Shell (United States)

A theory is developed for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid. The emphasis of the present treatment is on materials where fluid and solid are of comparable densities as for instance in the case of water-saturated rock. The paper denoted here as Part I is restricted to the lower frequency range where the assumption of Poiseuille flow is valid. The extension to the higher frequencies will be treated in Part II. It is found that the material may be described by four nondimensional parameters and a characteristic frequency. There are two dilatational waves and one rotational wave. The physical interpretation of the result is clarified by treating first the case where the fluid is frictionless. The case of a material containing viscous fluid is then developed and discussed numerically. Phase velocity dispersion curves and attenuation coefficients for the three types of waves are plotted as a function of the frequency for various combinations of the characteristic parameters.

The theory of propagation of stress waves in a porous elastic solid developed in Part I for the low-frequency range is extended to higher frequencies. The breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes. As in Part I the emphasis of the treatment is on cases where fluid and solids are of comparable densities. Dispersion curves for phase and group velocities along with attenuation factors are plotted versus frequency for the rotational and the two dilational waves and for six numerical combinations of the characteristic parameters of the porous systems. Asymptotic behavior at high frequency is also discussed.

A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid-solid medium is treated as a complex physical-chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.

The author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.

Abstract Quantitative information from electron spectroscopy for chemical analysis requires the use of suitable atomic sensitivity factors. An empirical set has been developed, based upon data from 135 compounds of 62 elements. Data upon which the factors are based are intensity ratios of spectral lines with F1s as a primary standard, value unity, and K2p 3/2 as a secondary standard. The data were obtained on two instruments, the Physical Electronics 550 and the Varian IEE‐15, two instruments that use electron retardation for scanning, with constant pass energy. The agreement in data from the two instruments on the same compounds is good. How closely the data can apply to instruments with input lens systems is not known. Calculated cross‐section data plotted against binding energy on a log‐log plot provide curves composed of simple linear segments for the strong lines: 1s, 2p 3/2 , 3d 5/2 and 4f 7/2 . Similarly, the plots for the secondary lines, 2s, 3p 3/2 , 4d 5/2 and 5d 5/2 , are shown to be composed of linear segments. Theoretical sensitivity factors relative to F1s should fall on similar curves, with minor correction for the combined energy dependence of instrumental transmission and mean free path. Experimental intensity ratios relative to F1s were plotted similarly, and best fit curves were calculated using the shapes of the theoretical curves as a guide. The intercepts of these best fit curves with appropriate binding energies provide sensitivity factors for the strong lines and the secondary lines for all of the elements except the rare earths and the first series of transition metals. For these elements the sensitivity factors are lower than expected, and variable, because of multi‐electron processes that vary with chemical state. From the data it can be shown that many of the commonly‐accepted calculated cross‐section data must be significantly in error—as much as 40% in some cases for the strong lines, and far more than that for some of the secondary lines.

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

The traveling-salesman problem is a generalized form of the simple problem to find the smallest closed loop that connects a number of points in a plane. Efforts in the past to find an efficient method for solving it have met with only partial success. The present paper describes a method of solution that has the following properties (a) It is applicable to both symmetric and asymmetric problems with random elements (b) It does not use subjective decisions, so that it can be completely mechanized (c) It is appreciably faster than any other method proposed (d) It can be terminated at any point where the solution obtained so far is deemed sufficiently accurate.

