost circulation, and high-pressure zones are a constant problem. This has the advantage of eliminating trips while leaving sections of open hole exposed over shorter durations, as well as providing a larger annulus for better cement jobs. The ability to reach extremely deep reservoirs with 12 1/4-, 10 5/8-, and 8 1/2-in. wellbores enables operators to run larger and more complex production strings, and this in turn has had an enormous effect on exploration-and-production economics.

Influence of Nonuniform Distribution of Acoustic Wavefield Strength on Time‐Distance Helioseismology Measurements

By analyzing numerically simulated solar oscillation data we study the influence of nonuniform distribution of acoustic wave amplitude, acoustic source strength, and perturbations of the sound speed on the shifts of acoustic travel times measured by the time-distance helioseismology method. It is found that for short distances, the contribution to the mean travel-time shift caused by nonuniform distribution of acoustic sources in sunspots may be comparable to (but smaller than) the contribution from the sound-speed perturbation in sunspots, and that it has the opposite sign to the sound-speed effect. This effect may cause some underestimation of the negative sound-speed perturbations in sunspots just below the surface, which was found in previous time-distance helioseismology inferences. This effect cannot be corrected by artificially increasing the amplitude of oscillations in sunspots. For large time-distance annuli, the nonuniform distribution of wavefields does not have significant effects on the mean travel times, and thus the sound-speed inversion results. The measured travel-time differences, which are used to determine the mass flows beneath sunspots, can also be systematically shifted by this effect, but only by an insignificant magnitude.

Coiled Tubing "Vacuum" Restores North Slope Wells

Technology Update The North Slope of Alaska is home to thousands of oil wells, most drilled horizontally and then stimulated with hydraulic fracturing or allowed to flow through natural formation fractures. Wellbore plugging caused by proppant flowback and formation fines can be a problem in these wells, with severe impact on production. For most of these wells, conventional coiled-tubing (CT) cleanouts are possible, using nitrogen to lift the cleaning fluid and suspended proppant to surface. Some of these wells, however, are so underpressured that normal CT cleanouts are technically and/or economically unfeasible because of the massive amounts of nitrogen required to achieve returns to the surface. A Vacuum Cleanout Method One alternative is to clean out the fill by means of concentric coiled tubing (CCT) with a downhole-vacuum tool. The BJ Services Sand-Vac cleanout tool is based on a jet pump comprising a high-pressure nozzle, suction port, and diffuser (Fig. 1). High-pressure fluid is accelerated through the nozzle, creating a pressure drop that essentially draws in wellbore fluids, jetted fluids, and suspended solids. A diffuser allows the velocity of the combined flow to decrease and the pressure to increase. This pressure gain is sufficient to drive the column of return fluids back to the surface. To run the jet pump, power fluid is pumped down the center of a CCT string, with a portion of the fluid allowed to exit an external nozzle to fluidize wellbore solids. Returns come up the larger annulus between the inner and outer strings. Because the CCT string provides the additional flow path, the wellbore is not exposed to the return pressure and, therefore, nitrogen is not required. All of the supplied fluid is returned to the surface, leaving none in the well. This technology was born in the Canadian heavy-oil fields, and it has been proved in a decade of cleanouts around the world—especially in low-pressure, horizontal wells and in areas where nitrogen logistics are difficult or simply too expensive to justify. Alaska Gas Wells In 2006, for example, this technology was employed on the Tyonek platform in the Cook Inlet basin in southern Alaska (Rafferty et al. 2007). This platform ties together 14 wells that produce from the Cook Inlet and Beluga reservoirs, which have bottomhole-pressure (BHP) gradients of less than 0.1 psi/ft. Both reservoirs are composed of highly permeable, friable sandstones that tend to slump into unconsolidated sand piles upon exposure to water. Water breakthrough, therefore, creates major sand-production problems for wells in this area.

Replacement of the systemic atrioventricular valve with a mechanical prosthesis in children aged less than 6 years: Late clinical results of survival and subsequent replacement

