On the kinetic theory of wave propagation in random media

1973 ◽  
Vol 274 (1242) ◽  
pp. 523-549 ◽  
Keyword(s):  
Wave Propagation ◽  
Energy Transfer ◽  
Scattering Theory ◽  
Random Media ◽  
Order Approximation ◽  
Random Medium ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Conservation Of Energy ◽  
Transfer Processes

This paper considers the theory of the multiple scattering of waves in extensive random media. The classical theory of wave propagation in random media is discussed with reference to its practical limitations, and in particular to the inability of the lowest order approximation to the Bethe-Salpeter equation, which describes the propagation of correlations, to account for conservation of energy. An alternative kinetic theory is formulated, based on the theory of energy transfer processes in random media. The proposed theory satisfies conservation of energy and the Second Law of Thermodynamics. It is illustrated by a consideration of three problems each of which is difficult or impossible to treat by classical scattering theory. These involve the transmission of energy through a slab of random medium; the scattering theory of geometrical optics; and scattering by a randomly inhomogeneous half-space.

Conservation of energy in random media, with application to the theory of sound absorption by an inhomogeneous flexible plate

1973 ◽  
Vol 331 (1587) ◽  
pp. 479-496 ◽  
Keyword(s):  
Wave Propagation ◽  
Wave Field ◽  
Random Media ◽  
Mass Density ◽  
Second Law Of Thermodynamics ◽  
Coupled Systems ◽  
Flexible Plate ◽  
Random Component ◽  
Power Flux ◽  
Conservation Of Energy

This paper discusses the linear theory of wave propagation through conservative random media. By means of a simple illustrative example taken from acoustics it is verified that, at least uniformly to second order in an expansion parameter associated with the random fluctuations, the net flow of energy is from the mean, or coherent, wave field to the random component of the wave field (in accordance with the second law of thermodynamics). A general formula is derived for the distribution of the random modes of the system responsible for the power flux into the random field. These are demonstrated unambiguously (without recourse to the use of far field asymptotics) to be precisely those propagating modes which satisfy the homogeneous, non-random dispersion relation. The extension of the theory to a wider class of wave propagation problems is then outlined using an approach involving a Lagrangian density of wide generality. Finally the discussion is extended further to cover the case of coupled systems of wave-bearing media. An important analytical feature of such cases is the occurrence of ‘branch-cut’ integrals in the power flux formula. The situation is illustrated by an investigation of the power extracted from a plane sound wave incident on a flexible plate whose mass density is a random function of position. The division of the scattered power between the acoustic and plate bending modes is obtained, and comparison made with a heuristic argument leading to the same result.

Scattering of Poincaré waves by an irregular coastline

1973 ◽  
Vol 57 (1) ◽  
pp. 111-128 ◽  
Author(s):  
M. S. Howe ◽  
L. A. Mysak
Keyword(s):  
Energy Transfer ◽  
Random Function ◽  
Random Media ◽  
Kelvin Wave ◽  
Power Flux ◽  
Small Deviations ◽  
Transfer Processes ◽  
Dimensional Parameters ◽  
Gaussian Spectrum ◽  
Qualitative Discussion

This paper discusses the theory of the reflexion and scattering by an irregular coastline of a Poincaré-type wave on a rotating ocean. It is assumed that the coast is straight except for small deviations from the rectilinear form, and that these deviations may be regarded as a random function of position along the coast. The rigorous theory of energy-transfer processes in random media is applied to determine the power flux from the incident Poincard wave into the scattered Kelvin wave, which propagates in a unique direction along the coast, and into Poincard ocean wave noise. The relative efficiencies of generation of these waves is examined in some detail, and studied in particular for varying ranges of values of certain non-dimensional parameters characterizing the coastal configuration. Detailed estimates are given for a shoreline whose irregularities are specified by a Gaussian spectrum of Fourier components, and the results extra-polated in the concluding section of the paper to give a general qualitative discussion of the effects of an arbitrary coastline on an incident wave.

