882 resultados para Finite fields


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A simple extended finite field nuclear relaxation procedure for calculating vibrational contributions to degenerate four-wave mixing (also known as the intensity-dependent refractive index) is presented. As a by-product one also obtains the static vibrationally averaged linear polarizability, as well as the first and second hyperpolarizability. The methodology is validated by illustrative calculations on the water molecule. Further possible extensions are suggested

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In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

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In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence

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Two common methods of accounting for electric-field-induced perturbations to molecular vibration are analyzed and compared. The first method is based on a perturbation-theoretic treatment and the second on a finite-field treatment. The relationship between the two, which is not immediately apparent, is made by developing an algebraic formalism for the latter. Some of the higher-order terms in this development are documented here for the first time. As well as considering vibrational dipole polarizabilities and hyperpolarizabilities, we also make mention of the vibrational Stark effec

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The guidelines presented in this document are a preliminary strategy for establishing a comprehensive policy for the needs of training and education wiyhin the sector and adjoining areas, across fields of knowledge and professions concerned, on relevant levels and for the varies institutions and operators. The objective of these guidelines is to analysis the problems, objectives and goals for development of a far reaching system of educational and training programs and courses for museums, cultural heritage and related fields of activities. This objective comprises a close collaboration between museum, cultural heritage organizations and educating organizations, notably within universities and colleges, but also other kinds of educating bodies.

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Museology has emerged and has been organised as a field of knowledge, precisely to frame the technical, theoretical and methodological aspects, regarding the constitution, implementation and evaluation of the processes that societies establish for the selection, treatment and extroversion of the memory indicators, transforming them into patrimonial references and projecting them into the constitutive fields of cultural heritage. It is therefore, one of the areas of knowledge that deals with the framing of heritage and their professionals are agents of memory education. The constitution of the parameters that define and delimit the museological action field has been outlined in the course of the centuries, if we consider the technical efforts related to the identification and organisation of collections, in addition to the curatorial treatment of specimens from nature, of objects, of the intangible heritage registers. The same length of elaboration is true if we evaluate the communication initiatives and of education of the senses.

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This paper investigates finite-stretching corrections to the classical Milner-Witten-Cates theory for semi-dilute polymer brushes in a good solvent. The dominant correction to the free energy originates from an entropic repulsion caused by the impenetrability of the grafting surface, which produces a depletion of segments extending a distance $\mu \propto L^{-1}$ from the substrate, where $L$ is the classical brush height. The next most important correction is associated with the translational entropy of the chain ends, which creates the well-known tail where a small population of chains extend beyond the classical brush height by a distance $\xi \propto L^{-1/3}$. The validity of these corrections is confirmed by quantitative comparison with numerical self-consistent field theory.