The Movement of the Spermatozoa of the Bull

1958 ◽  
Vol 35 (1) ◽  
pp. 96-108 ◽  
Author(s):  
J. GRAY
Keyword(s):  
Phase Difference ◽  
Transverse Velocity ◽  
Longitudinal Axis ◽  
Average Frequency ◽  
Whole Cell ◽  
Bending Waves ◽  
Transverse Movement ◽  
Speed Of Propagation ◽  
The Waves ◽  
Bending Wave

1. The maximum extent to which an element of the tail of a bull's spermatozoon bends during its contractile cycle is not the same for all elements; the nearer the element lies towards the tip of the tail the greater is the amount of bending. 2. The phase difference between successive elements varies along the length of the tail; and consequently the speed of propagation of the bending wave decreases as the latter moves backwards. 3. The amplitude of transverse movement relative to the head increases progressively along the tail towards the distal end. 4. Distal elements execute figure-of-eight movements relative to the head. 5. The frequency of the bending cycles and the propulsive velocity of the whole cell vary considerably. The average frequency for thirty-one cells was 9.1/sec., and the average propulsive speed for 235 cells was 94 µsec. 6. Cells moving freely in water ‘flashed’ with a frequency similar to that of the bending waves. The rotation of the head about its longitudinal axis appears to be due to the fact that all elements of the tail are not executing their transverse movements in exactly the same plane during the whole of their contractile cycles. 7. The rate at which an element can propel itself forward cannot be greater than about one-third to one-quarter of its average transverse velocity. 8. The distal elements of the tail exert their propulsive effort against the fulcrum provided by the proximal elements. 9. It is impracticable to relate the speed of propulsion to the form and speed of propagation of the waves passing along the tail.

Studies in Animal Locomotion

1933 ◽  
Vol 10 (1) ◽  
pp. 88-104 ◽  
Author(s):  
J. GRAY
Keyword(s):  
Muscular Contraction ◽  
The Body ◽  
Transverse Motion ◽  
Forward Movement ◽  
Extreme Position ◽  
Nervous Impulse ◽  
Direction Of Movement ◽  
Transverse Movement ◽  
Speed Of Propagation ◽  
The Waves

I. The waves of muscular contraction which pass along the body of a swimming eel occur also in other fish. The waves vary greatly in speed of propagation, amplitude and frequency. The speed of propagation of the waves is too low to be controlled by the rate of conduction of a simple nervous impulse. 2. The movements executed by a localised area on the surface of the body are such that each area moves in a direction transvene to the line of forward movement. During these movements the leading surface of the body is inclined backwards towards the tail and at an angle to the path of motion of the area concerned. The angle of inclination and the angle made with the path of motion vary with (a) different regions of the body, and (b) with different phases in the motion of each region. 3. Each point on the body travels in a horizontal figure of 8 relative to a transvene axis which is moving forward at the same average velocity as the whole fish. A segment of the body at the mid-point of its transverse motion is travelling forwards at a rate slightly less than that of a segment at the extreme position of its transverse movements. These movements are the mechanical result of the inextensibility of the body, and they effect significant changes in the angle between the surface of the body and its direction of movement. 4. The movements of each part of the body are shown to be such as to generate a forward thrust which drives the fish forwards against the resistance of the water. The magnitude of the forward thrust depends among other things on (a) the angle which the surface of the fish makes with its own path of motion, and (b) on the angle between the surface of the fish and the axis of forward movement of the whole fish, (c) on the velocity of transverse movement of the body. 5. The propulsive properties of each segment of the body are greatest as the segment is crossing the axis of forward movement.

Incorporating Compressional and Shear Wave Types Into Fuzzy Structure Models for Plates

1995 ◽  
Author(s):  
Judith L. Rochat ◽  
Victor W. Sparrow
Keyword(s):  
Thin Plate ◽  
Shear Waves ◽  
Wave Theory ◽  
Structure Theory ◽  
Detailed Knowledge ◽  
Bending Waves ◽  
Incident Plane ◽  
Dependent Mass ◽  
Mass Spring ◽  
Bending Wave