Accurate and efficient seismic modeling in random media

Geophysics ◽  
1993 ◽  
Vol 58 (4) ◽  
pp. 576-588 ◽  
Author(s):  
Guido Kneib ◽  
Claudia Kerner
Keyword(s):  
Wave Propagation ◽  
Finite Difference ◽  
Random Media ◽  
Polynomial Interpolation ◽  
Random Medium ◽  
High Order ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Finite Difference Schemes ◽  
Seismic Modeling

The optimum method for seismic modeling in random media must (1) be highly accurate to be sensitive to subtle effects of wave propagation, (2) allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths. This is necessary to obtain statistically meaningful overall attributes of wavefields. High order staggered grid finite‐difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling. Investigations for random media reveal that both methods lead to nearly identical wavefields. The small differences can be attributed mainly to differences in the numerical dispersion. This result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous. The differentiator can be longer than the medium scale length. High order staggered grid finite‐difference schemes are more efficient than pseudospectral methods in two‐dimensional (2-D) elastic random media.

Wave propagation in random media

1971 ◽  
Vol 45 (4) ◽  
pp. 769-783 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Wave Propagation ◽  
General Theory ◽  
Random Media ◽  
Random Medium ◽  
Dispersive Media ◽  
Transverse Waves ◽  
Small Deviations ◽  
The Mean ◽  
Density Inhomogeneities ◽  
Rough Boundaries

This paper discusses a general theory of wave propagation through a random medium whose random inhomogeneities are confined to small deviations from the mean. The theory is initially worked out in detail for the propagation of transverse waves along an infinite stretched string whose density is a random function of position. The manner in which the mean wave profile is modified by scattering from the density inhomogeneities is discussed in great detail, with particular emphasis on physical interpretation. The general theory of wave propagation in arbitrary dispersive or non-dispersive media is then discussed, and it is shown how the theory may be extended to wave propagation problems involving scattering from rough boundaries.

scholarly journals ANALISIS EKSERGI PENGERINGAN IRISAN TEMULAWAK

2016 ◽  
Vol 36 (01) ◽  
pp. 96
Author(s):  
Lamhot Parulian Manalu ◽  
Armansyah Halomoan Tambunan
Keyword(s):  
Exergy Analysis ◽  
Second Law Of Thermodynamics ◽  
Exergy Efficiency ◽  
Energy Utilization ◽  
Second Law ◽  
Process Conditions ◽  
Drying Process ◽  
Conservation Of Energy ◽  
Thin Layer Drying ◽  
Curcuma Xanthorrhiza

Java turmeric (Curcuma xanthorrhiza Roxb.) is a medicinal plant used as raw material for making herbal medicine, its rhizome cut into slices and dried so called simplicia. Curcuma has a harvest moisture content is high enough to need a great energy for drying. Generally, the theory used to analyze the energy efficiency is the first law of thermodynamics that describes the principle of conservation of energy. However, this theory has limitations in measuring the loss of energy quality. To determine whether the energy used in the drying process has been used optimally in terms of quality, the second law of thermodynamics -known as exergy analysis- is used. The purpose of this study is to determine the efficiency of the thin layer drying of curcuma slices with exergy analysis. The results show that the process conditions affect the energy utilization ratio and exergy efficiency of drying. Exergy analysis method based on the second law of thermodynamics has been used to determine the amount of exergy destroyed so that the efficiency of the drying process can be determined more accurately. Exergy efficiency varies between 96.5%-100% for temperatures of 50 °C to 70 °C at 40% RH and 82.3% - 100% for 20% to 40% RH at 50 °C.Keywords: Drying, energy, exergy efficiency, curcuma slices ABSTRAKTemulawak (Curcuma xanthorrhiza Roxb.) merupakan tanaman obat yang simplisianya digunakan sebagai bahan baku pembuatan jamu atau obat tradisional. Pengeringan merupakan proses utama dalam memproduksi simplisia. Untuk menganalisis efisiensi energi suatu proses pengeringan umumnya digunakan hukum termodinamika pertama yang menjelaskan tentang prinsip kekekalan energi. Akan tetapi teori ini mempunyai keterbatasan dalam mengukur penurunan kualitas energi. Untuk mengetahui apakah energi yang digunakan pada proses pengeringan sudah digunakan secara optimal dari sisi kualitas, digunakan hukum termodinamika kedua atau yang dikenal dengan analisis eksergi. Tujuan penelitian ini adalah menentukan efisiensi proses pengeringan lapisan tipis irisan temulawak dengan metode analisis energi dan eksergi. Dalam studi ini, metode analisis energi dan eksergi berdasarkan hukum termodinamika pertama dan kedua telah digunakan untuk menghitung rasio penggunaan energi dan besaran eksergi yang musnah (exergy loss). sehingga efisiensi proses pengeringan irisan temulawak dapat ditentukan secara akurat. Hasil penelitian menunjukkan bahwa kondisi proses pengeringan mempengaruhi rasio penggunaan energi dan efisiensi eksergi pengeringan. Semakin tinggi suhu dan RH pengeringan maka rasio penggunaan energi semakin rendah dan efisiensi eksergi semakin tinggi. Efisiensi eksergi pengeringan temulawak bervariasi antara 96,5%-100% untuk selang suhu 50 oC hingga 70 oC pada RH 40% serta 82,3% - 100% untuk selang RH 20% hingga 40% pada suhu 50 oC. Kata kunci: Pengeringan, energi, efisiensi eksergi, temulawak

