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Asset and cash flow gains are expected when one company acquires another, from the point of view of the market. Since the gains are not on operations, but rather social gains and gains for stockholders, it could also be said that gains are not expected.

Calculations of the photoionization cross section and asymmetry parameter, β, are performed at the density functional theory (DFT) and time-dependent density functional theory (TDDFT) levels for all 32 valence levels of C60. Accurate numerical results are obtained for the isolated molecule in icosahedral symmetry. A detailed analysis based on the comparison between the DFT and TDDFT results allows the identification of four types of resonances: the well-known confinement resonances of mainly geometrical origin, shape resonances native to the ionization channel, induced shape resonances, and autoionization resonances brought about by interchannel coupling, as well as their different prominence in cross section or asymmetry parameter. Generally, cross sections are enhanced at the TDDFT level, which includes contribution from the bound-state excitations from closed channels, neglected at the DFT level, and the effect persists even well above the highest ionization threshold. This effect is best seen in the total cross section, although not as dramatic as found from simpler models, probably due to the stiffer electronic structure inherent in the full molecular description. The effects of interchannel coupling on individual native resonances are rather less predictable, leading to both enhancement and decreases and often altering the details of the structure significantly. A comparison with the previous accurate total cross-sectional calculations, as well as with the available experimental data, is very good for cross sections but slightly inferior for β’s. The results reported can serve as a reference to compare the effects of different environments on C60, as well as chemical substitution, notably endohedral fullerenes.

For the complex systems modeller, uncertainty is ever-present. While uncertainty cannot be eliminated, we suggest that formally incorporating an assessment of uncertainty into our models can provide great benefits. Sources of uncertainty arise from the model itself, theoretical flaws, design flaws, and logical errors. Management of uncertainty and error in complex systems models calls for a structure for uncertainty identification and a clarification of terminology. In this paper, we define complex systems and place complex systems models into a common typology leading to the introduction of complex systems specific issues of error and uncertainty. We provide examples of complex system models of land use change with foci on errors and uncertainty and finally discuss the role of data in building complex systems models.

We investigate the case of resonance-induced deviations of the angular distribution anisotropy parameter, ?, from its nominal value of 2.0 for the Kr 4s-subshell at the 3d ? mp(m? 5) excitations and the Xe 5s-subshell in the region of the 4d ? mp(m? 6) excitations. We observe small but unmistakable variations of ? from 2.0 at these resonances. In the case of Kr the largest deviation from 2.0 is a mere ?0.030(6), ?4s= 1.970(6), while in Xe it is definitively larger at ?0.080(6), ?5s= 1.920(6). To understand these results in more detail, we have carried out relativistic random phase and relativistic multi-channel quantum defect calculations. Our theoretical results clearly indicate deviations of ? from 2.0 for these photolines in these resonance regions, although the degree of variation is predicted to be larger than what is observed.

The effects of spin–orbit induced interchannel coupling on the dipole photoelectron angular asymmetry parameter β_3d for Xe, Cs and Ba are explored using a modified version of the spin-polarized random phase approximation with exchange (SPRPAE) methodology. For Xe, _3/2 → εf shape resonance, and this effect is significantly more pronounced in Cs where the resonance is larger. In Ba, however, where f-wave orbital collapse has occurred, the shape resonance has moved below threshold and the effect of interchannel coupling on _3/2 threshold is negligible. But below the 3d_3/2 threshold, _3/2 → 4f resonance.

The relativistic resonances between the 2p3/2and 2p1/2thresholds of the first three members of the Ne isoelectronic sequence are shown to evolve in a highly complex manner along the sequence. The phenomenon is explained, and its generality over the entire periodic table is established. These results show that the coupling scheme required for accurate calculations can change dramatically from species to species along a sequence. This can have important implications for calculations of near-threshold photoionization and low-energy electron-ion recombination rates of astrophysical importance.

Simple procedures are presented for treating cumulative fatigue damage under complex loading history using either the Damage Curve concept or the Double Linear Damage Rule. A single equation is provided for use with the Damage Curve approach; each loading event providing a fraction of damage until failure is presumed to occur when the damage sum becomes unity. For the Double Linear Damage Rule, analytical expressions are provided for determining the two phases of life. The procedure involves two steps, each similar to the conventional application of the commonly used Linear Damage Rule. When the sum of cycle ratios based on Phase I lives reaches unity, Phase I is presumed complete, and further loadings are summed as cycle ratios based on Phase II lives. When the Phase II sum reaches unity, failure is presumed to occur. No other physical properties or material constants than those normally used in a conventional Linear Damage Rule analysis are required for application of either of the two cumulative damage methods described. Illustrations and comparisons of both methods are discussed.

