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

Letting Accuracy \u27Sync\u27 In: The Role of Synchrony in Perceptions of Personality Traits and Affective States

The human propensity to synchronize their behaviors to one another seems to be an ever-present aspect of our social lives. While a breadth of approaches have been taken to explain this phenomenon, the benefit of individuals temporally aligning their behaviors to one another during an interaction remains to be precisely identified. Some have argued that by becoming synchronized to the movements and actions of another, one may become a better perceiver of that other’s internal attributes (Hoehl et al., 2021). The purpose of the present thesis was to explore this potential benefit of synchrony by examining its relation to one’s ability to accurately judge the personality traits and affective states of an interaction partner. A secondary purpose was to explore whether these two interpersonal processes central to face-to-face interactions, synchrony and interpersonal accuracy, would be hindered if they took place over a videoconferencing platform. Groups of two strangers (N = 196 participants, N = 98 dyads) logged onto a videoconferencing platform (Zoom) with an experimenter and were asked to engage in a five-minute long recorded “getting-to-know-you” interaction. Subsequently, participants were asked to complete a variety of questionnaires including judgments of their partner’s personality traits and affective states from the prior interaction. Accuracy for judgments of personality traits and affective states was operationalized as the correlation between participant’s judgments of their partners states and traits, and their partner’s self-reported states and traits. The recordings derived from these interactions underwent rigorous coding by eight trained research assistants in order to determine the extent to which interactants’ behaviors were synchronized with one another during the first 30-seconds, middle 30-seconds, and last 30-seconds of conversation. Results supported that dyads whose movements were more synchronized with one another during their interaction were subsequently more accurate judges of their interaction partner’s personality traits and affective states. However, this relationship was only significant when examined during the beginning of the interaction, indicating that becoming temporally aligned to an interaction partner within the first 30-seconds of conversation seems to be most important for facilitating accuracy for interpersonal judgments of that person. In addition, the predictive validity relationships observed between synchrony, interpersonal accuracy, and a collection of theoretically-related outcome variables suggested that individuals’ tendency to synchronize with one another, as well as form accurate judgments of another’s states and traits, was likely not substantially hindered by videoconferencing platforms. These findings not only help refine existing theoretical frameworks regarding synchrony and accuracy, but help to address core questions regarding the benefits of humans’ innate tendency to synchronize their behaviors with one another

Extended graphical calculus for categorified quantum sl(2)

A categorification of the Beilinson-Lusztig-MacPherson form of the quantum sl(2) was constructed in the paper arXiv:0803.3652 by the second author. Here we enhance the graphical calculus introduced and developed in that paper to include two-morphisms between divided powers one-morphisms and their compositions. We obtain explicit diagrammatical formulas for the decomposition of products of divided powers one-morphisms as direct sums of indecomposable one-morphisms; the latter are in a bijection with the Lusztig canonical basis elements. These formulas have integral coefficients and imply that one of the main results of Lauda's paper---identification of the Grothendieck ring of his 2-category with the idempotented quantum sl(2)---also holds when the 2-category is defined over the ring of integers rather than over a field.Comment: 72 pages, LaTeX2e with xypic and pstricks macro

Long-term correlations in hourly wind speed records in Pernambuco, Brazil

AbstractWe study the statistical properties of hourly wind speed time series detected at four weather stations in the state of Pernambuco, Brazil, in the period 2008–2009. We find that the average and maximum hourly wind speeds deviate from a mutual linear relationship, and that they may be well explained individually by a Weibull distribution, however, with different shape parameter values. On the other hand, the long-term correlations of both of these observables obey the same power-law behavior, with two distinct scaling regimes. Our results agree with previous studies on wind speed series correlations in other regions of the world, which is suggestive of universal behavior

Rotor clearance design and evaluation for an oil injected twin screw compressor

Designing twin screw compressors to safely operate at higher than normal temperatures poses a challenge as the compressor must accommodate larger peak thermal distortions while ideally maintaining efficiency at nominal operating conditions. This paper will present a case study of an oil injected compressor tested at elevated discharge temperatures with original and revised clearances. The local thermal distortions occurring within the compressor during operation were estimated using a procedure developed by the authors - thermodynamic results from a chamber model were used to approximate component temperature distributions that are then used to predict possible thermal distortions and the resulting affect on clearance gaps. The original and revised clearance designs are evaluated and performance penalties incurred due to the modifications are discussed

Turbulent Flow Measurements near the Discharge Port of a Screw Compressor

Mean flow and turbulence characteristics have been measured within the male and female rotors close to the discharge port of a double screw compressor at different radial positions, two axial positions from the exit port, Hp, and two radial planes, αp. Cycle-resolved axial and tangential mean flow measurements and their corresponding turbulent velocity fluctuations were made over a time window of 1° using a laser Doppler velocimetry, LDV, system. Measurements were performed through two transparent windows near the inlet of the discharge port inside the male and female working chambers. The results revealed a highly complex 3-D flow within the male and female working chambers, in particular, near the discharge port with two distinct flow zones 1 and 2 before and after the opening of the port, respectively. The flow in zone 1 was controlled by the rotor motion while in zone 2 was greatly influenced by the discharge process. In zone 2, both components of mean velocities were subjected to a sudden increase in velocity forming strong axial and tangential jet flows due to rapid change in pressure across the port as the flow is exposed into the discharge port. It was found that the flow structures have been affected considerably by the position of the discharge port, radial planes and radial positions. Axial and tangential RMS velocity distributions within both rotors were found to be relatively high and less affected by the flow changes of zones 1 and 2 with almost uniform distribution. The measured magnitudes of axial and tangential RMS velocities suggest it would be reasonable to assume the local turbulence to be isotropic for the modelling purposes. To authors’ knowledge, the results are unique, original and in great details not only to describe the flow structure, but also, they can be used in CFD codes to establish a reliable model of the flow and pressure distribution within twin screw machines

Investigation of turbulent flow characteristics within screw compressor

The material presented in this paper is part of a research project dedicated to investigate the fluid mean velocity distribution and the corresponding turbulence fluctuations at various cross-sections across the working and discharge chambers of a screw compressor, in order to characterise the flow development through the working chamber and its discharge port at different phase angles. The axial mean flow and the corresponding turbulent fluctuation were measured inside the machine, both upstream and downstream of the discharge port, with high spatial and temporal resolution using laser Doppler Velocimetry (LDV) at a rotational speed of 1000 rpm and a pressure ratio of 1.0