NONLINEAR ENERGY TRANSFER IN ELASTIC WAVES

Geophysics ◽  
1968 ◽  
Vol 33 (5) ◽  
pp. 734-746 ◽  
Author(s):  
Geoffrey Holstrom
Keyword(s):  
Energy Transfer ◽  
High Frequency ◽  
Finite Amplitude ◽  
Second Order ◽  
Loss Mechanism ◽  
Low Frequencies ◽  
Nonlinear Energy Transfer ◽  
Apparent Loss ◽  
Apparent Attenuation ◽  
The One

If an elastic pulse of finite amplitude propagates through a solid, the energy originally associated with one frequency is partially transferred to other frequencies. This transfer can lead, for lossless compressive pulses, to the formation of a shock wave. Changes of entropy occur in steady shocks only in terms beginning with third order in the compression, and hence a perturbation treatment neglecting heat conduction is valid to second order. The one‐dimensional mass and momentum conversation equations are solved to second order, and the solutions are used to study energy transfer. Generally speaking, transfer occurs from lows to highs, leading to apparent attentuation of frequencies in the seismic range. A drop in energy of low frequencies might occur even if the only apparent loss mechanism is high frequency scattering. Formulas are developed giving the apparent attenuation over propagation distances or oscillation times small enough that perturbation treatment remains valid. It appears that this process could be important as a loss mechanism at low frequencies if initial pulses are sufficiently sharp, or if initial free oscillations have sufficiently large high‐frequency content.

A note on the correspondence between the x, t-plane and the characteristic plane in a problem of interaction of plane waves of finite amplitude

1951 ◽  
Vol 47 (3) ◽  
pp. 518-527 ◽  
Author(s):  
P. M. Stocker ◽  
R. E. Meyer
Keyword(s):  
Limit Point ◽  
Plane Waves ◽  
Finite Amplitude ◽  
Second Order ◽  
Physical Aspect ◽  
Isentropic Flow ◽  
Characteristic Plane ◽  
Simple Compression ◽  
Simple Expansion ◽  
The One

AbstractThe head-on interaction, in the one-dimensional, unsteady isentropic flow of a perfect gas, of a simple compression wave and a simple expansion wave is studied by considering typical examples. The physical aspect of the problem is discussed in (1); in this note the possibility of shock formation is ignored, and the correspondence defined by the complete mathematical solution of the equations of isentropic flow between the x, t-plane and the plane of the characteristic variables is elucidated.The solution is distinguished by the appearance of two limit lines and a second-order limit point where they meet. It is found that the image of the characteristic plane in the x, t-plane is four-sheeted; all sheets overlap each other, but each covers only part of the plane, and the only point common to all sheets is the second-order limit point, where both limit lines are cusped (§ 3·1).The solution also contains an edge of regression, and a discussion of the properties of this type of singularity will be found in §§ 2 and 2·1.

scholarly journals Mechanical and Dielectric Behaviour of CaCu3Ti4O12 and Nb Doped CaCu3Ti4O12 Poly(vinylidene fluoride) Composites

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Anshuman Srivastava ◽  
Karun Kumar Jana ◽  
Pralay Maiti ◽  
Devendra Kumar ◽  
Om Parkash
Keyword(s):  
Dielectric Relaxation ◽  
High Frequency ◽  
Vinylidene Fluoride ◽  
Low Frequency ◽  
Transition Metal Ions ◽  
Low Frequencies ◽  
Dielectric Relaxations ◽  
Poly Vinylidene Fluoride ◽  
State Ceramic ◽  
The One

PVDF has been reinforced with different amount of CaCu3Ti4-5x/4NbxO12 with x=0.05 powder prepared by solid state ceramic method. Composites were prepared by melt extrusion method. Phase composition was studied using powder X-ray diffraction (XRD). Microstructural, dielectric, and mechanical properties have also been studied. These composites have Young’s modulus more than that of pure PVDF. Two dielectric relaxations, one at low frequency and the other at high frequency, have been observed in these composites. Dielectric relaxation at low frequencies is of Maxwell-Wagner type while the one observed at high frequency is due to hopping of electrons among different valent states of transition metal ions. Nature of dielectric relaxation has been analysed using H-N function.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

scholarly journals Earless toads sense low frequencies but miss the high notes

2017 ◽  
Vol 284 (1864) ◽  
pp. 20171670 ◽  
Author(s):  
Molly C. Womack ◽  
Jakob Christensen-Dalsgaard ◽  
Luis A. Coloma ◽  
Juan C. Chaparro ◽  
Kim L. Hoke
Keyword(s):  
High Frequency ◽  
Species Differences ◽  
Low Frequency ◽  
Auditory Brainstem ◽  
Low Frequencies ◽  
Hearing Sensitivity ◽  
Sensory Pathways ◽  
Airborne Sound ◽  
Vibrational Sensitivity ◽  
Species Specific

Sensory losses or reductions are frequently attributed to relaxed selection. However, anuran species have lost tympanic middle ears many times, despite anurans' use of acoustic communication and the benefit of middle ears for hearing airborne sound. Here we determine whether pre-existing alternative sensory pathways enable anurans lacking tympanic middle ears (termed earless anurans) to hear airborne sound as well as eared species or to better sense vibrations in the environment. We used auditory brainstem recordings to compare hearing and vibrational sensitivity among 10 species (six eared, four earless) within the Neotropical true toad family (Bufonidae). We found that species lacking middle ears are less sensitive to high-frequency sounds, however, low-frequency hearing and vibrational sensitivity are equivalent between eared and earless species. Furthermore, extratympanic hearing sensitivity varies among earless species, highlighting potential species differences in extratympanic hearing mechanisms. We argue that ancestral bufonids may have sufficient extratympanic hearing and vibrational sensitivity such that earless lineages tolerated the loss of high frequency hearing sensitivity by adopting species-specific behavioural strategies to detect conspecifics, predators and prey.