Dipole-allowed single photoionization of some closed shell atoms and ions has been investigated in the relativistic random-phase approximation (RRPA). Application of relativisticmultichannel quantum defect theory (RMQDT) is made together with RRPA to analyse autoionizing resonances. Analysis points to the importance of interchannel coupling in high energy photoionization and reveals various degeneracies in relativistic atomic spectra to influence the low energy dynamics. Interesting threshold behavior in photoelectron spin polarization has been seen. Prospective future studies have been indicated.

A brief review is presented of developments in analysis of creep-rupture data, including Time-Temperature Parameters, the Minimum Commitment Method, and Successive Regression. The role of Dr. Robert Goldhoff in this progress is emphasized.

Using extensive data on forty-seven materials including steels, aluminum, and titanium alloys, a new equation has been derived for estimating fatigue properties from simple tensile data at the temperature of interest in the sub-creep range. Compared to the Universal Slopes Equation previously proposed by Manson and Hirschberg, the new equation provides predictions that agree more closely with the measured fatigue properties over the entire life range. The earlier Universal Slopes Equation now in common use involves only ductility in the estimation of the plastic line whereas the improved equation involves both tensile strength and ductility in the estimation of the plastic line. A new equation was also derived for a large class of materials suitable for use in the cryogenic temperature range (ten different structural alloys and metals tested at liquid helium and liquid nitrogen temperatures). Here, as in the original Universal Slopes Equation, the plastic line did not require a tensile strength term. Although new constants were derived for the cryogenic range, the final predictions provided about the same degree of accuracy as the original Universal Slopes Equation.

A discussion is presented of the fatigue process as one of initiating a crack and propagating it to failure, and a formula is presented for estimating the effective point of crack initiation. This formula is speculatively applied to three interface problems in fatigue: (a) Life of a quasi-brittle material which can sustain only a relatively small crack before failure takes place according to the laws of fracture mechanics. An example is presented to illustrate the procedure and to indicate the probable validity of the approach. (b) Estimation of the fatigue characteristics at high temperatures within the creep range of materials. By assuming that intercrystalline cracking has the effect of by-passing much of the crack initiation process, the number of cycles to failure becomes related more importantly to the crack propagation period. A numerical procedure for estimating life in terms of applied strain range is described, and its validity investigated by application to a number of materials for which data have been presented in the literature. (c) Application of a linear damage rule individually to crack initiation and crack propagation. It is possible to predict the effect of order of application of loads in a two-step cumulative fatigue test. The method is checked by using literature data.

A method using finite-difference recurrence relations is presented for direct extrapolation of families of curves. The method is illustrated by applications to creep-rupture data for several materials and it is shown that good results can be obtained without the necessity for any of the usual parameter concepts.

An approximate method for computing transient thermal stresses in hollow cylinders, plates, and hollow spheres is presented. The method makes use of polynomial approximations to the temperature distribution by means of which the partial differential equation of the problem is reduced to a set of first-order ordinary differential equations. Nonuniform initial temperature distribution and heat transfer from both surfaces can be treated without difficulty making possible the practical solution of problems with relatively little labor for which an exact solution requires a great expenditure of labor and time. Several examples are presented and compare favorably with more accurate solutions.

The dependence of thermal-shock resistance on two parameters k and σf/Eα (when k is conductivity, σf the fracture stress, E the elastic modulus, and α the coefficient of thermal expansion) is experimentally demonstrated by the fact that the relative ratings of two materials may change with a change of quench severity. The theory of thermal-shock resistance of a disk quenched at the periphery is developed, making use of the results of Jaeger. Two criteria for failure are considered; namely, the maximum normal-stress criterion, and the criterion of maximum “risk of rupture” based on the Weibull statistical theory. Equipment for subjecting these specimens to a wide range of quench severities of known surface heat-transfer coefficients is described, and results are presented for thermal-shock tests of steatite and glass disks. The results for steatite are then utilized for determination of thermal-shock parameters by four independent methods, the results showing good agreement.

