Abstract – The present paper is an attempt to study rectangular laser light effects on optoacoustic waves of first and second sounds in superfluidHelium theoretically considering electrostrictive mechanism. There are two mechanisms in Heliumsuperfluid: thermal and electrostrictive. Since the paper studied crystal parts of Helium and coefficient of absorption in these parts is zero, the only dominant mechanism is electrostriction mechanism. To carry out the research the researcher emitted Laser light into crystal parts of superfluidHelium and observed and analyzed its results on first soundwaves (pressure vibration) and secondsoundwaves (temperature vibration).
superfluid is known to be related to the formation of a Bose-Einstein condensate. This is made obvious by the fact that superfluidity occurs in liquid helium-4 at far higher temperatures than it does in helium-3. Each atom of helium-4 is a boson particle, by virtue of its zero spin. Helium-3, however, is a fermion particle, which can form bosons only by pairing with itself at much lower temperatures, in a process similar to the electron pairing in su- perconductivity.
We have shown in experiments with a turbulent system of secondsoundwaves in a high-Q resonator filled with superfluidhelium that acoustic waves with fre- quency lower than the driving frequency may be generated due to nonlinearity: a sound wave with frequency equal to half the driving frequency (subharmonic of the driving frequency) may be excited at relatively large ac heat flux densi- ties. We suppose that the subharmonic is generated through a decay instability of the wave excited by an external drive. We have also found in both experiments and numerical calculations that application of an additional low frequency driving force to a turbulent system of secondsoundwaves results in the excitation of addi- tional acoustic oscillations with frequencies equal to combination frequencies of the main and additional driving forces. The amplitudes of the secondsoundwaves in the high frequency spectral domain are decreased when the additional driving force is applied. Suppression of the turbulent cascade in the high-frequency do- main is probably caused by redistribution of the wave energy among newly excited states in the low-frequency energy-containing region.
We review studies of the generation and propagation of nonlinear and shocksoundwaves in He II 共 the superfluid phase of 4 He 兲 , both under the saturated vapor pressure 共 SVP 兲 and at elevated pressures. The evolution in shape of second and first soundwaves excited by a pulsed heater has been investigated for increasing power W of the heat pulse. It has been found that, by increasing the pressure P from SVP up to 25 atm, the temperature T ␣ , at which the nonlinearity coefficient ␣ of secondsound reverses its sign, is decreased from 1.88 to 1.58 K. Thus at all pressures there exists a wide temperature range below T where ␣ is negative, so that the temperature disconti- nuity 共shock front兲 should be formed at the center of a propagating bipolar pulse of secondsound. Numerical estimates show that, with rising pressure, the amplitude ratio of linear first and secondsoundwaves generated by the heater at small W should increase significantly. This effect has allowed us to observe at P = 13.3 atm a linear wave of heating 共rarefaction兲 in first sound, and its transformation to a shock wave of cooling 共compression兲. Measurements made at high W for pressures above and below the critical pressure in He II, P cr = 2.2 atm, suggest that the main
(2.17c) Many acoustic phenomena, resonances in tubes and cavities, for example, can with advantage be studied in the frequency domain. Linearity implies that a disturbance that varies sinusoidally with time with the frequency T , a vibrating solid surface, for example, will gen- erate a sound field in which the sound pressure p varies sinusoidally with time with the fre- quency T at all positions, and so will the particle velocity and the perturbations of the density and the temperature. It follows that we can describe any linear (first-order) quantity in such a harmonic sound field as the real part of a complex amplitude that varies with the position multiplied with a factor of e j T t , which takes account of the time dependence. This leads to the
When a sound source is moving toward you, you hear a slightly higher pitch than if the sound source is at rest relative to you. By the same token, when a sound source is moving away from you, you hear a slightly lower pitch. This phenomena is called the Doppler effect. For example, if a train is traveling toward you while blowing its horn at a certain pitch, the waves will appear to be arriving at your ear more frequently, increasing the pitch you perceive.