In the recent years, lithium-ion batteries have become the battery technology of choice for portable devices, electric vehicles and grid storage. While increasing numbers of car manufacturers are introducing electrified models into their offering, range anxiety and the length of time required to recharge the batteries are still a common concern. The high currents needed to accelerate the charging process have been known to reduce energy efficiency and cause accelerated capacity and power fade. Fast charging is a multiscale problem, therefore insights from atomic to system level are required to understand and improve fast charging performance. The present paper reviews the literature on the physical phenomena that limit battery charging speeds, the degradation mechanisms that commonly result from charging at high currents, and the approaches that have been proposed to address these issues. Special attention is paid to low temperature charging. Alternative fast charging protocols are presented and critically assessed. Safety implications are explored, including the potential influence of fast charging on thermal runaway characteristics. Finally, knowledge gaps are identified and recommendations are made for the direction of future research. The need to develop reliable onboard methods to detect lithium plating and mechanical degradation is highlighted. Robust model-based charging optimisation strategies are identified as key to enabling fast charging in all conditions. Thermal management strategies to both cool batteries during charging and preheat them in cold weather are acknowledged as critical, with a particular focus on techniques capable of achieving high speeds and good temperature homogeneities.

Ion-molecule reactions of the sort observed as secondary reactions in mass spectrometers have been treated by the methods of the modern kinetic theory; that is, the rate of reaction is expressed in terms of the velocity distribution functions of the reactants and the cross section for the reaction. The cross section, which is calculated by means of the properties of the classical collision orbits, is found to have an inverse square root dependence on energy. The ion distribution function, which is far from Maxwellian, is found by means of an explicit solution of the Boltzmann equation. A simple relation is given which relates the mass spectrometric data to the specific rate of the same reaction under thermal conditions. For the simpler molecules, this rate may be calculated completely a priori, with excellent agreement with experiment.

The theory of acoustic propagation in porous media is extended to include anisotropy, viscoelasticity, and solid dissipation. A more refined analysis of the relative motion of the fluid in the pores is also developed by introducing the concept of viscodynamic operational tensor. The nature of this operator is analyzed by applying variational and Lagrangian methods. Viscoelasticity and solid dissipation are introduced by applying the correspondence principle as derived from thermodynamics in earlier work by the author. Various dissipative models are discussed and the corresponding operators and relaxation spectra are derived. The physical chemistry of the multiphase porous medium including surface effects lies within the scope of the thermodynamic theory. The nature of thermoelastic dissipation and electrokinetic effects in relation to the thermodynamic theory is also brought out.

Abstract We review the highlights of the 1988 symposium on Palaeozoic Biogeography and Palaeogeography, and present a revised set of 20 Palaeozoic base maps that incorporate much of the new data presented at the symposium. The maps include 5 major innovations: (1) A preliminary attempt has been made to describe the motion of the Cathaysian terranes during the Palaeozoic; (2) a more detailed description of the events surrounding the Iapetus Ocean is presented; (3) an alternative apparent polar wandering path for Gondwana has been constructed using the changing distributions of palaeoclimatically restricted lithofacies; (4) new palaeomagnetic data have been incorporated that places Laurentia and Baltica at more southerly latitudes, and adjacent to Gondwana, during the Early Devonian; Siberia is also placed further south in the light of biogeographic data presented at the symposium; (5) Kazakhstan is treated as a westward extension of Siberia, rather than as a separate palaeocontinent. The relationships between climatic changes, sea level changes, evolutionary radiations and intercontinental migrations are discussed

Abstract The origin of interfacial turbulence, spontaneous agitation of the interface between two unequilibrated liquids, has been explained in terms of classical flow, diffusion, and surface processes. The essence of the explanation is the long‐known though much neglected Marangoni effect, wherein movement in an interface is caused by longitudinal variations of interfacial tension. It is proposed that interfacial turbulence is a manifestation of hydrodynamic instability, which is touched off by ever present, small, random fluctuations about the interface. A simplified mathematical model has been analyzed in order to detail the mechanism of the “interfacial engine” which supplies the mechanical energy of interfacial turbulence. In its present form the analysis incorporates several drastic simplifications, though ways of removing some of these have been suggested. The groundwork has been laid for the more elaborate analyses that are needed for a decisive test of the theory. The analysis shows how some systems may be stable with solute transfer in one direction yet unstable with transfer in the opposite direction, a striking result. It also suggests that interfacial turbulence is usually promoted by (1) solute transfer out of the phase of higher viscosity, (2) solute transfer out of the phase in which its diffusivity is lower, (3) large differences in kinematic viscosity and solute diffusivity between the two phases, (4) steep concentration gradients near the interface, (5) interfacial tension highly sensitive to solute concentration, (6) low viscosities and diffusivities in both phases, (7) absence of surface‐active agents, and (8) interfaces of large extent. That some of these effects have been observed in the laboratory lends credence to the theory.