The fatigue behavior of several steels, AISI 4130, E52100, and 304 ELC stainless, as well as that of a nonferrous alloy, 5456-H311, was investigated in rotating bending fatigue after these materials were subjected to a prestress for different cyclic histories. The data obtained corroborated the hypothesis proposed by the authors earlier that lines representing the S – log N relation of a material prestressed in varying amounts will intersect the S – log N line of the original material near a common point. A correlation was found between the stress at this intersection point and the ultimate tensile strength. Thus, the only requirements for establishing the fatigue behavior of a prestressed material in the range of stresses where the S – log N line is inclined are the S – log N line of the original material and the ultimate tensile strength. The importance of determining the new endurance limit of a material after prestressing was shown analytically. The omission from cycle ratio summations of cyclic histories applied below the original, but above the new, endurance limit of a material was shown for an illustrative example to result in a cycle ratio summation less than unity, which leads to unconservative estimates of fatigue life. Cyclic histories so applied can produce damage and must be taken into account. A new hypothesis based upon actual fatigue behavior and incorporating a cycle ratio-modified stress ratio factor is suggested, which holds promise for predicting more accurately the new endurance limit than most existing methods. Extensive additional tests are required to verify this concept.

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A general method is presented for the solution of creep problems by the use of successive approximations. The method is equally applicable to different creep laws and loading paths. Examples are presented for the creep in a flat plate with a temperature gradient and for several cases of rotating disks. In these disk problems the transient conditions prior to the establishment of steady-state stress distribution are included and shown to have an appreciable effect on the total creep strains. The use of different cumulative creep laws such as the time-hardening and strain-hardening laws are illustrated.

Charts that speed heat-exchanger calculations and aid analysis of other ducted gas flows are illustrated and examples of their use are presented.

Calculations of the photoionization cross section of the 2p and 3s subshells of free Ar and Ar@C60 as examples have been performed using the molecular structure of the confined system and time-dependent density functional theory for the dynamical quantities. The results for Ar2p in the combined system exhibit significant confinement resonances with the lower-energy ones being quite sharp, in contrast to the results of jellium-model calculations. In addition, calculations done with and without interchannel coupling between the photoionization channels of the 2p subshell of the Ar atom and the 1s subshell of the C60 shell show that, in this case, the coupling is of negligible importance, even though the C1s cross section is more than an order of magnitude larger than that of Ar2p in the 300 eV range. The Ar3s, which is not hybridized, also exhibits confinement resonances, but is very strongly affected by interchannel coupling with photoionization channels from the C60 shell. The phenomenology of both 2p and 3s subshells is explained in terms of the interchannel-coupling matrix elements. These results should be applicable to inner-shell ionization of essentially any endohedral fullerene system. [ABSTRACT FROM AUTHOR]

Experimental cross sections and cross-section ratios reported in the literature for direct double ionization of the outer shells of helium, neon, and argon atoms resulting from bare ions ranging from protons to uranium and for antiprotons are analyzed in terms of a first- and second-order interference model originally proposed by McGuire [J. H. McGuire, Phys. Rev. Lett. 49, 1153 (1982)]. Empirical formulas for the various contributions to double ionization plus information about the phase difference between the first- and second-order mechanisms are extracted from the data. Projectile and target scalings are also extracted. Total cross sections and their ratios determined using these formulas and scalings are shown to be in very good agreement with experimental data for lower-Z projectiles and impact velocities larger than 1 a.u. For very-high-Z projectiles, the amount of double ionization is overestimated, probably due to saturation of probabilities that is not accounted for in scaling formulas. [ABSTRACT FROM AUTHOR]

It is demonstrated that the effect of a static cage potential on the photoionization of endohedrally enclosed atoms can be incorporated into standard /¿-matrix calculations using one of two independent methods. For photoionization processes occurring entirely within the fullerene, the outer-region solutions can be modified by the additional cage potential to yield phase-shifted Coulomb functions that are matched to the inner-region R matrix. Alternatively, if the cage potential is contained within the /¿-matrix “box,” it can be directly incorporated into the formalism via simple one-electron integral contributions to the Hamiltonian, yielding a modified R matrix. Both methods are applied to the photoionization of Xe@C6o in the vicinity of the giant 4d → ∊f shape resonance and are found to be in excellent agreement with each other [ABSTRACT FROM AUTHOR]