Upgraded Railway Front Searchlight Design Plastic Deformations by its Vibrations with Resonance Frequencies

2016 ◽  
Vol 684 ◽  
pp. 111-119 ◽  
Author(s):  
Stanislav Rafaelevich Abulkhanov ◽  
Dmitrii Sergeevich Goryainov
Keyword(s):  
Natural Frequencies ◽  
Ansys Software ◽  
Software Environment ◽  
Low Frequencies ◽  
Plastic Deformations ◽  
Vibration Resistance ◽  
First Case ◽  
Resonance Frequencies ◽  
The One ◽  
Electric Lamp

Natural frequencies of the four upgraded front searchlight designs were received in ANSYS software environment. In the first case serial front searchlight incandescent electric lamp was replaced by a LED group which was mounted on the one-piece cylinder backing. The second front searchlight design had the backing which was upgraded by a radial ribs and concentric rigidity ferrules. Analyze of the backing deformation character by vibrations with the natural frequencies established a number of design solutions which make it possible to raise front searchlight vibration resistance. By the front searchlight model were established that the natural frequencies of the searchlight with the one-piece backing appertain to the whole range of the train vibrations. Natural frequencies of the backing with perforation, rigidity ferrules, and radial ribs appertain to the low frequencies of the railway locomotive vibrations spectrum. On basis of devised methodology of analyze of the deformation and natural frequencies of the surface carrying a LED group the vibration-proof searchlight design was introduced and researched.

scholarly journals The Estimation of Hydrometeor Profiles from Wideband Microwave Observations

2000 ◽  
Vol 39 (10) ◽  
pp. 1645-1656 ◽  
Author(s):  
Gail M. Skofronick-Jackson ◽  
James R. Wang
Keyword(s):  
High Frequency ◽  
Cloud Water ◽  
Tropical Ocean ◽  
Low Frequencies ◽  
High Frequencies ◽  
Atmospheric Research ◽  
Brightness Temperatures ◽  
Microphysical Properties ◽  
Ice Microphysics ◽  
Updraft Region

Abstract Profiles of the microphysical properties of clouds and rain cells are essential in many areas of atmospheric research and operational meteorology. To enhance the understanding of the nonlinear and underconstrained relationships between cloud and hydrometeor microphysical profiles and passive microwave brightness temperatures, estimations of cloud profiles for an anvil region, a convective region, and an updraft region of an oceanic squall were performed. The estimations relied on comparisons between radiative transfer calculations of incrementally estimated microphysical profiles and concurrent dual-altitude wideband brightness temperatures from the 22 February 1993 flight during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment. The wideband observations (10–220 GHz) are necessary for estimating cloud profiles reaching up to 20 km. The low frequencies enhance the rain and cloud water profiles, and the high frequencies are required to detail the higher-altitude ice microphysics. A microphysical profile was estimated for each of the three regions of the storm. Each of the three estimated profiles produced calculated brightness temperatures within ∼10 K of the observations. A majority of the total iterative adjustments were to the estimated profile’s frozen hydrometeor characteristics and were necessary to match the high-frequency calculations with the observations. This requirement indicates a need to validate cloud-resolving models using high frequencies. Some difficulties matching the 37-GHz observation channels on the DC-8 and ER-2 aircraft with the calculations simulated at the two aircraft heights (∼11 km and 20 km, respectively) were noted, and potential causes were presented.

scholarly journals The dual-slope conversion improvement

2014 ◽  
Vol 11 (3) ◽  
pp. 351-363
Author(s):  
Radojle Radetic ◽  
Marijana Pavlov-Kagadejev ◽  
Nikola Milivojevic
Keyword(s):  
High Frequency ◽  
Frequency Noise ◽  
Good Resolution ◽  
Practical Realization ◽  
Digital Conversion ◽  
Low Frequencies ◽  
Analog To Digital ◽  
High Frequency Noise ◽  
Low Input ◽  
Analog To Digital Conversion

The dual-slope ADC (DSADC) is a type of analog-to-digital conversion with low input bandwidths. It is pretty slow, but its ability to reject high-frequency noise and fixed low frequencies such as 50 Hz or 60 Hz makes it useful in noisy industrial environments and applications. It provides very good resolution. For the practical measurements in the Institutes laboratory an instrument is designed and realized. The base DSADC method is used, but improved by multiple conversions to make the measuring more precise and the time shorter. The special attention is paid to the problems occurred in practical realization and the way to overcome them. The paper describes the proposed and applied solutions, functional principles and achieved performances of the realized instrument.

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