scholarly journals I. On the waves produced by a single impulse in water of any depth, or in a dispersive medium

1887 ◽  
Vol 42 (251-257) ◽  
pp. 80-83 ◽  
Keyword(s):  
Wave Velocity ◽  
Dispersive Medium ◽  
Wave Length ◽  
Periodic Waves ◽  
Two Dimensional ◽  
Group A ◽  
Two Sides ◽  
The Waves

For brevity and simplicity consider only the case of two-dimensional motion . All that it is necessary to know of the medium is the relation between the wave-velocity and the wave-length of an endless procession of periodic waves. The result of our work will show us that the velocity of progress of a zero, or maximum, or minimum, in any part of a varying group of waves, is equal to the velocity of progress of periodic waves of wave-length equal to a certain length, which may be defined as the wave-length in the neighbourhood of the particular point looked to in the group (a length which will generally be intermediate between the distances from the point considered to its next-neighbour corresponding points on its two sides).

scholarly journals Experiments on the diffraction of cathode rays

1928 ◽  
Vol 117 (778) ◽  
pp. 600-609 ◽  
Keyword(s):  
Wave Velocity ◽  
Direct Evidence ◽  
Wave Length ◽  
General Nature ◽  
Preliminary Account ◽  
Freely Moving ◽  
Mathematical Difficulties ◽  
Moving Particle ◽  
Slow Electrons ◽  
The Waves

1. M. L. de Broglie has introduced a theory of mechanics according to which a moving particle behaves as a group of waves whose velocity and wave-length are governed by the speed and mass of the particle. In fact if m 0 is the mass for slow speed and v the speed of a freely moving particle, the wave-length is given by λ = h √1- v 2 / c 2 / m 0 v , and the wave velocity V by V = c 2 / v , the group velocity being v , the velocity of the particle. Here c is the velocity of light and it will be seen that the wave velocity is greater than c . There is nothing impossible in this because the waves are regarded as purely geometrical —“phase waves”—not as carrying energy. Compare, in ordinary optical theory, the case of substances, such as sodium, for which the refractive index is less than unity. The above is for free space; in the presence of a field of force V varies, and the consequent bending of the waves by refraction corresponds, on the new theory, to the deviation of the path of the particle by the field of force, on the old. The consequences of this theory have been worked out by de Broglie, Schrödinger and others and applied to problems in spectroscopy where they have provided the solution of several outstanding difficulties left by the older theory of orbits. In view, however, of the extremely fundamental nature of the theory it is highly desirable that it should rest on more direct evidence, and, in particular, that it should be shown capable of predicting as well as of merely explaining. Dymond has obtained some remarkable results on the scattering of slow electrons in helium which are of the general nature to be expected in this theory, but our knowledge of the structure of helium, together with the mathematical difficulties of the problem have so far prevented any exact comparision of the theory with experiment. Davisson and Kunsman and Davisson and Germer have obtained results on the reflection of slow electrons from the surfaces of crystals, especially nickel, which show good qualitative agreement with the theory but a discrepancy of 30 per cent. in certain magnitudes. It is hoped that the experiments described in this paper will advance the matter a stage further. They are a development of some experiments of which a preliminary account appeared recently in ‘Nature.’

scholarly journals The Movement of Sea-Urchin Spermatozoa

1955 ◽  
Vol 32 (4) ◽  
pp. 775-801 ◽  
Author(s):  
J. GRAY
Keyword(s):  
Wave Length ◽  
Bending Waves ◽  
Left Handed ◽  
Transverse Bending ◽  
Clockwise Direction ◽  
Central Elements ◽  
A Cell ◽  
Curved Track ◽  
Two Sides ◽  
The Waves

