Carrier Wave Frequency Research Articles

Derivation of the third-order evolution equations for weakly nonlinear water waves propagating over uneven bottoms

Using the multi-scale perturbation methods, the evolution equations for the modulated wave groups over an uneven bottom are derived. The bottom topography consists of two components: the slowly varying component whose horizontal lenght scale is longer than the carrier wave lenght, and the fast varying component with the carrier wave lenght as the horizontal lenght scale. The size of the fast varying depth component is, however, much smaller than the carrier wave amplitude. Assuming that the nonlinearity parameter ε is in the same order of magnitude as the modulation parameter δ, a detailed perturbation expansion analysis based on the carrier wave frequency and carrier wave number is presented. The third-order evolution equation is coupled with a long wave equation which describes the generation and the propagation of a second-order long wave associated with the modulated wave train. It is also shown that the real part of the evolution equation represents a modified wave action equation, while the imaginary part of the evolution equation gives the second-order dispersion relation. For quasi-steady state problems simplifications are made to derive a nonlinear parabolic wave equation.

Effects of short-term electrical stimulation on the ultrastructure of rat skeletal muscles.

The purpose of this study was to determine the effects of short-term, 2,500-Hz carrier-wave frequency electrical stimulation on the ultrastructure of fast-twitch rat skeletal muscles. Thirteen Sprague-Dawley male rats were divided into three groups: daily treatment (Group 1), every-other-day treatment (Group 2), and control (Group 3). The medial quadriceps femoris and hamstring (semitendinosus and semimembranosus) muscles of the right thigh were treated with short-term electrical stimulation. After treatment, the animals were sacrificed, and their treated and sham quadriceps femoris and hamstring muscles were removed, fixed by immersion, and processed for electron microscopy. Morphometric measurements were made on electron micrographs using a Videoplan computer system, and the results were analyzed statistically. The results revealed that mitochondria, triads, and glycogen content of the fast-twitch muscles changed to resemble those of slow-twitch muscles. In view of these results, clinicians should consider the possibility that similar changes also might occur in human subjects under clinical conditions.

A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation

In existing experiments it is known that the slow evolution of nonlinear deep-water waves exhibits certain asymmetric features. For example, an initially symmetric wave packet of sufficiently large wave slope will first lean forward and then split into new groups in an asymmetrical manner, and, in a long wavetrain, unstable sideband disturbances can grow unequally to cause an apparent downshift of carrier-wave frequency. These features lie beyond the realm of applicability of the celebrated cubic Schrödinger equation (CSE), but can be, and to some extent have been, predicted by weakly nonlinear theories that are not limited to slowly modulated waves (i.e. waves with a narrow spectral band). Alternatively, one may employ the fourth-order equations of Dysthe (1979), which are limited to narrow-banded waves but can nevertheless be solved more easily by a pseudospectral numerical method. Here we report the numerical simulation of three cases with a view to comparing with certain recent experiments and to complement the numerical results obtained by others from the more general equations.

The coherent non-linear light propagation in crystal in the exciton range of the spectrum

The phenomenon of self-induced transparency (SIT) in the exciton range of the spectrum consists of the propagation through the crystal of solitary wave packets of coherent excitons and photons with anomalous small losses. In the running frame of reference at the site occupied by the soliton a single aperiodic transformation of photons into excitons and a reverse motion of the energy into the field takes place. The solutions of the SIT equations have been received in the slowly-varying amplitude approximation. Taking into account the phase modulation, the authors have shown the appearance of the branch of the carrier wave frequency with anomalous dispersion not only at the given pulse width but at the given pulse amplitude. They have also found the exact solution of the above mentioned equations taking into account the effect of saturation of the dipole momentum transition from the crystal ground state to the exciton state. It leads to the increasing of the soliton time width, to the decreasing of its amplitude and worsens the SIT observation.

Steady propagation of a coherent light pulse in a dielectric medium. III. Dynamical behaviour of a long pulse

For pt.II see ibid., vol.12, p.1105 (1979). The dynamical process by which the steady propagation of a coherent light pulse of long width takes place in a dielectric medium is studied. In the absence of direct interaction between atomic dipoles, the nonlinear polariton is unstable against a small perturbation and develops self-modulation of its envelope. Nonlinear Schrodinger equations describing this self-modulation are derived for the two cases where the carrier wave frequency lies outside and inside the polariton gap. It is shown that an arbitrary incoming pulse of long width outside the polariton gap evolves as composite pulse of multiple peak structure, which is regarded as a bound state of the steady pulses obtained in a previous paper. The evolution process of pulse inside the polariton gap and the effect of direct interaction between atoms are also discussed.

Reflection of pulse by multiple-dielectric layers

The reflection of a pulse by two dielectric slabs is treated both analytically and numerically. The reflected wave is obtained by expanding the reflection coefficient of an elementary plane wave in a series, including the special case for which total reflection occurs. The effect of the carrier frequency of a pulse-modulated carrier wave on the reflected wave form is also discussed.

Reflection of a pulse by multiple-dielectric layers

The reflection of a pulse by multiple-dielectric layers is treated theoretically. The reflected wave is obtained by expanding the reflection coefficient of an elementary plane wave in a series, including the special case for which total reflection occurs. The pulsed waves reflected by two-dielectric slabs are considered in detail both analytically and numerically. The effect of a carrier frequency of a pulse-modulated carrier wave on the reflected wave form is also discussed.

