Local Rules: Emergence on Organizational Landscapes

This paper proposes that the theory of local rules provides a model for explaining organizational behavior as an emergent property of a fitness landscape. While local rule theory has its genesis in evolutionary biology, this paper links it to work in computational mathematical organizational theory. It further proposes that there are conditions, characterized by coadaptation, under which rules will survive in relatively stable forms, and other conditions, characterized by competition, under which local rules will change. The paper then discusses how catastrophe analysis can provide insights into changing patterns of organizational interactions. A discussion of methodology outline shows developments in agent-based simulation modeling can contribute to the development of local rule theory.     

Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

A comparison between the cnoidal wave and an approximate periodic solution to the Korteweg-de Vries equation

Summary The motion of small-but finite-amplitude waves in shallow water is often modeled by the well-known Korteweg-de Vries (KdV) equation. Here we consider a case in which no solitons are present and compare the exact periodic travelling-wave solutions of the KdV equation (the cnoidal wave) to an approximate periodic solution of this equation previously obtained by the authors. We find that the approximate wave form is graphically indistinguishable from the cnoidal wave for a wide range of wave amplitudes. Furthermore, by extending the amplitude range up to the breaking wave limit we find that the approximate wave form is still a close representation of the cnoidal wave. This suggests that the approximate solution, which is just a simple formula, might be used for many practical calculations in place of the more difficult to compute cnoidal wave.

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Riassunto L'evoluzione in acqua bassa di onde di ampiezza piccola ma finita è spesso descritta dalla classica equazione di Korteweg-de Vries (KdV). è qui considerato un caso senza solitoni e l'esatta soluzione stazionaria periodica dell'equazione di KdV (nota come onda cnoidale) è confrontata con una soluzione periodica approssimata precedentemente ottenuta dagli autori. I risultati del confronto mostrano che la soluzione approssimata è graficamente indistinguibile dall'onda cnoidale in un ampio intervallo di ampiezze d'onda. Aumentando l'ampiezza d'onda fino al limite della rottura dell'onda stessa si mostra che la soluzione approssimata è ancora una buona rappresentazione dell'onda cnoidale. Questi risultati suggeriscono che la soluzione approssimata, espressa da una formula molto semplice, possa essere usata in molti calcoli applicativi al posto della piú complicata onda cnoidale.

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Резюме Движение волн с малой, но конечной амплитудой на мелкой воде часто моделируется с помощью хорошо известного уравнения Кортевега-де Вриса. В этой работе мы рассматриваем случай отсутствия солитонов и сравниваем точное периодическое распространяющее волновое решение уравнения Кортевега-де Вриса (?кноидальная? волна) с приближенным периодическим решением этого уравнения, ранее полученным авторами. Мы находим, что приближенная волновая форма графически наразличима от ?кноидальной? волны в широкой области амплитуд. Кроме того, распространяя область амплитуд вплоть до нарушення волнового предела, мы получаем, что приближенная волновая форма еще хорошо аппроксимирует ?кноидальную? волну. Этот результат позволяет предположить, что приближенное решение, которое описывается простой формулой, мож⪟т быть использовано в большом числе практических вычислений вместо более сложного выражения.

     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

Detection of triplet-singlet transitions by magnetic circular dichroism,with application to the spectrum of acrolein

An apparatus constructed for the purpose of investigating high resolution gas phase magnetic circular dichroism (MCD) spectra of triplet-singlet transitions is described. It has been used to obtain MCD spectra of acrolein with path lengths up to 28 meters and magnetic fields up to 3 kG. Some of the relative merits of MCD and magnetic rotation spectra (MRS) are discussed.     

A note on the numerical solution of a periodic parabolic problem

A direct method is presented for the numerical determination of solutions of the heat conduction equation having periodT in time. A simple error analysis which improves previous results is given.     

Transition metal derivatives of 1,1′-dichloroferrocene

Complexes of the general formula [Cl₂Fc] _nML, (Cl₂Fc = C1C₅H₄FeC₅H₃Cl; ML = Fe(CO)₂C₅H₅, AuP(C₆H₅)₃, Mn(CO)₅ or Ir(CO)[P(C₆H₅)₃]₂ when n = 1; ML = Ti(C₅H₅)₂ when n = 2) have been prepared from a salt elimination reaction between 1,1′-dichloro-2-lithioferrocene and transition metal halide complexes. Spectroscopic properties of the compounds are reported. The titanium complex exists in meso and dl forms.     

The numerical solution of a periodic parabolic problem subject to a nonlinear boundary condition

The numerical solution by finite differences of a periodic parabolic problem subject to a nonlinear boundary condition is considered. It is shown that Newton's method can be used to solve the nonlinear equations provided a suitable initial approximation is known, and a method for constructing this first approximation is given.