ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF THE HELMHOLTZ EQUATION CONCENTRATED NEAR THE AXIS OF A DEEP-WATER WAVEGUIDE IN A RANGE-INDEPENDENT MEDIUM

2004 ◽  
Vol 12 (01) ◽  
pp. 67-83 ◽  
Author(s):  
NATALIE S. GRIGORIEVA ◽  
GREGORY M. FRIDMAN
Keyword(s):  
Helmholtz Equation ◽  
Deep Water ◽  
Normal Modes ◽  
Principal Term ◽  
Parabolic Cylinder ◽  
Asymptotic Behavior Of Solutions ◽  
Narrow Strip ◽  
Left Hand ◽  
Residual Difference ◽  
Separable Case

To derive the integral representation for the axial wave describing the interference of near-axial waves in an arbitrary deep-water waveguide in a range-independent medium in long-range acoustic propagation in the ocean, it is necessary to construct the solutions of the homogeneous Helmholtz equation concentrated near the waveguide axis in a narrow strip having a width of order ω-1/2, where ω is a cyclic frequency. In a range-independent (separable) case the desired solutions coincide with the principal term of the uniform asymptotic expansion as ω→∞ of normal modes when a mode number is a value of order of unity. In this paper, the solutions of the homogeneous Helmholtz equation concentrated near the waveguide axis in a range-independent ocean and which decrease exponentially outside a strip containing the axis are constructed in the form admitting generalization to the case of a range-dependent medium. The solutions are represented as the product of exponentials and parabolic cylinder functions whose arguments are infinite series in powers of ω-1/2. Coefficients of these series are found from a recurrent system of partial differential equations up to terms allowing to get a residual (difference between the left-hand side of the Helmholtz equation and zero) of order ω-1/2. Numerical results are obtained for medium parameters corresponding to the Munk canonical sound-speed profile.

SOLUTIONS OF THE HELMHOLTZ EQUATION CONCENTRATED NEAR THE AXIS OF A DEEP-WATER WAVEGUIDE IN A RANGE-DEPENDENT MEDIUM

2006 ◽  
Vol 14 (02) ◽  
pp. 237-263 ◽  
Author(s):  
NATALIE S. GRIGORIEVA ◽  
GREGORY M. FRIDMAN
Keyword(s):  
Differential Equations ◽  
Helmholtz Equation ◽  
Deep Water ◽  
Deterministic Model ◽  
Geographic Location ◽  
Parabolic Cylinder ◽  
Left Hand ◽  
Residual Difference ◽  
Recurrent System ◽  
Limiting Case

This paper examines a two-dimensional deep-water waveguide in a range-dependent medium. Solutions of the homogeneous Helmholtz equation concentrated near the waveguide axis and which decrease exponentially outside a strip containing the axis are constructed. These solutions have the form of exponentials multiplied by parabolic cylinder functions whose arguments are an infinite series in powers of ω-1/2, where ω is a cyclic frequency. Coefficients of these series are found from a recurrent system of differential equations up to terms allowing to get a residual (difference between the left-hand side of the Helmholtz equation and zero) of order ω-1/2. Arbitrary constants of general solutions of arising differential equations are calculated going over to the limiting case of a range-independent medium. Numerical simulations are carried out for a deterministic model of a range-dependent ocean, where the range-dependence results for change in geographic location. Parameters of this medium model are matched with the AET experiment.

Benthic foraminiferal zonation in deep-water carbonate platform margin environments, northern Little Bahama Bank

1988 ◽  
Vol 62 (01) ◽  
pp. 1-8 ◽  
Author(s):  
Ronald E. Martin
Keyword(s):  
Deep Water ◽  
Benthic Foraminifera ◽  
Carbonate Platform ◽  
Sedimentary Facies ◽  
Depositional Environments ◽  
Near Surface ◽  
Sediment Gravity Flows ◽  
Gravity Flows ◽  
Platform Margin ◽  
Water Carbonate

The utility of benthic foraminifera in bathymetric interpretation of clastic depositional environments is well established. In contrast, bathymetric distribution of benthic foraminifera in deep-water carbonate environments has been largely neglected. Approximately 260 species and morphotypes of benthic foraminifera were identified from 12 piston core tops and grab samples collected along two traverses 25 km apart across the northern windward margin of Little Bahama Bank at depths of 275-1,135 m. Certain species and operational taxonomic groups of benthic foraminifera correspond to major near-surface sedimentary facies of the windward margin of Little Bahama Bank and serve as reliable depth indicators. Globocassidulina subglobosa, Cibicides rugosus, and Cibicides wuellerstorfi are all reliable depth indicators, being most abundant at depths >1,000 m, and are found in lower slope periplatform aprons, which are primarily comprised of sediment gravity flows. Reef-dwelling peneroplids and soritids (suborder Miliolina) and rotaliines (suborder Rotaliina) are most abundant at depths <300 m, reflecting downslope bottom transport in proximity to bank-margin reefs. Small miliolines, rosalinids, and discorbids are abundant in periplatform ooze at depths <300 m and are winnowed from the carbonate platform. Increased variation in assemblage diversity below 900 m reflects mixing of shallow- and deep-water species by sediment gravity flows.