1. The spermatozoa of Psamtneckinus irnliaris (P. L. S. Müller; Gmelin) propel themselves by projecting transverse bending waves along their tails. All points on the tail normally execute their movements in approximately the same plane, their envelope forming a plane (or slightly twisted) lamina. The radius of maximum curvature is of the order of 4µ 2. In fresh suspensions at about 180° C. the waves are generated at a frequency of 30-40 per sec. and travel along the tail at a velocity of 800-1000µ per sec. The average amplitude of the waves is 4µ and the average wave-length 24µ 3. Elements of the tail situated near the head seldom bend to the same extent on their two sides. The symmetrical bending cycle of the central elements, on the other hand, sometimes imposes on the tail the form of a sine curve. 4. When moving over the surface of a glass slide the passage of each wave along the tail propels the head of the spermatozoon through a distance of 5-6µ, and at the same time causes it to oscillate laterally through a distance of about 4µ. The rate of forward propulsion of the head is seldom constant during all phases of the bending cycle; in extreme cases the head may move backwards during certain phases of the cycle. This asymmetry is probably due to the asymmetry of bending on the two sides of the tail. 5. Spermatozoa swimming over the surface of a slide travel at an average speed of about 190µ per sec, but their path of progression is seldom straight; most cells travel along a curved track whose radius is usually 30-100µ. Cells swimming farther away from the surface of a slide roll about their longitudinal axes with a frequency of 0.5-3.0 per sec., and their axis of progression is straight. The path of a cell which yaws and rolls as it progresses forms a helix whose properties depend on the rate of yaw, frequency of roll and the rate of the cell's forward progression. 6. Eighty per cent of the cells moving over the surface of a slide yaw in a counter-clockwise direction relative to the observer. This phenomenon can be explained on the assumption that most of the cells when moving freely in a bulk of fluid behave as ‘left-handed’ screws rolling counter-clockwise as they advance; proximity to a surface prevents the cells from rolling and impresses on them an appearance of yawing in a counter-clockwise direction irrespective of whether they are yawing towards their right or left sides. 7. Evidence, is presented which supports the view that all regions of the tail are actively contractile although mechanical forces may affect the propagation of bending waves along the filament.

scholarly journals On the formation of water waves by wind

1925 ◽  
Vol 107 (742) ◽  
pp. 189-206 ◽  
Keyword(s):  
Water Waves ◽  
Relative Velocity ◽  
Wave Length ◽  
Horizontal Displacement ◽  
Two Fluids ◽  
Critical Wind Velocity ◽  
Irrotational Motion ◽  
Lord Kelvin ◽  
Two Sides ◽  
The Waves

It is well known that in certain circumstances a type of instability may arise at the surface of separation of two fluids when there is a finite difference between the velocities on the two sides of the surface. Some disturbances of the surface, of simple harmonic type, may increase exponentially in amplitude until the customary simplifying assumption, that the terms of the second degree in the displacements from the undisturbed state can be ignored, breaks down. One would naturally expect that in the case, for instance, of a wind blowing over the surface of water, waves would be first formed when the velocity of the wind is just great enough to make one particular type of wave grow; thus the critical wind velocity and the wave-length of the waves first formed will constitute checks on any theory of wave formation. The problem for frictionless fluids has been solved by Lord Kelvin, subject to the restriction that the disturbances considered are two-dimensional, no horizontal displacement occurring across the relative velocity of the fluids. Since, however, the possible initial deformations of a horizontal surface will not as a rule satisfy this condition, an investigation of the growth or decay of deformations of other types is desirable. 1. Hypothesis of Irrotational Motion . Let the two fluids be incompressible (a legitimate approximation so long as the wave velocity is small compared with that of sound in either fluid) and of great vertical extent. Let the origin be in the undisturbed position of the surface of separation and the axis of z vertically upwards. Let ζ be the elevation of the surface, and suppose the two fluids to have initially velocities U and U' parallel to the axis of x , accents referring to the upper fluid. Let the densities of the fluids be respectively ρ and ρ', and the velocity potentials in them Ф and Ф' . Let the operators ∂/∂ t , ∂/∂ x , ∂/∂ y , ∂/∂ z be denoted by σ, p , q , and ϑ respectively. Putting r 2 for — ( p 2 + q 2 we see that ∇ 2 Φ = 0 (1) is equivalent to (ϑ 2 — r 2 ) Ф = 0, (2) whence Ф = U x + e rz A, (3) where A is a function of x and y , determined by the value of Ф where z is zero.

On the Transition from Homogeneous to Bubbling Fluidization

1997 ◽  
Vol 62 (11) ◽  
pp. 1698-1709
Author(s):  
Miloslav Hartman ◽  
Zdeněk Beran ◽  
Václav Veselý ◽  
Karel Svoboda
Keyword(s):  
Elastic Wave ◽  
Froude Number ◽  
Wave Velocity ◽  
Density Ratio ◽  
Elastic Wave Velocity ◽  
Solid Density ◽  
Archimedes Number ◽  
Group A ◽  
Experimental Findings

The onset of the aggregative mode of liquid-solid fluidization was explored. The experimental findings were interpreted by means of the dynamic (elastic) wave velocity and the voidage propagation (continuity) wave velocity. For widely different systems, the mapping of regimes has been presented in terms of the Archimedes number, the Froude number and the fluid-solid density ratio. The proposed diagram also depicts the typical Geldart's Group A particles fluidized with air.

