Resonant X-Ray Scattering and the<i> j</i>_eff=1/2 Electronic Ground State in Iridate Perovskites

The resonant x-ray scattering (magnetic elastic, RXMS, and inelastic, RIXS) of Ir4+ at the L2,3 edges relevant to spin-orbit Mott insulators An+1IrnO3n+1 (A=Sr, Ba, etc.) are calculated using a single-ion model which treats the spin-orbit and tetragonal crystal-field terms on an equal footing. Both RXMS and RIXS in the spin-flip channel are found to display a nontrivial dependence on the direction of the magnetic moment, μ. Crucially, we show that for μ in the ab plane, RXMS in the cross-polarized channel at the L2 edge is zero irrespective of the tetragonal crystal field; spin-flip RIXS, relevant to measurements of magnons, behaves reciprocally, being zero at L2 when μ is perpendicular to the ab plane. Our results have important implications for the assignment of a jeff=1/2 ground state on the basis of resonant x-ray experiments

Об уравнениях типа Буссинеска полностью нелинейных и одного порядка дисперсии: вывод и сравнительный анализ

В настоящей работе дан альтернативный вывод однослойной и двухслойной нелинейной модели типа Буссинеска порядка O(μ2 ) (μ -параметр дисперсии) в терминах градиента от задаваемого потенциала скорости на поверхностях слоя жидкости, определяемых свободными параметрами. Проведено сравнение линейных дисперсионных и нелинейных характеристик с моделями типа Буссинеска порядка O(μ2 ) , записанными в терминах компонент вектора скорости, равного градиенту потенциала, заданного на произвольных поверхностях слоя воды, а также в терминах средней скорости.У даній роботі наведено альтернативне отримання одношарової та двошарової нелінійної моделі типу Бусінеска порядку O(μ2 ) (μ -параметр дисперсії) у термінах градієнта від заданого потенціалу швидкості на поверхнях шару рідини, що визначається довільними параметрами. Проведено порівняння лінійних дисперсійних та нелінійних характеристик з моделями типу Бусінеска порядку O(μ2 ) , записаними у термінах компонент вектора швидкості, що дорівнює градієнту потенціала, який задається на довільних поверхнях шару води, а також у термінах середньої швидкості.Alternative derivation of Boussinesq-type one-layer and two-layer nonlinear model of O(μ2 ) order (μ is dispersion parameter) written with terms of gradient of velocity potential is presented. The last is being determined on the fluid layers surface defined by free parameters. Both linear dispersion and nonlinear characteristics comparisons for Boussinesq-type models of the order O(μ2 ) written with terms of the velocity vector equal to potential gradient defined on the arbitrary surface of the water layer, and with terms of the average velocity were fulfilled

A New Look at the So-Called Trammel of Archimedes

The paper begins with an elementary treatment of a standard trammel (trammel of Archimedes), a line segment of fixed length whose ends slide along two perpendicular axes. During the motion, points on the trammel trace ellipses, and the trammel produces an astroid as an envelope that is also the envelope of the family of traced ellipses. Two generalizations are introduced: a zigzag trammel, obtained by dividing a standard trammel into several hinged pieces, and a flexible trammel whose length may vary during the motion. All properties regarding traces and envelopes of a standard trammel are extended to these more general trammels. Applications of zigzag trammels are given to problems involving folding doors. Flexible trammels provide not only a deeper understanding of the standard trammel but also a new solution of a classical problem of determining the envelope of a family of straight lines. They also reveal unexpected connections between various classical curves; for example, the cycloid and the quadratrix of Hippias, curves known from antiquity

