90 research outputs found
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
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Calculation of clearances in twin screw compressors
Clearances between rotating and stationary parts in a screw compressor are set to ensure the efficient operation and allow for thermal deformation without unwanted contacts. The change in clearances is caused by both pressure and temperature changes within the machine. If clearances are too large, the increased leakage flows will reduce efficiency. However, if the nominal clearances are too small, contacts between the rotating and stationary parts can occur as a consequence of rotor and casing deformations. In order to determine the operational clearances, a numerical analysis of deformation of screw compressor rotors and casing has to be performed. This paper discusses how the temperature of rotor and casing surfaces calculated from the one-dimensional chamber model in the SCORG could be used as a boundary conditions for a steady state thermal and structural analysis of a screw compressor solid parts. Deformations of rotors and casing under temperature load were calculated using a commercial Finite Element Analysis code ANSYS. Operational clearance are estimated from these deformations and some recommendations for further work are proposed
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
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
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Muscle architecture and passive lengthening properties of the gastrocnemius medialis and Achilles tendon in children who idiopathically toe-walk
Children who idiopathically toe-walk (ITW) habitually operate at greater plantarflexion angles and thus, at shorter muscle-tendon unit (MTU) lengths than typically developing (TD) children. Therefore, it is often assumed that habitual use of the gastrocnemius muscle in this way will cause remodelling of the muscle-tendon architecture compared to TD children. However, the gastrocnemius muscle architecture of children who ITW has never been measured. It is essential that we gain a better understanding of these muscle-tendon properties, to ensure that appropriate clinical interventions can be provided for these children. Five children who ITW (age 8 ± 2 years) and 14 TD children (age 10 ± 2 years) participated in this study. Ultrasound was combined with isokinetic dynamometry and surface electromyography, to measure muscle architecture at common positions and passive lengthening properties of the gastrocnemius muscle and tendon across full range of motion. Regardless of which common condition groups were compared under, both the absolute and normalised to MTU muscle belly and fascicle lengths were always longer, and the Achilles tendon length was always shorter in children who ITW than TD children (p 0.05); however, passive joint stiffness was greater in children who ITW at maximum dorsiflexion (p = 0.001) and at a joint moment common to all participants (p = 0.029). Consequently, the findings of this pilot study indicate a remodelling of the relative MTU that does not support the concept that children who ITW commonly experience muscle shortening. Therefore, greater consideration of the muscle and tendon properties are required when prescribing clinical interventions that aim to lengthen the MTU, and treatments may be better targeted at the Achilles tendon in children who ITW
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