Abstract Although realistic complex structures are usually difficult to model theoretically, fuzzy structure theory enables one to produce such a model without a detailed knowledge of the entire structure. Using the theory established by Pierce et al. [A. D. Pierce, V. W. Sparrow, and D. A. Russell, J. Vib. Acoust. (to be published), also ASME 93-WA/NCA-17.] regarding fundamental structural-acoustic idealizations for structures with imprecisely known or fuzzy internals, the effects that fuzzy attachments have on different wave types in a primary (or master) structure are examined in this paper. In the theory by Pierce et al., the primary structure that undergoes vibrations is a thin plate mounted in an infinite baffle. On one side of the plate are fuzzy attachments, represented as an array of attached mass-spring-dashpot systems, which are excited by an incident plane pulse. This known theory explains the effects of these attachments on bending waves in the plate. In this paper, the theory is extended to isolated compressional and shear waves in a plate. While studying this new problem, it is discovered that coupling effects occur when the plate and attachment properties are not uniform in the direction perpendicular to the wave propagation. Hence, unlike the bending wave theory which models a finite thin plate with point attached oscillators, the new wave type theory uses a thin plate infinite in one direction with line attached oscillators also infinite in the same direction. For both the compressional and shear waves, it is found that the fuzzy attachments add an apparent frequency dependent mass and damping to the plate. These results are similar to those for the bending wave theory.

A note on the helical movement of micro-organisms

1971 ◽  
Vol 178 (1052) ◽  
pp. 327-346 ◽  
Keyword(s):  
Angular Velocity ◽  
Practical Interest ◽  
Longitudinal Axis ◽  
Physical Parameters ◽  
Cross Sectional ◽  
Helical Wave ◽  
Bending Waves ◽  
Spherical Head ◽  
Circular Frequency ◽  
Micro Organisms

This note seeks to evaluate the self-propulsion of a micro-organism, in a viscous fluid, by sending a helical wave down its flagellated tail. An explanation is provided to resolve the paradoxical phenomenon that a micro-organism can roll about its longitudinal axis without passing bending waves along its tail (Rothschild 1961, 1962; Bishop 1958; Gray 1962). The effort made by the organism in so doing is not torsion, but bending simultaneously in two mutually perpendicular planes. The mechanical model of the micro-organism adopted for the present study consists of a spherical head of radius a and a long cylindrical tail of cross-sectional radius b , along which a helical wave progresses distally. Under the equilibrium condition at a constant forward speed, both the net force and net torque acting on the organism are required to vanish, yielding two equations for the velocity of propulsion, U , and the induced angular velocity, Ω , of the organism. In order that this type of motion can be realized, it is necessary for the head of the organism to exceed a certain critical size, and some amount of body rotation is inevitable. In fact, there exists an optimum head-tail ratio a/b at which the propulsion velocity U reaches a maximum, holding the other physical parameters fixed. The power required for propulsion by means of helical waves is determined, based on which a hydromechanical efficiency η is defined. When the head-tail ratio a/b assumes its optimum value and when b is very small compared with the wavelength λ, η ≃ Ω/ω approximately ( Ω being the in­duced angular velocity of the head, ω the circular frequency of the helical wave). This η reaches a maximum at kh ≃ 0.9 ( k being the wavenumber 2π/ λ , and h the amplitude of the helical wave). In the neighbourhood of kh = 0.9, the optimum head-tail ratio varies in the range 15 < a/b < 40, the propulsion velocity in 0.08 < U/c < 0.2 ( c = ω/k being the wave phase velocity), and the efficiency in 0.14 < η < 0.24, as kb varies over 0.03 < kb < 0.2, a range of practical interest. Furthermore, a comparison between the advantageous features of planar and helical waves, relative to each other, is made in terms of their propulsive velocities and power consumptions.