direction coincides with the direction of R. It is believed that the expression (2) is universal and fully describes the propagation of waves. This means that (2) is applicable to any type of audio sources and any direction of wave propagation, since no restriction of applicability speak. It is known that the phase of the periodic type functions cos ϕ , sin ϕ always—the scalar. Indeed, in determining (2) the direction of propagation of the sound wave is absent, although the phase consists of two vectors, but the scalar product of parallel vectors kR, —scalar. In  it is shown that the direction of the waves should set the initial conditions as is done in the solution of any problem. The sound wave is a vector perpendicular to the plane of the vibrating membrane. We propose to introduce the direction of propagation of the wave in it amplitude, consider it is a vector, which coincides with the velocity vector (trajectory) of sound in the liquid. It will reflect the physical essence of traveling wave—its propagation, and clearly mark its direction. Vector representation of the amplitude of the wave will eliminate unjustified change in the wave phase the value of π, produced by many authors to account the change in the sign of the reflected wave. When the amplitude is the scalar the sign of amplitude p(x, y, z, t) in (2) does not change during propagation. In addition to the need for a definition of semantic amplitude—vector of the running wave this results in line with its name. This notation is universal, applicable in any type of wave source, and any di- rection of wave propagation, because the phase ϕ of periodic functions of the type cos ϕ , sin ϕ is always a scalar quantity and not depend on the vector’s direction that forms it.
AN INVESTIGATION OF DETACHED SHOCK WAVES Thesis by Bernard ~alter Marschner In Partial Fulfillment or the Requirements ror the Degree of Aeronautical Engineer Calirornia Institute of Technology fasade[.]
We conduct empirical methods in quiet place (environment), considered easy to recognize gestures such as a library or a calm place. In these locations, usually at survival signals emitted soundwaves or less random noise existed to affect the classification process and gestures recognization. At the same time, we also experimentally do the same in noisy places such as classroom, locations are often available randomly or other source of soundwaves that are not only caused by. Through noisy places or quiet ones, we evaluate the effectiveness of methods for environmental use. Also, in both quiet environment (library) and noisy (classrooms) for many different users to assess the impact (in terms of speed, direction of movement) of the election different only for the method. To review the stability and effectiveness of the methods implemented, we use a number of different types of computers. The computers operate in different modes but (allowing applications to run simultaneously in multiple time difference) to control a number of applications such as web surfing, browse PDF documents, PPT slides, or browse Photos in the browser application using four hand gestures which were introduced instead of using direct or mouse navigation keys on the keyboard. By aggregating data in the evaluation method mentioned above, we found that the method can recognize gestures resulting noise and very reliable.
Now, we can always qualitatively tell the intensity of sound- stand next to speakers at a rock concert, and you're bound to hear the phrase "That's so intense!" at some point in the night. In a similar way, some things can be intensely quiet. Neither of these measures are mathematical, but we can actually quantify these intensities. First, we start with how powerful the source is, and allow the sound to spread out, either at the edge of a circle or on the edge of a sphere. For short distances, either will suffice; for longer distances, the spherical form will yield better results, but requires remembering the expression for the surface area of a sphere.
Such studies reveal that either the system and / or the underlying physical mechanisms have char- acteristic scale invariance behavior (resulting in the power index n becoming complex) or that we observe a sound wave in hadronic matter (resulting in the temperature oscillations) which has a self similar solution (in log-periodic form). In the former case the discrete scale invariance and its asso- ciated complex exponents n can appear spontaneously, without a pre-existing hierarchical structure . In the latter case the corresponding wave equation has self-similar solutions of the second kind connected with the so called intermediate asymptotic (observed in phenomena which do not depend on the initial conditions because su ffi cient time has already passed, although the system considered is still out of equilibrium) [20–23]. This suggests that both in p + p and Pb + Pb collisions one deals with an inhomogeneous medium with the density and the velocity of sound both depending on the position and this can have some interesting experimental consequences.