We analyzed the survival, clinical course, and role of prosthesis-patient mismatch after systemic atrioventricular valve replacement in children. From 1974 to 2006, 69 patients underwent systemic atrioventricular valve replacement (median age 1.2 years, range 1.1 months to 5.4 years), with 17 patients requiring re-replacement of the systemic atrioventricular valve. Prosthesis-patient relationship was analyzed by comparing (1) the prosthetic valve diameter and the predicted annulus diameter based on the body surface area and (2) the prosthetic valve diameter and the measured annulus diameter. Survival was 73% at 1 year and 65% at 5, 10, and 15 years. Age, weight, body surface area, predicted annulus diameter, prior surgery, underlying disease, and ratio of prosthetic valve diameter to body weight were significant predictors of death. Variables associated with re-replacement of the systemic atrioventricular valve were body surface area, prosthetic valve diameter, predicted annulus diameter, and presence of multiple left-sided obstructive lesions. The majority of patients received a prosthesis larger than the predicted annulus diameter. There was good correlation between the prosthetic valve diameter and the measured annulus diameter (r = 0.85). Mismatch, as described by the difference in z scores of prosthetic valve diameter and measured annulus diameter, was not a significant predictor of death or re-replacement of the systemic atrioventricular valve. Although valve replacement is considered the last therapeutic option after failed attempts of valvuloplasty, long-term outcome is favorable. Selection of the prosthesis is made on the basis of the measured annulus diameter. An elevated ratio of prosthetic valve diameter to body weight is associated with patients with low body weight or a large native annulus in dilated ventricles.

Double-stranded DNA translocation: structure and function of hexameric FtsK

FtsK is aDNA translocase that coordinates chromosome segregation and cell division in bacteria. In addition to its role as activator of XerCD site-specific recombination, FtsK can translocate double-stranded DNA rapidly and directionally, and reverse direction. We present crystal structures of the FtsK motor domain monomer, showing it has a RecA-like core, and the Ftsk hexamer, showing it is a ringwith a large central annulus. Electron microscopy demonstrates the DNA-dependent existence of hexamers in solution and shows that duplex DNA passes through the middle of each ring. Comparison of FtsK monomer structures from two different crystal forms highlights a conformational change that we propose is the structural basis for a rotary inchworm mechanism of DNA translocation. We also show that two hexamers of FtsK can form a head-to-head double-ring, which suggests a model for bidirectional DNA translocation by this protein. m06.o03

Double-Stranded DNA Translocation: Structure and Mechanism of Hexameric FtsK

FtsK is a DNA translocase that coordinates chromosome segregation and cell division in bacteria. In addition to its role as activator of XerCD site-specific recombination, FtsK can translocate double-stranded DNA (dsDNA) rapidly and directionally and reverse direction. We present crystal structures of the FtsK motor domain monomer, showing that it has a RecA-like core, the FtsK hexamer, and also showing that it is a ring with a large central annulus and a dodecamer consisting of two hexamers, head to head. Electron microscopy (EM) demonstrates the DNA-dependent existence of hexamers in solution and shows that duplex DNA passes through the middle of each ring. Comparison of FtsK monomer structures from two different crystal forms highlights a conformational change that we propose is the structural basis for a rotary inchworm mechanism of DNA translocation.

Double balloon pulmonary valvuloplasty: Multi‐track system versus conventional technique

To evaluate whether double balloon pulmonary valvuloplasty (DBPV) with the Multi-Track system (MTS) may help to simplify the procedure. DBPV is usually required for patients with pulmonary valve stenosis with large annulus. However, it needs two venous accesses and can be technically demanding. From 07/03, 20 consecutive patients (19 +/- 10 yrs) with typical pulmonary valve stenosis underwent DBPV using the MTS (G1). The results were compared with those achieved by conventional DBPV performed in a matched historical group of 28 patients (21 +/- 11 yrs; P = NS) (G2). MTS balloons were easily advanced through the skin and inflated across the valve. Similar results were observed in regards to residual gradients (12 +/- 11 vs 14 +/- 10 mm Hg; P = NS) and right ventricular to systemic pressures (0.35 +/- 0.22 vs 0.37 +/- 0.26; P = NS). Procedure and fluoroscopic times were significant lower in G1 (78 +/- 24 vs 126 +/- 28; 15 +/- 12 vs 25 +/- 8 min, respectively; both P < 0.001). There was no major complication. Median follow-up was 1.8 yr for G1 and 5 yr for G2 (P = 0.037). At the last visit, peak instantaneous gradient across the right ventricular outflow tract by echocardiography was a mean 22 +/- 10 mm Hg for G1 and 25 +/- 9 mm Hg for G2 (P = NS). No patient had severe pulmonary insufficiency or required reintervention. The use of the MTS helped to expedite the procedure providing satisfactory midterm clinical outcomes, similar to those observed with the conventional DBPV technique.