Sideband Instabilities of a Large-Amplitude Whistler Wave Due to Phase-Bunching of Resonant Particles with Small Perpendicular Velocities

New types of sideband instabilities associated with a large-amplitude whistler wave propagating parallel to an external magnetic field B 0 are proposed and investigated. The instabilities are due to a spiral beam consisting of resonant particles of small velocities, v ⊥ , perpendicular to B 0 . It is shown analytically that in collisionless plasmas the angles ζ between the wave magnetic field and v ⊥ of these particles, when started from a random distribution, bunch quickly to π/2. A spiral beam is formed when there exist collisions which are insufficient to destroy this phase bunching, but are sufficient to prevent any other systematic variation of ζ. Under these conditions, three different whistler modes are found unstable in the immediate vicinity of the carrier wave frequency. Their growth rates can become greater than those of previously investigated sideband instabilities if the resonance velocity substantially exceeds the thermal velocity.

Solitons in nonlinear optics. I. A more accurate description of the 2π pulse in self-induced transparency

A more accurate description of the 2 pi pulse of self-induced transparency is obtained. This is an exact solution of an approximate form of the Maxwell-Bloch equations in which only backscattering is neglected; the equations are valid at densities less than about 1018 atoms cm-3. At such densities the 2 pi sech pulse of McCall and Hahn (1967, 1969) remains a good approximate well into the picosecond range. The more accurate solution is chirped by a factor proportional to the square of the ratio of the spectral width of the pulse to its carrier wave frequency. The stability of this pulse solution and other N soliton solutions of the approximate Maxwell-Bloch equations is demonstrated.

Spontaneous Emission of Plasma Waves in the Presence of a Finite Amplitude Wave

The spontaneous Cerenkov emission of longitudinal waves in a plasma with small but finite amplitude wave (hereafter referred as the carrier wave) is investigated. Two effects of the carrier wave are taken into account; one is the modification of the test-particle orbit and the other that of the dielectric character of the plasma. It is shown that particles trapped in the potential-energy troughs of the carrier wave emit a discrete spectrum of sideband waves (in addition to the carrier wave itself) whose frequencies are different from the carrier-wave frequency by approximately integral multiples of the bounce frequency. An untrapped particle also emits waves at several different frequencies, including the one which satisfies the ordinary Cerenkov condition, but these frequencies depend on the particle velocity. The results are compared with those reported in our previous paper where only the effect of the orbit modification is taken into consideration.

Brain stimulation, experience, and behavior.

An apparatus was constructed for the electrical stimulation of the brain by a modified radio frequency carrier wave to a receiving unit fastened subfascially over the cranium of 8 rhesus monkeys (4 with brain lesions) and 6 cats. The uni-or bipolar electrodes were stereotactically implanted in the median forebrain bundle or the septal, thalamic, hypothalamic or mesencephalic reticular areas. Animals with varied preceding experiences were subjected to conflict-inducing air blast or shock stimuli while discriminating external (tone, light) vs. internal (brain stimulation) cues, and developed adaptational conflicts characterized by the disruption of learned skills, persistent and generalized aversions, organic dysfuctions, loss of body weight and other deviations of conduct. All behavior patterns were evaluated on highly reliable rating scales. Our results were as follows: 1. "Threshold" stimulation of various regions of the brain did not interfere with previously established auditory-visual discriminations. 2. Intracranial self-stimulation (ICS) was variously ignored, avoided, or sought for prior to its establishment as a discriminative cue. 3. The response patterns to ICS were not significantly correlated with anatomical location or species (except that cats uniformly ignored it) but were influenced by prior preferences, and were reversible as the externally applied electrical brain stimulation (EBS) became differentially meaningful. 4. All animals readily learned to discriminate liminal EBS from a tone or light signal, but facility in this varied directly with the general adaptability of each animal. 5. Discrimination of brain stimulation was retained up to 4 months without practice and could be transferred immediately to the interruption of a continued squaredpulse stimulation. 6. Adaptational conflicts produced generalized "neurotic" behavioral deviations which included "conditioned anxiety" reactions to EBS, but these effects again varied with the length and adequacy of each animal's laboratory adaptation. 7. Stimulus generalization gradients for EBS frequency were similar in animals with different brain lesions, but varied greatly with each animal's previous experiences. 8. Chemotherapy with Ritalin and Librium failed to mitigate behavioral deviations and showed no essential interactions with EBS.

Amplituda a frekvence modulované nosné vlny

Amplituda a frekvence modulované nosné vlny

New Broadcasting System

ACCOEDING to a recent report by the New York Correspondent of The Times, a new type of wireless transmission and reception will be used in an experimental station now being erected at Columbia University by Major E. H. Armstrong, professor of electrical engineering in the University, and inventor of the now well-known supersonic-heterodyne receiver. The station will use the frequency-modulation system of transmission, as distinct from the amplitude-modulation system at present used by all broadcasting stations. In the former method, the frequency of the emitted carrier wave is varied by the speech and music modulation; whereas in the methods so far employed, the frequency of the carrier wave remains constant and its amplitude is varied by the applied audio-frequencies. The principles of frequency-modulation have been known since the earliest days of radio-telephony, but it has remained for Prof. Armstrong to demonstrate how these may be brought into practical use with modern valves and circuit arrangements. Among the advantages claimed for the new system are that it effects a considerable reduction of interference in radio reception, and that a much larger number of broadcasting channels will become available in any given wave-length band. Against these, however, is the serious disadvantage that special receivers are necessary for frequency-modulated transmissions, and this factor is likely to involve serious delay in the introduction of the new system into modern broadcasting technique. The first transmitting station on the new system will be at Alpine, New Jersey, opposite New York City, and it has a licence to broadcast on a frequency of 40 megacycles per second (wave-length 7.5 metres). It is also understood that suitable receivers are already being manufactured, so that the result of this practical experiment will be awaited with interest.