Thermodynamic Limit for the Ising Model on the Cayley Tree

While the Ising model on the Cayley tree has no spontaneous magnetization at nonzero temperatures in the thermodynamic limit, we show that finite systems of astronomical sizes remain magnetically ordered in a wide temperature range, if the symmetry is broken by fixing an arbitrary single (bulk or surface) spin. We compare the behavior of the finite size magnetization of this model with that of the Ising model on both the Sierpinski Gasket, and the one-dimensional linear chain. This comparison reveals the analogy of the behavior of the present model with the Sierpinski Gasket case.Comment: 5 pages, 4 figure

Identification and analysis of screw compressor mechanical losses

Screw compressors are compact machines, used for a wide range of applications where gases or vapours are required to be delivered at moderate pressures with high efficiency and reliability. They are most effective when the compressed medium requires power inputs, approximately in the 10 kW - 1-2 MW range. At lower inputs alternatives such as reciprocating and scroll compressors are preferable and at higher inputs turbo-compressors are more suitable. In industrialised countries, compressors absorb 15-20% of the total electrical power generated. Hence there is a continuing demand to improve their efficiency. This is normally expressed as the specific power consumption, which is the power required to compress unit mass of gas delivered. There already exist mathematical models to assist in the design of such machines and to estimate their performance, which include the estimation of the dynamic loads acting on the rotors and bearings and these loads determine their mechanical efficiency. However, these models do not estimate the magnitude of the mechanical losses, which are only guesstimated as an additional increment to the power required to compress the gas. Such an approximation does not enable the optimum selection of bearings and lubricating oil to minimise the frictional power losses. The aim of the study, described in this paper, was to estimate the effect of the individual parameters responsible for mechanical power loss in oil injected screw compressors and is focussed on the losses incurred in the gear box, bearings and shaft seals. It was found that in the gearbox, meshing, bearing and seal losses all increase both with speed and gear ratio. In the main rotors, it was found that sliding friction losses in the bearings are not significantly affected by the radial load, nor are rolling friction losses significantly dependent on the axial load. However, both axial and radial loads have a significant effect on the total frictional power loss. Lubricant viscosity affects the frictional power losses but the oil level does not

Introduction to Khovanov Homologies. I. Unreduced Jones superpolynomial

An elementary introduction to Khovanov construction of superpolynomials. Despite its technical complexity, this method remains the only source of a definition of superpolynomials from the first principles and therefore is important for development and testing of alternative approaches. In this first part of the review series we concentrate on the most transparent and unambiguous part of the story: the unreduced Jones superpolynomials in the fundamental representation and consider the 2-strand braids as the main example. Already for the 5_1 knot the unreduced superpolynomial contains more items than the ordinary Jones.Comment: 33 page

Functional Brain Network Changes Associated with Maintenance of Cognitive Function in Multiple Sclerosis

In multiple sclerosis (MS) functional changes in connectivity due to cortical reorganization could lead to cognitive impairment (CI), or reflect a re-adjustment to reduce the clinical effects of widespread tissue damage. Such alterations in connectivity could result in changes in neural activation as assayed by executive function tasks. We examined cognitive function in MS patients with mild to moderate CI and age-matched controls. We evaluated brain activity using functional magnetic resonance imaging (fMRI) during the successful performance of the Wisconsin card sorting (WCS) task by MS patients, showing compensatory maintenance of normal function, as measured by response latency and error rate. To assess changes in functional connectivity throughout the brain, we performed a global functional brain network analysis by computing voxel-by-voxel correlations on the fMRI time series data and carrying out a hierarchical cluster analysis. We found that during the WCS task there is a significant reduction in the number of smaller size brain functional networks, and a change in the brain areas representing the nodes of these networks in MS patients compared to age-matched controls. There is also a concomitant increase in the strength of functional connections between brain loci separated at intermediate-scale distances in these patients. These functional alterations might reflect compensatory neuroplastic reorganization underlying maintenance of relatively normal cognitive function in the face of white matter lesions and cortical atrophy produced by MS

User defined nodal displacement of numerical mesh for analysis of screw machines in FLUENT