Polarographic and spectrophotometric behaviour of some N-p-phenyl substituted benzamidines

1991 ◽  
Vol 56 (12) ◽  
pp. 2791-2799 ◽  
Author(s):  
Juan A. Squella ◽  
Luis J. Nuñez-Vergara ◽  
Hernan Rodríguez ◽  
Amelia Márquez ◽  
Jose M. Rodríguez-Mellado ◽  
...  
Keyword(s):  
Spectrophotometric Study ◽  
Absorption Bands ◽  
Electrochemical Parameters ◽  
Wide Ph Range ◽  
Group A ◽  
Substituent Constants ◽  
Ph Range ◽  
The Waves

Five N-p-phenyl substituted benzamidines were studied by DC and DP polarography in a wide pH range. Coulometric results show that the overall processes are four-electron reductions. Logarithmic analysis of the waves indicate that the process are irreversible. The influence of the pH on the polarographic parameters was also studied. A UV spectrophotometric study was performed in the pH range 2-13. In basic media some variations in the absorption bands were observed due to the dissociation of the amidine group. A determination of the pK values was made by deconvolution of the spectra. Correlations of both the electrochemical parameters and spectrophotometric pK values with the Hammett substituent constants were obtained.

scholarly journals Dipole-induced Ohmic contacts between monolayer Janus MoSSe and bulk metals

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Ning Zhao ◽  
Udo Schwingenschlögl
Keyword(s):  
First Principles ◽  
Ohmic Contacts ◽  
Electrode Materials ◽  
Electronic Device ◽  
Two Dimensional ◽  
First Principles Calculations ◽  
Fermi Level Pinning ◽  
Common Electrode ◽  
Two Sides ◽  
Metallic Electrodes

AbstractUtilizing a two-dimensional material in an electronic device as channel layer inevitably involves the formation of contacts with metallic electrodes. As these contacts can dramatically affect the behavior of the device, we study the electronic properties of monolayer Janus MoSSe in contact with different metallic electrodes by first-principles calculations, focusing on the differences in the characteristics of contacts with the two sides of MoSSe. In particular, we demonstrate that the Fermi level pinning is different for the two sides of MoSSe, with the magnitude resembling that of MoS2 or MoSe2, while both sides can form Ohmic contacts with common electrode materials without any further adaptation, which is an outstanding advantage over MoS2 and MoSe2.

Effects of plane progressive irrotational waves on thermal boundary layers

1971 ◽  
Vol 50 (2) ◽  
pp. 321-334 ◽  
Author(s):  
James Witting
Keyword(s):  
Boundary Layers ◽  
Deep Water ◽  
Maximum Amplitude ◽  
Capillary Waves ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Inviscid Incompressible Fluid ◽  
Mean Temperature ◽  
The Waves ◽  
Thermal Boundary Layers

The average changes in the structure of thermal boundary layers at the surface of bodies of water produced by various types of surface waves are computed. the waves are two-dimensional plane progressive irrotational waves of unchanging shape. they include deep-water linear waves, deep-water capillary waves of arbitrary amplitude, stokes waves, and the deep-water gravity wave of maximum amplitude.The results indicate that capillary waves can decrease mean temperature gradients by factors of as much as 9·0, if the average heat flux at the air-water interface is independent of the presence of the waves. Irrotational gravity waves can decrease the mean temperature gradients by factors no more than 1·381.Of possible pedagogical interest is the simplicity of the heat conduction equation for two-dimensional steady irrotational flows in an inviscid incompressible fluid if the velocity potential and the stream function are taken to be the independent variables.

Internal waves in a viscous atmosphere

1975 ◽  
Vol 72 (4) ◽  
pp. 773-786 ◽  
Author(s):  
W. L. Chang ◽  
T. N. Stevenson
Keyword(s):  
Energy Source ◽  
Incompressible Fluid ◽  
Internal Waves ◽  
Infinite Number ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
The Waves ◽  
Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

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