Identification of Asbestos Fibres in a Water Sample by X-Ray Microanalysis

1975 ◽  
Vol 33 ◽  
pp. 274-275
Author(s):  
K. A. Brookes ◽  
D. Finbow ◽  
Madeleine Samuel
Keyword(s):  
Water Sample ◽  
Background Radiation ◽  
X Ray ◽  
Left Hand ◽  
Transmission Imaging ◽  
Different Types ◽  
Normal Specimen ◽  
Liquid Nitrogen Cooling ◽  
Normal Transmission ◽  
Additional Port

Investigation of the particulate matter contained in the water sample, revealed the presence of a number of different types and certain of these were selected for analysis.An A.E.I. Corinth electron microscope was modified to accept a Kevex Si (Li) detector. To allow for existing instruments to be readily modified, this was kept to a minimum. An additional port is machined in the specimen region to accept the detector, with the liquid nitrogen cooling dewar conveniently housed in the left hand cupboard adjacent to the microscope column. Since background radiation leads to loss in the sensitivity of the instrument, great care has been taken to reduce this effect by screening and manufacturing components that are near the specimen from material of low atomic number. To change from normal transmission imaging to X-ray analysis, the special 4-position specimen rod is inserted through the normal specimen airlock.

The microtubule associated protein (MAP) tau forms a new class of triple-stranded left-hand helical fibrous protein polymer

1992 ◽  
Vol 50 (1) ◽  
pp. 540-541
Author(s):  
G. C. Ruben ◽  
K. Iqbal ◽  
I. Grundke-Iqbal ◽  
H. Wisniewski ◽  
T. L. Ciardelli ◽  
...  
Keyword(s):  
Axial Ratio ◽  
Normal Structure ◽  
Paired Helical Filaments ◽  
Left Hand ◽  
New Class ◽  
Protein Polymer ◽  
Fibrous Protein ◽  
Protein Map ◽  
Neurotransmitter Transport ◽  
Alzheimer Neurofibrillary Tangles

In neurons, the microtubule associated protein, tau, is found in the axons. Tau stabilizes the microtubules required for neurotransmitter transport to the axonal terminal. Since tau has been found in both Alzheimer neurofibrillary tangles (NFT) and in paired helical filaments (PHF), the study of tau's normal structure had to preceed TEM studies of NFT and PHF. The structure of tau was first studied by ultracentrifugation. This work suggested that it was a rod shaped molecule with an axial ratio of 20:1. More recently, paraciystals of phosphorylated and nonphosphoiylated tau have been reported. Phosphorylated tau was 90-95 nm in length and 3-6 nm in diameter where as nonphosphorylated tau was 69-75 nm in length. A shorter length of 30 nm was reported for undamaged tau indicating that it is an extremely flexible molecule. Tau was also studied in relation to microtubules, and its length was found to be 56.1±14.1 nm.

Single molecule optical diffraction: A tool for understanding the structure of triple stranded left-hand helical cellulose

1989 ◽  
Vol 47 ◽  
pp. 1024-1025
Author(s):  
George C. Ruben ◽  
William Krakow
Keyword(s):  
Single Molecule ◽  
Helical Structure ◽  
Optical Diffraction ◽  
Maximum Diameter ◽  
Primary Cell Wall ◽  
Cellulose Synthesis ◽  
Left Hand ◽  
Left Handed ◽  
Freeze Dried ◽  
Diffraction Patterns