that interactions between one normal-fluid and many superfluid vortex rings generate a ten- dency towards energy-level matching in the wavenumber intervals of the velocity spectra which correspond to the normal-fluid ring diameter scale. Remarkably, there is no accom- panying vorticity matching, because, for typical normal-fluid Reynolds numbers, the inertia of the normal-fluid ring is much stronger than mutual-friction effects on superfluid vortices, hence, the latter cannot be coaxed into aligning with the former within the time-scales of normal-fluid ring motion. Fig.1 (left) shows the isosurfaces of enstrophy in homogeneous, isotropic Navier-Stokes turbulence of Taylor Reynolds number Re λ ≈ 100. The results have
The final decision as to the best type of thermal switch to use was greatly influenced by certain design features incorporated into the experimental region of the cryostat. The liquid sample of 140 ccs of ^He was contained, together with the main refrigerant, in a cell made from Epibond lOQA epoxy resin. The liquid was condensed into the cell via a long narrow capillary thermally anchored at each cooling stage by a sintered copper heat exchanger, and wound into isolation spirals between the various stages. To allow changes of the liquid level during the course of the experiments, the cell terminated in a stainless steel bellows, operated directly from the cryostat top plate through a mechanical linkage. At temperatures above IK, the thermal conductivity of superfluid ^He is extremely high. By a careful choice of cell geometry and bellows size, the cell filling capillary was made to function as a thermal switch. Full compression of the bellows forced the liquid ^He back up the capillary to make thermal contact between cell, guard salt and vortex refrigerator.
6. A block with a mass M is attached to a vertical spring with a spring constant k. When the block is displaced from equilibrium and released its period is T. A second identical spring k is added to the first spring in parallel. What is the period of oscillations when the block is suspended from two springs?
In order to observe the first subharmonic wave, the experiments [6, 7] were carried out in a tank, into which a sound wave at frequency 1.948 MHz was transmitted. Only a sound wave with the same frequency was received when the water in the tank was static (cf. figure 1). On the other hand, if the medium was disturbed by a stick or a stirrer [6, 7], an appreciable first subharmonic (0.974MHz) was observed (figure 2).
As is well known from transformation theory a lot of new information on nonlinear wave equations can be obtained from transformed equations by means of for instance Hopf-Cole, Miura or B¨acklund type. In a somewhat similar spirit we also exploit here the knowledge of a transformation in form of an explitly known PT -symmetrical deformation. Here we will mainly focus on the question of what kind of effect a PT -deformation has on a shock wave. It is well known that a shock forms when the crest of a wave overtakes the troughs. The challenge for a mathematical description is that one can no longer describe this phe- nomenon by a function since the surface of the wave becomes multi-valued. For real wave equations solvable with the method of characteristics, this happens when two character- istics cross each other or more generally when the first derivative becomes infinite. For PT -deformed equations remaining real, we argue here that the first derivative is discontin- uous but remains finite, whereas the second derivative tends to infinity. Solitonic solutions with this type of behaviour are often referred to as peakons . When the deformation parameters are non odd integers, one is forced to consider complex solutions even in the undeformed case if one demands a real soltution for the deformed one. However, evolving this real deformed solution in time will convert it into a complex one. In addition, when compared to the real scenario, the peaks vanish and we observe discontinuties, which are generated due to the imposition of physical asymptotic boundary conditions.
subsonic regions upstream the nose of central body and near the walls of the channel. Further reducing of the inlet Mach number leads to a restructuring of shockwaves and splitting of supersonic regions at another inlet Mach number. At reduced Mach number the small subsonic regions increases at the walls of the channel and the central body.
Now the structure problem for MFD shocks is the above four simultaneous ﬁrst- order nonlinear diﬀerential equations must be integrated between equilibrium points. This problem has been studied before by many authors, when the dissipation coeﬃ- cients are continuous functions of T [4, 5, 7, 10, 11, 13, 14, 20]. We will describe these works in more details in Section 2. However, in the case of ionizing shock, the electri- cal conductivity of the gas is assumed to be zero (or very small) in the pre-shock gas and it continues to zero (or very small) until a value ¯ T is reached by the temperature. At this point in the shock structure the electrical conductivity jumps to inﬁnity (or a high value) which remains the same through the remainder of the shock wave. The analogy with the ignition temperature in ﬂame and detonation problems is evident [9, 12, 26, 27, 29]. In other words, we have