Formation of Bending-Wave Band Structures in Bicoupled Beam-Type Phononic Crystals

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
Y. Q. Guo ◽  
D. N. Fang
Keyword(s):  
Dispersion Relation ◽  
Closed Form ◽  
Phononic Crystals ◽  
Formation Mechanisms ◽  
Wave Band ◽  
Band Structures ◽  
Bending Waves ◽  
Beam Type ◽  
Thickness Shear ◽  
Bending Wave

Beam-type phononic crystals as one kind of periodic material bear frequency bands for bending waves. For the first time, this paper presents formation mechanisms of the phase constant spectra in pass-bands of bending waves (coupled flexural and thickness-shear waves) in bicoupled beam-type phononic crystals based on the model of periodic binary beam with rigidly connected joints. Closed-form dispersion relation of bending waves in the bicoupled periodic binary beam is obtained by our proposed method of reverberation-ray matrix (MRRM), based on which the bending-wave band structures in the bicoupled binary beam phononic crystal are found to be generated from the dispersion curves of the equivalent bending waves in the unit cell due to the zone folding effect, the cut-off characteristic of thickness-shear wave mode, and the wave interference phenomenon. The ratios of band-coefficient products, the characteristic times of the unit cell and the characteristic times of the constituent beams are revealed as the three kinds of essential parameters deciding the formation of bending-wave band structures. The MRRM, the closed-form dispersion relation, the formation mechanisms, and the essential parameters for the bending-wave band structures in bicoupled binary beam phononic crystals are validated by numerical examples, all of which will promote the applications of beam-type phononic crystals for wave filtering/guiding and vibration isolation/control.

Transient Bending Wave Propagation in Anisotropic Plates

1998 ◽  
Vol 65 (4) ◽  
pp. 930-938 ◽  
Author(s):  
K.-E. Fa¨llstro¨m ◽  
O. Lindblom
Keyword(s):  
Experimental Data ◽  
Wave Propagation ◽  
Integral Representation ◽  
Orthotropic Plate ◽  
Representation Formula ◽  
Rotary Inertia ◽  
Anisotropic Plates ◽  
Bending Waves ◽  
Integral Representation Formula ◽  
Bending Wave

In this paper we study transient propagating bending waves. We use the equations of orthotropic plate dynamics, derived by Chow about 25 years ago, where both transverse shear and rotary inertia are included. These equations are extended to include anisotropic plates and an integral representation formula for the bending waves is derived. Chow’s model is compared with the classical Kirchoff’s model. We also investigate the influence of the rotary inertia. Comparisons with experimental data are made as well.

scholarly journals ECONOMIC EVALUATION OF POWER WAVES AT THE BEACH TEGAL

2017 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Soebyakto Soebyakto
Keyword(s):  
Wave Velocity ◽  
Electrical Power ◽  
Average Frequency ◽  
Economic Research ◽  
Wave Power ◽  
Maximum Height ◽  
Average Value ◽  
Port Area ◽  
Tapered Channel ◽  
The Waves

Observations of electric power of the waves hitting beach Tegal is obtained by finding the value of the speed, frequency and height of the waves on the beach Tegal. The average value of the wave velocity of 0.15 m/s, the average frequency of 0.17 Hz and a maximum height of 0.6 m on average. This data is still too low to generate electrical power from the mechanical power of the waves. We are still conducting research to increase the speed and height of the waves with a method of "Tapered Channel". This method is expected to raise the value of the wave height of 0.5 m to 2.2 m. Waves of electrical power is estimated to rise to 15.4 Watt/m2 25-50 Watt/m2.In economic calculation, the power of the waves starting from the value of the wave power per m2 per 4 m2. If we need a 100 Watt power of the waves, the beach area that required 4 m2. Economic development beach with waves generate electrical power, built outside the port area, so that the fishermen keep doing the fishing business as it should be. Based on the results of research in theory, the power of the waves is the speed of the wave function that describes the linear curve. However, the results of research that has been done show that the power of the waves is a function of the speed of the waves, which described as a hyperbolic curve. Wave power increases with increasing speed of the waves. While the formulation used is the wave velocity is a function of the height of the waves. By using the method of "Tepered Channel" to catch a wave, the wave speed will be higher. The results of economic research to generate electrical waves can be calculated byeconomic aspects of the compute power of the waves and technological aspects by counting the frequency of the waves

Wave dislocation lines threading interferometers

2007 ◽  
Vol 463 (2083) ◽  
pp. 1697-1711 ◽  
Author(s):  
M.V Berry
Keyword(s):  
Wave Function ◽  
Large Class ◽  
Phase Difference ◽  
Flux Line ◽  
Phase Shifts ◽  
Closed Circuit ◽  
Threading Dislocations ◽  
Aharonov Bohm ◽  
The Waves