The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.

Summary We use the tectonics of Eastern Anatolia to exemplify many of the different aspects of collision tectonics, namely the formation of plateaux, thrust belts, foreland flexures, widespread foreland/hinterland deformation zones and orogenic collapse/distension zones. Eastern Anatolia is a 2 km high plateau bounded to the S by the southward-verging Bitlis Thrust Zone and to the N by the Pontide/Minor Caucasus Zone. It has developed as the surface expression of a zone of progressively thickening crust beginning about 12 Ma in the medial Miocene and has resulted from the squeezing and shortening of Eastern Anatolia between the Arabian and European Plates following the Serravallian demise of the last oceanic or quasioceanic tract between Arabia and Eurasia. Thickening of the crust to about 52 km has been accompanied by major strike-slip faulting on the right-lateral N Anatolian Transform Fault (NATF) and the left-lateral E Anatolian Transform Fault (EATF) which approximately bound an Anatolian Wedge that is being driven westwards to override the oceanic lithosphere of the Mediterranean along subduction zones from Cephalonia to Crete, and Rhodes to Cyprus. This neotectonic regime began about 12 Ma in Late Serravallian times with uplift from wide-spread littoral/neritic marine conditions to open seasonal wooded savanna with colluvial, fluvial and limnic environments, and the deposition of the thick Tortonian Kythrean Flysch in the Eastern Mediterranean. Earthquake hypocentres are scattered throughout the region but large earthquakes are concentrated mainly on the major faults and are mostly shallow, supporting the idea of a brittle elastic lid with hypocentres concentrated towards its base with more ductile deformation in the middle and lower crust. Neotectonic magmatic suites are nepheline-hypersthene normative alkali basalts of mantle origin, and silicic/intermediate/mafic calcalkaline suites, both suites occurring in pull-apart basins in strike-slip regimes and along N-S extensional fissures, and both suites showing a strong change to central activity in the Pliocene. Upper-crustal strains appear to be discontinuous in space and time, with zones of strong shortening representing shoaling of crustal detachment zones flattening between 5 and 10 km. Approximately NW- (dextral) and NE- (sinistral) trending lineaments bound less deformed wedges (low relief seismically ‘dead’ areas) and vary from simple strike-slip faults to complicated braided transform-flake boundaries with pull-apart and compressional segments (N and E Anatolian Transform Faults). Volcanoes lie in grabens on N-S ‘cracks’ that extend into the Arabian Foreland and in transcurrent pull-aparts. Major extensional basins lie at plate (Adana) and flake (Karliova) triple junctions and result from compatibility problems.

The formation of a single product from terminal functionalization of linear alkanes from a transition metal-catalyzed reaction is reported. The rhodium complex Cp*Rh(eta(4)-C(6)Me(6)) (Cp*, C(5)Me(5); Me, methyl) catalyzes the high-yield formation of linear alkylboranes from commercially available borane reagents under thermal conditions. These reactions now allow catalytic, regiospecific functionalization of alkanes under thermal conditions. The organoborane products are among the most versatile synthetic intermediates in chemistry and serve as convenient precursors to alcohols, amines, and other common classes of functionalized molecules.

Abstract Equations of elasticity and consolidation for a porous elastic material containing a fluid have been previously established (1, 5). General solutions of these equations for the isotropic case are developed, giving directly the displacement field or the stress field in analogy with the Boussinesq-Papkovitch solution and the stress functions of the theory of elasticity. General properties of the solutions also are examined and the viewpoint of eigenfunctions in consolidation problems is introduced.