The atomic orbitals of the topological atom

The effective atomic orbitals have been realized in the framework of Bader’s atoms in molecules theory for a general wavefunction. This formalism can be used to retrieve from any type of calculation a proper set of orthonormalized numerical atomic orbitals, with occupation numbers that sum up to the respective Quantum Theory of Atoms in Molecules (QTAIM) atomic populations. Experience shows that only a limited number of effective atomic orbitals exhibit significant occupation numbers. These correspond to atomic hybrids that closely resemble the core and valence shells of the atom. The occupation numbers of the remaining effective orbitals are almost negligible, except for atoms with hypervalent character. In addition, the molecular orbitals of a calculation can be exactly expressed as a linear combination of this orthonormalized set of numerical atomic orbitals, and the Mulliken population analysis carried out on this basis set exactly reproduces the original QTAIM atomic populations of the atoms. Approximate expansion of the molecular orbitals over a much reduced set of orthogonal atomic basis functions can also be accomplished to a very good accuracy with a singular value decomposition procedure

An inverse of the evaluation functional for typed Lambda-calculus

In any model of typed λ-calculus conianing some basic arithmetic, a functional p - * (procedure—* expression) will be defined which inverts the evaluation functional for typed X-terms, Combined with the evaluation functional, p-e yields an efficient normalization algorithm. The method is extended to X-calculi with constants and is used to normalize (the X-representations of) natural deduction proofs of (higher order) arithmetic. A consequence of theoretical interest is a strong completeness theorem for βη-reduction, generalizing results of Friedman [1] and Statman [31: If two Xterms have the same value in some model containing representations of the primitive recursive functions (of level 1) then they are provably equal in the βη- calculus

Uncertainty and stepwise investment

We analyze the optimal investment strategy of a firm that can complete a project either in one stage at a single freely chosen time point or in incremental steps at distinct time points. The presence of economies of scale gives rise to the following trade-off: lumpy investment has a lower total cost, but stepwise investment gives more flexibility by letting the firm choose the timing individually for each stage. Our main question is how uncertainty in market development affects this trade-off. The answer is unambiguous and in contrast with a conventional real-options intuition: higher uncertainty makes the single-stage investment more attractive relative to the more flexible stepwise investment strategy

Occupational choice, number of entrepreneurs and output: theory and empirical evidence with Spanish data

This paper extends the (Lucas, Bell J Econ 9:508–523,1978) model of occupational choices by individuals with different skills, beyond the simple options of self-employment or wage-employment, by including a second choice for the self-employed. That is, an option to hire employees and so become self-employed with employees (SEWEs), or to be self-employed without employees (SEWNEs). We solve for the market equilibrium and examine the sensitivity of relative sizes of occupational groups, and of the level of productivity, to changes in the exogenous parameters. The results show that the positive (negative) association between number of SEWEs (SEWNEs) and productivity, observed in the Spanish data, can be explained, under certain conditions, as the result of cross-region and time differences in average skills. These findings point to the importance of distinguishing between SEWEs and SEWNEs in drawing valid conclusions concerning any link between entrepreneurship and economic development

Dynamic one-sided out-of-plane behavior of unreinforced-masonry wall restrained by elasto-plastic tie-rods

Past earthquakes have shown the high vulnerability of existing masonry buildings, particularly to out-of-plane local collapse mechanisms. Such mechanisms can be prevented if façades are restrained by tie rods improving the connections to perpendiculars walls. Whereas in the past only static models have been proposed, herein the nonlinear equation of motion of a monolithic wall restrained by a tie rod is presented. The façade, resting on a foundation and adjacent to transverse walls, rotates only around one base pivot and has one degree of freedom. Its thickness is explicitly accounted for and the tie rod is modeled as a linear elastic—perfectly plastic spring, with limited displacement capacity. The model is used to investigate the response to variations of wall geometry (height/thickness ratio, thickness), tie rod features (vertical position, length, prestress level), and material characteristics (elastic modulus, ultimate elongation, yield strength) typical of historical iron. The most relevant parameter is the steel strength, whereas other characteristics play minor roles allowing to recommend reduced values for pre-tensioning forces. The force-based procedure customary in Italy for tie design is reasonably safe and involves protection also against collapse, although probably not enough as desirable