Solutions of the Polchinski ERG equation in the O(N) scalar model

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit $N=\infty$, where many properties can be analyzed analytically.Comment: 34 pages, 10 figures. References added. Version accepted for publication in the International Journal of Modern Physics

Order and Disorder in AKLT Antiferromagnets in Three Dimensions

The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure

Prediction of stiffness from orientation data of glass reinforced injection moldings

The complex thermo-mechanical process developing in injection molding leads to through-thickness and point to point variation of fiber orientation. It is not economically viable to characterize experimentally the variation of fiber orientation. Thus, efforts have been put into modeling the fiber orientation in injection molding. Some commercially available programs already allow the prediction of fiber orientation distribution in moldings. If the fiber orientation field is known it is possible to calculate the major elastic properties, which can be input into finite-element structural analysis codes to predict product performance. That approach was followed in this work to compare the experimental flexure behavior of glass fiber reinforced polycarbonate injection molded discs with predictions obtained from FEM simulations. The data used in the FEM code was calculated from the fiber orientation data predicted using the software C-Mold.(undefined

Optimized generation of spatial qudits by using a pure phase spatial light modulator

We present a method for preparing arbitrary pure states of spatial qudits, namely, D-dimensional (D > 2) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with complex transmission are displayed on a spatial light modulator (SLM). In a recent work we have shown a method that requires a single phase-only SLM to control independently the complex coefficients which define the quantum state of dimension D. The amplitude information was codified by introducing phase gratings inside each slit and the phase value of the complex transmission was added to the phase gratings. After a spatial filtering process we obtained in the image plane the desired qudit state. Although this method has proven to be a good alternative to compact the previously reported architectures, it presents some features that could be improved. In this paper we present an alternative scheme to codify the required phase values that minimizes the effects of temporal phase fluctuations associated to the SLM where the codification is carried on. In this scheme the amplitudes are set by appropriate phase gratings addressed at the SLM while the relative phases are obtained by a lateral displacement of these phase gratings. We show that this method improves the quality of the prepared state and provides very high fidelities of preparation for any state. An additional advantage of this scheme is that a complete 2\pi modulation is obtained by shifting the grating by one period, and hence the encoding is not limited by the phase modulation range achieved by the SLM. Numerical simulations, that take into account the phase fluctuations, show high fidelities for thousands of qubit states covering the whole Bloch sphere surface. Similar analysis are performed for qudits with D = 3 and D = 7.Comment: 12 pages, 7 figure

Prediction of low frequency vibration and sound propagation through reinforced concrete structures

Prediction of low frequency sound fields generated in buildings by internal sources as machines or external sources such as road or rail traffic is a difficult task. Assuming that the source is well known, predictions are generally based on the Finite Element Method (FEM), which is used to model building structures and vibration and sound fields, but other hybrid or coupling methods also can be used. In general, these methods are too much time consuming and provide results which are reliable only below 100-150 Hz. Reliability at higher frequencies requires much larger models. It is, thus, important to develop simpler methods to be used with confidence by acousticians and other consultants. In the present paper a method for prediction of vibration propagation to building slabs based on the use of simplified transfer functions between fundamental joints of the structure is presented. The method was developed numerically for traditional multi-storey building with reinforced concrete slabs supported by reinforced concrete beams and columns and also was experimentally validated. The method can be used together with theoretical modal analysis to predict sound fields in dwellings

Caracterização da propagação de vibração através de estruturas de edifícios de betão armado

Este artigo descreve os parâmetros que controlam a propagação da vibração através de estruturas de edifícios de betão armado para frequências abaixo de 200 Hz. A influência das propriedades dos materiais e das dimensões dos elementos estruturais foi avaliada com modelos de elementos finitos validados experimentalmente, considerando cinco tipos de funções de transferência de aceleração: i) da fundação para o primeiro piso; ii) entre pisos intermédios; iii) do último piso para a cobertura; iv) entre troços do mesmo piso intermédio; e v) entre troços da cobertura. Os resultados mostram que a transmissão de vibração depende não tanto do número de pisos mas mais de parâmetros como a espessura da laje, no caso da transmissão da vibração num pavimento, ou a esbelteza dos pilares, no caso da propagação de vibração das fundações para o primeiro piso. Observa-se que, apesar da amplitude de vibração ser maior para elementos estruturais mais flexíveis, os elementos mais rígidos transmitem efectivamente mais energia devido a um menor efeito dissipativo. Os resultados também mostram que a atenuação piso-a-piso é aproximadamente constante para todos os pisos excepto a cobertura, onde a atenuação diminui por via da redução do número de caminhos de dissipação de energia.info:eu-repo/semantics/publishedVersio