Tobacco primary cell wall and normal bacterial Acetobacter xylinum cellulose formation produced a 36.8±3Å triple-stranded left-hand helical microfibril in freeze-dried Pt-C replicas and in negatively stained preparations for TEM. As three submicrofibril strands exit the wall of Axylinum , they twist together to form a left-hand helical microfibril. This process is driven by the left-hand helical structure of the submicrofibril and by cellulose synthesis. That is, as the submicrofibril is elongating at the wall, it is also being left-hand twisted and twisted together with two other submicrofibrils. The submicrofibril appears to have the dimensions of a nine (l-4)-ß-D-glucan parallel chain crystalline unit whose long, 23Å, and short, 19Å, diagonals form major and minor left-handed axial surface ridges every 36Å.The computer generated optical diffraction of this model and its corresponding image have been compared. The submicrofibril model was used to construct a microfibril model. This model and corresponding microfibril images have also been optically diffracted and comparedIn this paper we compare two less complex microfibril models. The first model (Fig. 1a) is constructed with cylindrical submicrofibrils. The second model (Fig. 2a) is also constructed with three submicrofibrils but with a single 23 Å diagonal, projecting from a rounded cross section and left-hand helically twisted, with a 36Å repeat, similar to the original model (45°±10° crossover angle). The submicrofibrils cross the microfibril axis at roughly a 45°±10° angle, the same crossover angle observed in microflbril TEM images. These models were constructed so that the maximum diameter of the submicrofibrils was 23Å and the overall microfibril diameters were similar to Pt-C coated image diameters of ∼50Å and not the actual diameter of 36.5Å. The methods for computing optical diffraction patterns have been published before.

Editorial Note

1946 ◽  
Vol 11 (1) ◽  
pp. 2-2
Keyword(s):  
Editorial Note ◽  
Speech Sounds ◽  
Left Hand ◽  
Hand Column ◽  
Right Hand ◽  
Infant Speech ◽  
The Right

In the article “Infant Speech Sounds and Intelligence” by Orvis C. Irwin and Han Piao Chen, in the December 1945 issue of the Journal, the paragraph which begins at the bottom of the left hand column on page 295 should have been placed immediately below the first paragraph at the top of the right hand column on page 296. To the authors we express our sincere apologies.

The Influences of Goal and Laterality of a Prepared Hand Response on a Co-Occurring Visual Search

2015 ◽  
Vol 74 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Alexandre Coutté ◽  
Gérard Olivier ◽  
Sylvane Faure
Keyword(s):  
Visual Search ◽  
Visual Target ◽  
Motor Planning ◽  
Search Performance ◽  
Response Preparation ◽  
Manual Response ◽  
Response Hand ◽  
Computer Screen ◽  
Left Hand ◽  
Manual Interaction

Computer use generally requires manual interaction with human-computer interfaces. In this experiment, we studied the influence of manual response preparation on co-occurring shifts of attention to information on a computer screen. The participants were to carry out a visual search task on a computer screen while simultaneously preparing to reach for either a proximal or distal switch on a horizontal device, with either their right or left hand. The response properties were not predictive of the target’s spatial position. The results mainly showed that the preparation of a manual response influenced visual search: (1) The visual target whose location was congruent with the goal of the prepared response was found faster; (2) the visual target whose location was congruent with the laterality of the response hand was found faster; (3) these effects have a cumulative influence on visual search performance; (4) the magnitude of the influence of the response goal on visual search is marginally negatively correlated with the rapidity of response execution. These results are discussed in the general framework of structural coupling between perception and motor planning.

Shall I Move My Right or My Left Hand?

2003 ◽  
Vol 17 (2) ◽  
pp. 69-86 ◽  
Author(s):  
Claudio Babiloni ◽  
Fabio Babiloni ◽  
Filippo Carducci ◽  
Febo Cincotti ◽  
Claudio Del Percio ◽  
...  
Keyword(s):  
Bimanual Coordination ◽  
Central Area ◽  
Eeg Analysis ◽  
Complementary Information ◽  
Left Hand ◽  
Mirror Movements ◽  
Related Potentials ◽  
Motor Acts ◽  
Abstract Event

Abstract Event-related desynchronization/synchronization (ERD/ERS) at alpha (10Hz), beta (20Hz), and gamma (40Hz) bands and movement-related potentials (MRPs) were investigated in right-handed subjects who were “free” to decide the side of unilateral finger movements (“fixed” side as a control). As a novelty, this “multi-modal” EEG analysis was combined with the evaluation of involuntary mirror movements, taken as an index of “bimanual competition.” A main issue was whether the decision regarding the hand to be moved (“free” movements) could modulate ERD/ERS or MRPs overlying sensorimotor cortical areas typically involved in bimanual tasks. Compared to “fixed” movements, “free” movements induced the following effects: (1) more involuntary mirror movements discarded from EEG analysis; (2) stronger vertex MRPs (right motor acts); (3) a positive correlation between these potentials and the number of involuntary mirror movements; (4) gamma ERS over central areas; and (5) preponderance of postmovement beta ERS over left central area (dominant hemisphere). These results suggest that ERD/ERS and MRPs provide complementary information on the cortical processes belonging to a lateralized motor act. In this context, the results on vertex MRPs would indicate a key role of supplementary/cingulate motor areas not only for bimanual coordination but also for the control of “bimanual competition” and involuntary mirror movements.

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