Triple‐balloon pulmonary valvuloplasty: An advantageous technique for percutaneous repair of pulmonary valve stenosis in the large pediatric and adult patients

This report describes a new valvuloplasty procedure for the treatment of pulmonary valve stenosis (PVS) and large pulmonary valve annulus (PVA) diameters using a triple-balloon valvuloplasty (TBV) technique. We sought to demonstrate the safety and efficacy of this new technique. Percutaneous balloon pulmonary valvuloplasty (BPV) is the preferred treatment for PVS. BPV in older patients with large PVA remains a challenge, even when the double-balloon valvuloplasty technique is performed. The technique was first attempted in a case where a large single balloon was unsuccessful and double-balloon valvuloplasty met with technical difficulties. Three subsequent patients underwent the procedure safely and successfully. An algorithm is presented to determine balloon size for TBV. The median PVA diameter was 23.9 mm. Balloon diameters ranged from 12 to 18 mm. The median peak right ventricular-to-pulmonary artery systolic pressure gradient was 43.5 mm Hg before valvuloplasty and was reduced to 12 mm Hg following intervention. No major complications were encountered. Percutaneous valvuloplasty using TBV can be performed safely and provides excellent clinical results. This technique offers advantages over single-balloon and double-balloon valvuloplasty techniques, especially in treatment of PVS in large pediatric or adult patients.

Weakly dissipative Faraday waves in 2D large aspect ratio annuli

Weakly dissipative parametrically excited (by vertical vibration) surface gravity-capillary waves in a two-dimensional, horizontally periodic container are considered. A set of equations is derived for the coupled evolution of the left- and right-traveling surface waves and the associated mean flow, in the case when the container depth is small compared to its length but large compared to the wavelength of the excited waves. The stability of the spatially uniform standing waves (SWs) is first analyzed and then the large time spatio-temporal behavior of the system beyond threshold is numerically studied. The viscous mean flow is found to drastically affect the dynamics of the system and the resulting surface wave patterns.

A numerical and experimental investigation of stability of natural convective flows within a horizontal annulus

A numerical and experimental study of buoyancy-driven flow in the annulus between two horizontal coaxial cylinders at Rayleigh numbers approaching and exceeding the critical values is presented. The stability of the flow is investigated using linear theory and the energy method. Theoretical predictions of the critical Rayleigh number for onset of secondary flows are obtained for a wide range of radius ratio R and are verified by comparison with results of previous experimental studies. A subcritical Rayleigh number which provides a necessary condition for global flow stability is also determined. The three-dimensional transient equations of fluid flow and heat transfer are solved to study the manifestation of instabilities within annuli having impermeable endwalls, which are encountered in various applications. For the first time, a thorough examination of the development of spiral vortex secondary flow within a moderate gap annulus and its interaction with the primary flow is performed for air. Simulations are conducted to investigate factors influencing the size and number of post-transitional vortex cells. The evolution of stable three-dimensional flow and temperature fields with increasing Rayleigh number in a large gap annulus is also studied. The distinct flow structures which coexist in the large gap annulus at high Rayleigh numbers preceding transition to oscillatory flow, including transverse vortices at the end walls which have not been previously identified, are established numerically and experimentally. The solutions for the large-gap annulus are compared to those for the moderate-gap case to clarify fundamental differences in behaviour. Heat transfer results in the form of local Nusselt number distributions are presented for both the moderate- and large-gap cases. Results from a series of experiments performed with air to obtain data for validation of the numerical scheme and further information on the flow stability are presented. Additionally, the change from a crescent-shaped flow pattern to a unicellular pattern with centre of rotation at the top of the annulus is investigated numerically and experimentally for a Prandtl number of 100. Excellent agreement between the numerical and experimental results is shown for both Prandtl numbers studied. The present work provides, for the first time, quantitative three-dimensional descriptions of spiral convection within a moderate-gap annulus containing air, flow structures preceding oscillation in a large-gap annulus for air, and unicellular flow development in a large-gap annulus for large Prandtl number fluids.

Large smoke rings with concentrated vorticity

In this paper we study an incompressible inviscid fluid when the initial vorticity is sharply concentrated in N disjoint regions. This problem has been well studied when a planar symmetry is present, i.e., the fluid moves in R2. In this case we know that, when the diameter σ of each region supporting the vorticity is very small, the time evolution of the fluid is quite well described by a dynamical system with finite degrees of freedom called the “point vortex model.” In particular the connection between this model and the Euler equation has been proved rigorously as σ→0. In the present paper we discuss the “stability” of the point vortex model with respect to a particular small perturbation of the planar symmetry. More precisely we consider a fluid moving in R3 with a cylindrical symmetry without swirl in which each vortex is no longer a straight tube, but a vorticity ring. We prove that large annuli of radii r≈σ−β for any β&amp;gt;0 remain “localized” and hence we obtain the point vortex model as σ→0.