A distributed model predictive control (MPC) framework, suitable for controlling large-scale networked systems such as power systems, is presented. The overall system is decomposed into subsystems, each with its own MPC controller. These subsystem-based MPCs work iteratively and cooperatively towards satisfying systemwide control objectives. If available computational time allows convergence, the proposed distributed MPC framework achieves performance equivalent to centralized MPC. Furthermore, the distributed MPC algorithm is feasible and closed-loop stable under intermediate termination. Automatic generation control (AGC) provides a practical example for illustrating the efficacy of the proposed distributed MPC framework.

Selective partial oxidation of methane to methanol suffers from low efficiency. Here, we report a heterogeneous catalyst system for enhanced methanol productivity in methane oxidation by in situ generated hydrogen peroxide at mild temperature (70°C). The catalyst was synthesized by fixation of AuPd alloy nanoparticles within aluminosilicate zeolite crystals, followed by modification of the external surface of the zeolite with organosilanes. The silanes appear to allow diffusion of hydrogen, oxygen, and methane to the catalyst active sites, while confining the generated peroxide there to enhance its reaction probability. At 17.3% conversion of methane, methanol selectivity reached 92%, corresponding to methanol productivity up to 91.6 millimoles per gram of AuPd per hour.

A vibrational and attendant conformational analysis of the liquid n-paraffins and molten polyethylene is presented. For the purposes of the analysis a valence force field was derived which is applicable to both planar and nonplanar chains. The force field was evaluated from observed frequencies of trans (T) and gauche (G) n-C4H10; TT and GT n-C5H12; TTT, GTT, and TGT n-C6H14; and (T)∞ polyethylene, all of whose infrared spectra were assigned in detail. Infrared spectra of the liquid-n-paraffins n-C4H10 through n-C17H36 were measured at room temperature and n-C4H10 through n-C12H26 also at a temperature just above their melting point. Frequencies and normal coordinates were calculated for the extended forms and for forms having one gauche bond of n-C4H10 through n-C8H18. These quantities were also calculated for the conformations of n-C5H12 through n-C7H16 having two gauche bonds and for the nonplanar but regular conformations (TG)∞ and (G)∞ of polyethylene. Some bands attributable to forms of n-C5H12 and n-C6H14 having two gauche bonds were found. In the case of n-C5H12 the energy difference between the GT and TT states was found to be nearly the same as that between the GG and GT states. Bands in the region 1400–1300 cm−1 were found to be characteristic of specific conformations involving sequences of five or fewer methylenes, such as —GTTG— (1338 cm−1), —GTG (1368 and 1308 cm−1), —GG— (1352 cm−1), and terminal —TG groups (1344 cm−1). All these bands together with two broader ones centered near 1270 and 1080 cm−1 owe their intensity to the wagging of methylenes adjoining gauche bonds. An interpretation of the general features of the C–C-stretching, methylene-rocking, and methylene-scissoring regions is given. Bands associated with molecules or chains having trans sequences involving at least four methylene groups are found. In the region 1300–1150 cm−1 there are chain-length-dependent band progressions resembling those observed for the crystalline n-paraffins. These indicate the presence of molecules with gauche bonds, but these gauche bonds are few in number and are located near the ends of the chains. It is shown that for certain kinds of vibrations, particularly totally symmetric C–C stretching and ∠CCC bending, there is very little change in frequency in going from a fully extended chain to one having one or even two or more gauche bonds. Hence, it is very difficult in the case of the longer n-paraffins to distinguish spectroscopically between fully extended and almost fully extended conformations.

The onset of steady, cellular convection driven by surface tension gradients on a thin layer of liquid is examined in an extension of Pearson's (1958) stability analysis. By accounting for the possibility of shape deformations of the free surface it is found that there is no critical Marangoni number for the onset of stationary instability and that the limiting case of ‘zero wave-number’ is always unstable. Surface viscosity of a Newtonian interface is found to inhibit stationary instability. A simple criterion is found for distinguishing visually the dominant force, buoyancy or surface tension, in cellular convection in liquid pools.