Photoionization cross-section calculations are performed on the ground state ([Ne]3s23p64s2Se1/2) and the first two excited states {[Ne]3s23p63d2De3/2 and [Ne]3s23p63d2De5/2) of Ca+ ions for photon energies from threshold to 45.0 eV using the relativistic (Breit-Pauli) /f-matrix method. The discrete Ca2+ orbitals are generated using the computer program AUTOSTRUCTURE; 30 configurations are included in the configuration-interaction calculation for the states of Ca2+. The prominent 3p → 3d giant resonances are analyzed and identified, and our results are compared with experimental results, and rather good agreement is found. Using results of our previous photoionization calculations on Sc2+ and Ti3+ ions, the strongest and broadest resonances in the photoionization cross section of those three ions (Ca+, Sc2+, and Ti3+), in terms of width and oscillator strengths, are compared to show the evolution as a function of nuclear charge. [ABSTRACT FROM AUTHOR]

Photoionization cross sections and photoelectron angular distribution asymmetry parameters are calculated for the 4d10, 5s², 5p6, and 6s² subshells of atomic barium as a test of the relativistic multiconfiguration Tamm-Dancoff (RMCTD) method. The shape resonance present in the near-threshold region of the 4d subshell is studied in detail in the 4d photoionization along with the 5s, 5p, and 6s subshells in the region of the 4d thresholds, as the 4d shape resonance strongly influences these subshells in its vicinity. The results are compared with available experiment and other many-body theoretical results in an effort to assess the capabilities of the RMCTD methodology. The electron correlations addressed in the RMCTD method give relatively good agreement with the experimental data, indicating that the important many-body correlations are included correctly. [ABSTRACT FROM AUTHOR]

The effects of endohedral confinement on the correlation energy of Be, Mg, and Ca atoms have been investigated using modified Hartree-Fock and multiconfiguration Hartree-Fock methods where the endohedral system (A@C60) is approximated as an atom enclosed in an attractive spherically symmetric potential well of inner radius r∼5.8 a.u. and thickness of Δ∼1.89 a.u., and correlation energies are studied as a function of the depth of the confining potential (0≤U0≤1 a.u.) to give some idea as to how the correlation energy behaves in different endohedral environments. In general, we have found that as a function of well depth, starting from the free atom, valence electrons diffuse outward in the presence of the confining potential, which causes the electrons to be further apart, thereby decreasing the correlation energy; however, with further increase of well depth, the valence electrons become trapped in the confining well and, as a result of their being closer together, the correlation energy increases. [ABSTRACT FROM AUTHOR]

We conduct a systematic study of the dipole phase and the photoelectron group delay (Wigner time delay) in inner shell photoionization of noble gas atoms from Ne to Xe. Our study encompasses the tender x-ray spectral range and extends to 1 keV photoelectron energy. We employ both the relativistic and the nonrelativistic versions of the random-phase approximation with exchange. We identify the long-range Coulomb and short-range Hartree-Fock contributions to the dipole phase which governs the Wigner time delay variation from the threshold to the whole considered range of photoelectron energies. [ABSTRACT FROM AUTHOR]

Photoionization cross sections and dipole angular distribution asymmetry parameters, ß, of 5s and Ad shells of the closed-shell ions (La3+, La9+, and La11+) in the La isonuclear sequence have been studied using the relativistic random phase approximation. The positions of the 5s Cooper minima in La3+ and La9+ ions are found to be extremely sensitive to the details of electron correlation. The results show that the 5s cross sections of La3+ and La9+ do not lie along the same curve near the thresholds; the Ad cross sections, however, do match well in overlap regions so they lie along the same curve, over the isonuclear sequence, except for a shift in threshold towards higher energies with increasing degree of ionization. [ABSTRACT FROM AUTHOR]

Initial insight into time delay in Mn photoionization in the region of the 3p->,3d giant autoionization resonance is gained in the framework of the "spin-polarized" random-phase approximation with exchange. The dramatic effect of the giant autoionization resonance on the time delay of photoemission from the 3d and 4s valence subshells of the Mn atom is unraveled. Strong sensitivity of the time delay of the 4s photoemission to the final-state term of the ion remainder [Mn+(4s¹,5S) vs Mn+(4s¹', 7S)] is discovered. It is shown that photoionization time delay in the autoionizing resonance region is explicitly associated with the resonance lifetime, which can thus be directly measured in attosecond time-delay experiments. Similar features are expected to emerge in photoionization time delays of other transition-metal and rare-earth atoms with half-filled subshells that possess giant autoionization resonances as well. [ABSTRACT FROM AUTHOR]