Rise velocity of a Taylor bubble through concentric annulus

In the present work, an attempt has been made to predict the rise velocity of Taylor bubbles through concentric annuli. In order to obtain an expression of rise velocity, a potential flow field has been assumed at the nose of the bubble, whereas the effect of liquid viscosity has been considered in the falling films. The model has further been modified for very small and large annuli. The rise velocity data obtained experimentally in the present work show a close agreement with the theoretical predictions. The model predictions also agree closely with the experimental values of rise velocity reported in literature. Both experiments as well as theory indicate velocity to be a unique function of annulus dimension. The function has been obtained as a Froude number type of expression, viz., U=0.323 g(D 1+D 2) .

The multifractal structure of super-Brownian motion

We calculate the multifractal spectrum and mass exponents for super-Brownian motion in three or more dimensions. The former is trivial for points of unusually high density but not for points in the support of unusually low density. This difference is due to the presence of sets of points in the support (of positive dimension) about which there are asymptotically large empty annuli. This behaviour is quite different from that of ordinary Brownian motion and invalidates the multifractal formalism in the physics literature. The mass exponents for packing and Hausdorff measure are distinct, and both are piecewise linear.

Receptive-field properties of displaced starburst amacrine cells change following axotomy-induced degeneration of ganglion cells.

Starburst amacrine cells in the rabbit retina were labeled following an intraocular injection of the fluorescent dye, 4,6,diamidino-2-phenylindole (DAPI). From each eye a strip of retina was removed, mounted on a platform beneath an epifluorescence microscope, and superfused with a physiological solution. The tip of a tungsten microelectrode (for extracellular recording) was visually positioned near the cell body of a DAPI-labeled starburst amacrine cell that was located in the ganglion cell layer. Light-evoked responses from the displaced starburst amacrine cells were studied in normal retinas and in retinas that had received a small electrolytic lesion near the optic disk 5-9 months beforehand. In normal retinas, a small spot of light centered over the receptive field of a displaced starburst amacrine cell in nearly all cases evoked a brief burst of spikes only at light onset. When stimulated with a large spot or an annulus of light, many cells gave a small burst of spikes at light offset. In lesioned retinas, the light responses of displaced starburst amacrine cells were recorded in areas of the retina where ganglion cells had degenerated. All cells responded with a large burst of spikes at the onset and offset of a small, centered spot of light. Large spots and annuli of light also evoked robust ON/OFF responses from these cells. The results from this study show that the receptive-field properties of displaced starburst amacrine cells change following axotomy-induced degeneration of ganglion cells. This finding indicates that changes in either synaptic transmission or the membrane properties of neurons occur in the retina following degeneration of ganglion cells.

Experimental determination of gas migration velocities with non-newtonian fluids

The two-phase flow characteristics of gas in non-Newtonian fluids are important in many applications in various industries. Typical examples include the food processing industry, where it is sometimes desirable to aerate melted chocolate; also the chemical industry, where it is desirable to de-aerate non-drip paint. In the field of oil exploration the drilling mud is non-Newtonian. It is used for cooling the drilling bit, removing the drilled cuttings and maintaining the bottom hole pressure. Typical drilling muds have a yield stress to prevent sedimentation of drilled cuttings; they are also shear thinning to reduce pumping power and circulating pressures. An influx of gas into the wellbore is known as a gas kick and can lead to a blowout. One of the critical parameters in the evolution of a kick is the rate at which the gas influx rises up the well through the non-Netwonian drilling mud. The main parameters governing the gas velocity are the wellbore geometry (typically large annulus), the well inclination (vertical to horizontal), the volumetric flow rates, the volumetric gas fraction (0–100%) and the fluid rheology (yield stress and shear thinning). An experimental programme was set up at Schlumberger Cambridge Research to examine two-phase flows in large pipe and annular geometries using non-Newtonian liquids. The experiments were carried out in a 15 m inclinable flow loop, where air injection was used for the gas phase and aqueous xanthum gum solutions as well as water were used for the liquid. Using an instrumented test section it was possible to measure mean and spatially resolved void fractions together with gas and liquid velocities over a range of two-phase flow conditions. The results for vertical conditions showed that the air-water flows could be characterized as bubbly flows up to a void fraction of 15%, slug flow over 30% and transitional between. For the viscous muds the transition to slug flow occurred below a void fraction of 7.5%. This meant that for most flow conditions the gas would rise through the more viscous mud faster than it would in water. A description of the flow characteristics is developed in terms of the Zuber—Findlay relationship for both pipe and annular flow geometries.