scholarly journals Nature of Heat and Thermal Energy: From Caloric to Carnot’s Reflections, to Entropy, Exergy, Entransy and Beyond

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 584 ◽  
Author(s):  
Milivoje M. Kostic
Keyword(s):  
Energy Transfer ◽  
Internal Energy ◽  
Thermal Energy ◽  
Mechanical Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Generalized Entropy ◽  
Critical Issues ◽  
Thermal Phenomena

The nature of thermal phenomena is still elusive and sometimes misconstrued. Starting from Lavoisier, who presumed that caloric as a weightless substance is conserved, to Sadi Carnot who erroneously assumed that work is extracted while caloric is conserved, to modern day researchers who argue that thermal energy is an indistinguishable part of internal energy, to the generalization of entropy and challengers of the Second Law of thermodynamics, the relevant thermal concepts are critically discussed here. Original reflections about the nature of thermo-mechanical energy transfer, classical and generalized entropy, exergy, and new entransy concept are reasoned and put in historical and contemporary contexts, with the objective of promoting further constructive debates and hopefully resolve some critical issues within the subtle thermal landscape.

scholarly journals Discussion on the theory of relativity

1920 ◽  
Vol 97 (681) ◽  
pp. 66-79 ◽  
Keyword(s):  
Positive Result ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
The Sun ◽  
Theory Of Relativity ◽  
Universal Principle ◽  
Main Interest ◽  
Conservation Of Energy ◽  
Principle Of Relativity

Mr. J. H. Jeans: During the last century, two great dominating principles of physics emerged—the Conservation of Energy and the Second Law of Thermodynamics. The present century has already added a third member to this list, the principle of Relativity, which we are to discuss to-day. The three principles have in common that they do not explain how or why events happen; they merely limit the types of events which can happen. Thus the principle of Conservation of Energy shows that water cannot flow uphill; the Second Law of Thermodynamics shows that heat cannot flow from a cold body to a hot; the principle of Relativity shows that a planet cannot describe a perfect ellipse about the sun as focus. But it would be as unreasonable to expect the principle of Relativity to explain why a planet describes an orbit or how a ray of light is propagated as it would to propound the same questions to the principle of Conservation of Energy or the Second Law of Thermodynamics. All three principles deal with events, and not with the mechanism of events. The main interest of the new theory, however, is not merely that it discloses a new universal principle; it is rather that it discloses a new universe. Our former belief that the foundations of science had been laid for all time has been shattered; we now find that the land on which we had built was largely a mirage. New and mysterious continents appear for science to explore, but it is not for the theory of Relativity to explore them. The methods of that theory are destructive rather than constructive, and, when the theory predicts a positive result, it is invariably for the same reason, namely, that a process of exhaustion shows that any other result would be impossible.

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