Growing demands to reduce energy consumption are driving researchers towards in-depth analysis of positive displacement machines. Twin screw compressors are amongst the most common types of positive displacement machines. These machines have inherently complex geometry due to intricate rotor profiles used. As the details of the internal flows are difficult to obtain experimentally, Computational Fluid Dynamics (CFD) offers a good alternative for evaluation of internal flow patterns. However, implementation of CFD is challenging due complex deforming geometries. In this paper, a customised grid generator SCORGTM developed by authors is used to generate numerical meshes for commercially available solver ANSYS FLUENT. FLUENT is an unstructured solver which offers flexibility of using both segregated and coupled solution algorithms. Segregated algorithms are generally faster which results in shorter product development time. Interface with FLUENT is implemented by performing User Defined Nodal Displacements (UDND) of grids generated by SCORG in a parallel framework. For this purpose, SCORG and UDND are coupled and extended to work with FLUENT's parallel architecture. The developed code is compiled within the solver. The oil free air screw compressor with 'N' profile rotors and 3/5 lobe combination is modelled for 8000 RPM and 6000 RPM. Finally, the predicted performance values with FLUENT are compared to previously calculated CFX predictions and experimental results. FLUENT requires shorter solution time to obtain same accuracy of CFX

Peeling the Otolith of Fish: Optimal Parameterization for Micro-CT Scanning

In this paper, we aim to provide optimal parameters for micro-computed tomography scans of fish otoliths. We tested fifteen different combinations to sagittae. The images were scaled to Hounsfield units, and segmented in two distinct volumes-of-interest (external and internal). The strategy we applied, for identifying optimum scan settings for otoliths, included analyses of the sinogram, the distribution of the Hounsfield units and the signal-to-noise ratio. Based on these tests, the optimum sets of parameters for the acquisition of tomographic images of sagittal otoilths were 80 kV, 220 μA, and 0.5 mm aluminum filter. The method allowed 3D shape analysis, internal and external density distribution, layer-by-layer density segmentation, and a potential objective method to count growth rings in otoliths. It was possible to compare mean densities between species, and we observed a significant difference among them. In addition, there are ontogenic changes, which could be increasing or decreasing the density. In this study, we applied tomography for several otolith analysis, that could be of great interest for future studies in diverse areas that use otoliths as the basic structure of analysis, or represents a new research line called eco-densitometry of otoliths, where tomography could be applied to explore the density within an ecological perspective.Fil: Vasconcelos Filho, Jonas. Universidad Federal Rural Pernambuco; BrasilFil: Thomsen, Felix Sebastian Leo. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Stosic, Borko. Universidad Federal Rural Pernambuco; BrasilFil: Antonino, Antonio C. D.. Universidad Federal Rural Pernambuco; BrasilFil: Duarte, Daniel A.. Universidad Federal Rural Pernambuco; BrasilFil: Heck, Richard J.. University of Guelph; CanadáFil: Lessa, Rosangela P. T.. Universidad Federal Rural Pernambuco; BrasilFil: Santana, Francisco M.. Universidad Federal Rural Pernambuco; BrasilFil: Ferreira, Beatrice P.. Universidad Federal Rural Pernambuco; BrasilFil: Duarte Neto, Paulo J.. Universidad Federal Rural Pernambuco; Brasi

Giant and tunable excitonic optical anisotropy in single-crystal CsPbX3_3 halide perovskites

During the last years, giant optical anisotropy demonstrated its paramount importance for light manipulation which resulted in numerous applications ranging from subdiffraction light guiding to switchable nanolasers. In spite of recent advances in the field, achieving continuous tunability of optical anisotropy remains an outstanding challenge. Here, we present a solution to the problem through chemical alteration of the ratio of halogen atoms (X = Br or Cl) in single-crystal CsPbX$_3$ halide perovskites. It turns out that the anisotropy originates from an excitonic resonance in the perovskite, which spectral position and strength are determined by the halogens composition. As a result, we manage to continually modify the optical anisotropy by 0.14. We also discover that the halide perovskite can demonstrate optical anisotropy up to 0.6 in the visible range -- the largest value among non-van der Waals materials. Moreover, our results reveal that this anisotropy could be in-plane and out-of-plane, depending on perovskite shape -- rectangular and square. Hence, it can serve as an additional degree of freedom for anisotropy manipulation. As a practical demonstration, we created perovskite anisotropic nanowaveguides and show a significant impact of anisotropy on high-order guiding modes. These findings pave the way for halide perovskites as a next-generation platform for tunable anisotropic photonics.Comment: 18 pages, 3 figure

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page