Transplante de valva mitral heteróloga: Nova alternativa cirúrgica: estudo clínico inicial

Mitral valve replacement has been performed for the last 30 years using an aortic designed valve, to fulfil specific requirements of the left ventricle. The clinical results obtained by such devices have been generally favorable, although specific restrictions are obvious because of their design. The knowledge and experience acquired by Biocor Laboratories in the last two decades, in production of biological heart valve substitutes, contributed positively to the research, development and manufacture of the heterologous mitral valve substitute. This stentless heterologous mitral valve was implanted in 38 patients, without hospital mortality. Their mean age was 29 years. Female gender predominated (69%). The most common mitral dysfunction was the double mitral valve lesion (53%). Eighteen (47%) patients were in functional class III and 20 (53%) in class IV of the NYHA. There was one valve related complication (our first patient), due to disproportion of patients, large annulus and the incorrectly size chosen. This complication led us to the strict adherence of our protocol, which is based upon animal experimentation. The satisfactory operatory and clinical results, throughout this 12 months of follow-up, confirm that the stentless heterologous mitral valve is the natural mitral substitute, when considering mitral valve replacement. This first natural mitral valve substitute, tanned with a non-aldehyde tissue treatment, proved to avoid calcification and to produce no foreign reaction, hence it may be the best choice in order to obtain better quality of life and the desired valve durability. Using both, the natural design mitral valve and the non-aldehyde treatment, the last 6 patients of this series received this devicxe and is certainly hoped that, due to the more natural model and the non-calcificant and inhert tissue, patients own cells will be responsible to greatly delay tissue degeneration, providing longterm durability.

La périodicité de la croissance chez la femelle de l'esturgeon jaune (Acipenser fulvescens) du fleuve Saint-Laurent est-elle reliée à la périodicité de la reproduction?

Measurements of annual increments on cross-sections of the first ray of the pectoral fin of 125 St. Lawrence River female lake sturgeon (Acipenser fulvescens) aged 24 yr and older were used to test the correspondance between growth patterns at the margin of the sections and the state of maturity of the fish. For each of the 21 females aged 34 yr and older, and for the upper Ottawa River specimens presented by Roussow (1957. J. Fish. Res. Board Can. 14: 553–572), annual increments were treated as a temporal series and analysed with the contingency periodogram. The mean age at first spawning was determined using the age at the end of the first belt of crowded annuli, following Roussow. Only 3 of the 21 females aged 34 yr and older showed a typical succession of belts of large and narrow annuli. The most frequent periods were 5–11 yr, using the periodogram, as compared with 6–9 yr for Roussow' specimens. No significant correspondance was found between the pattern of the last five annual increments and the state of maturity. The mean age at first spawning, estimated at 19 yr by this technique, is lower than the mean age of sexual maturity determined for St. Lawrence River females based on the examination of the gonads (26 yr).

Brachydontium notorogenes sp. nov. (Seligeriaceae) from Southeastern Brazil

Brachydontium notorogenes is described from Parque Nacional do Itatiaia in south- eastern Brazil. It is distinguished from all other species in the genus by the combination of long- subulate leaves and eperistomate capsules. Brachydontium is a genus of small acrocarpous mosses with mitrate calyptrae, large annuli, and mostly plicate capsules. It differs from the confamil- ial Seligeria by just these characters, and usually by truncate peristome teeth. Plants of both genera have small smooth leaf cells, mostly flexuose setae with erect capsules, and haplolepideous peristomes. The previously described species of Brachydontium are the circum-North Temperate B. trichodes (Weber) Milde, B. flexisetum (Hampe) Paris from Andean Colombia (and more recently reported from Rwan- da, De Sloover 1973), B. intermedium Stone from southeastern Australia, B. curvisetum Crum from Mexico, B. olsonii Bowers & Allen from Honduras, and B. olympicum (Britton) McIntosh & Spence from the North American Pacific Northwest (Oregon to Alaska) and Japan. All but the last of these species are peristomate. Therefore, when another eperis- tomate species of Brachydontium was recently dis- covered in southeastern Brazil, it was relatively sim- ple to establish that it was undescribed.

A MODEL FOR VARIABILITY OF AGN

ABSTRACT The theory of AGN accretion disks is reviewed to determine a methodology for constructing time-dependent models of the disks which can be compared to observed continuum variations. Angular-momentum transport is identified as a problematic constituent of existing models, and internal waves are proposed as the mechanisms which can drive a dynamo and thereby transport angular momentum in thin, nongravitating Keplerian disks. The model developed predicts that the disks will show limited instabilities over large annuli with frequencies similar to the dynamo-growth rate and the wave-propagation rate.