In interferometers where a wave is divided into two beams that propagate along separate branches before being recombined, the closed circuit formed by the two branches must be threaded by wave dislocation lines. For a large class of interferometers, it is shown that the (signed) dislocation number, defined in a suitable asymptotic sense, jumps by +1 as the phase difference between the beams increases by 2 π . The argument is based on the single-valuedness of the wave function in the branches and leaking between them. In some cases, the jumps occur when the phase difference is an odd multiple of π . The same result holds for the Aharonov–Bohm wave function, where the waves passing above and below a flux line experience different phase shifts; in this case, where the wave is not concentrated onto branches, the threading dislocations coincide with the flux line.

scholarly journals Cable Force Identification Based on Bending Waves in Substructures

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Jing Huang ◽  
Jun Xiao ◽  
Jinxiang Zhang ◽  
Fanying Jiang ◽  
Yang Dai ◽  
...  
Keyword(s):  
Least Squares Method ◽  
External Disturbance ◽  
Sampling Point ◽  
Frequency Method ◽  
Force Identification ◽  
Bending Waves ◽  
Axial Tension ◽  
Cable Force ◽  
The Impact ◽  
Bending Wave

A method is proposed to study the dynamic characteristics of cable structures from the perspective of traveling waves based on the modified Timoshenko beam axial tension model. Considering the propagation characteristics of the bending wave in a beam structure, once the frequency response of the three measuring points is measured, the wave component coefficients can be obtained by the least squares method, and then the cable force and bending stiffness can be identified with the aim of minimizing the fitting residual. The accuracy of this method is verified by a numerical simulation experiment of the cable vibration. Compared with the traditional frequency method, this method focuses on the cable force identification of the substructure, so the effect of the shock absorber is invalid. Moreover, the cable force of each position of the cable can be calculated reversely by static analysis with the identified cable force of the substructure, which breaks the concept that the cable force is a single value. Furthermore, the cable force can be identified at each frequency sampling point, reducing the impact of the external disturbance.

A Quantitative Analysis of Flagellar Movement in Echinoderm Spermatozoa

1978 ◽  
Vol 76 (1) ◽  
pp. 85-104 ◽  
Author(s):  
YUKIO HIRAMOTO ◽  
SHOJI A. BABA
Keyword(s):  
Quantitative Analysis ◽  
High Speed ◽  
Single Equation ◽  
Entire Length ◽  
High Speed Camera ◽  
Sine Function ◽  
Active Force ◽  
Bending Waves ◽  
The Waves ◽  
Flagellar Axoneme

Computerized analyses were performed on the movement of spermatozoa recorded with a high-speed camera. These provide evidence for active bending waves over the entire length of the flagellum and a single equation for waves in all cases examined. In the equation, the angular direction of the flagellum at any distance from the base is expressed by a sine function of time plus a constant, and thus flagellar waves are ‘sine-generated’. To explain the waves a model was proposed in which the active force required to generate sliding between peripheral microtubules is propagated along and around the flagellar axoneme.

Endogenous Waves in Hippocampal Slices

2003 ◽  
Vol 89 (1) ◽  
pp. 81-89 ◽  
Author(s):  
Don Kubota ◽  
Laura Lee Colgin ◽  
Malcolm Casale ◽  
Fernando A. Brucher ◽  
Gary Lynch
Keyword(s):  
Hippocampal Slices ◽  
Average Frequency ◽  
Irregular Waves ◽  
Temporal Region ◽  
Sharp Waves ◽  
Cortical Inputs ◽  
The Waves ◽  
Lines Of Evidence

Sharp waves (SPWs) are thought to play a major role in intrinsic hippocampal operations during states in which subcortical and cortical inputs to hippocampus are reduced. This study describes evidence that such activity occurs spontaneously in appropriately prepared rat hippocampal slices. Irregular waves, with an average frequency of approximately 4 Hz, were recorded from field CA3 in slices prepared from the temporal region of hippocampus. The waves persisted for hours and were not accompanied by aberrant discharges. Multi-electrode analyses established that they were locally generated within each of the subfields of CA3 and yet were coherent between subfields. The sharp waves were reversibly blocked by either cholinergic or serotonergic stimulation. Various lines of evidence indicate that they are propagated by the CA3 associational system.

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