The Randic index and the diameter of graphs

The {\it Randi\'c index} $R(G)$ of a graph $G$ is defined as the sum of 1/\sqrt{d_ud_v} over all edges $uv$ of $G$, where $d_u$ and $d_v$ are the degrees of vertices $u$ and $v,$ respectively. Let $D(G)$ be the diameter of $G$ when $G$ is connected. Aouchiche-Hansen-Zheng conjectured that among all connected graphs $G$ on $n$ vertices the path $P_n$ achieves the minimum values for both $R(G)/D(G)$ and $R(G)- D(G)$. We prove this conjecture completely. In fact, we prove a stronger theorem: If $G$ is a connected graph, then $R(G)-(1/2)D(G)\geq \sqrt{2}-1$, with equality if and only if $G$ is a path with at least three vertices.Comment: 17 pages, accepted by Discrete Mathematic

Novel magnetoinductance effects in Josephson Junction Arrays: A single-plaquette approximation

Using a single-plaquette approximation, novel magnetoinductance effects in Josephson junction arrays (JJAs) are predicted, including the appearance of steps in the temperature behavior of magnetic susceptibility. The number of steps (as well as their size) is controlled by the kinetic inductance of the plaquette whose field dependence is governed by the Abrikosov vortices penetrating superconducting regions of the array. The experimental conditions under which the predicted effects should manifest themselves in artificially prepared JJAs are discussed.Comment: Accepted for publication in PL

Potential Causes of Increased Vocalisation in Elderly Cats with Cognitive Dysfunction Syndrome as assessed by their owners

The objectives of this study were to explore owner perception of the causes of increased vocalisation in cats diagnosed with cognitive dysfunction syndrome (CDS) and consider what impact this vocalisation may have on the cat’s household. Owners of cats diagnosed with CDS that presented with increased vocalisation were invited to complete an online survey. The survey consisted of 28 questions including the cat’s signalment, its medical history, and questions pertaining to the owner’s perception of what motivated their cat´s increased vocalisation. This was determined by looking at the cat’s behaviour when vocalising, where it was looking when it was vocalising, and if the vocalisation stopped when the owner interacted with it, e.g., petting or feeding it. The owners were also asked how stressful they found their cat’s vocalisation. There were 37 responses. The majority of owners reported that the main cause of their cat’s vocalisation appeared to be disorientation (40.5%) or attention seeking (40.5%). Seeking a resource such as food was reported in 16.2%, and pain was perceived to be the cause in only 2.7% of cats. However, the majority of owners (64.8%) believed there was >1 cause of their cat’s increased vocalisation. Importantly, when owners were asked how stressful they found their cat’s increased vocalisation, 40.5% scored ≥3 (where 1 = not stressful; 5 = significantly stressful). This study provides novel insight into owner perception of feline CDS, as well as potential causes for increased vocalisation; this will allow veterinarians to better advise owners on how to manage their cat with CDS

Dynamical reentrance and geometry imposed quantization effects in Nb-AlOx-Nb Josephson junction arrays

In this paper, we report on different phenomena related to the magnetic properties of artificially prepared highly ordered (periodic) two-dimensional Josephson junction arrays (2D-JJA) of both shunted and unshunted Nb-AlOx-Nb tunnel junctions. By employing mutual-inductance measurements and using a high-sensitive bridge, we have thoroughly investigated (both experimentally and theoretically) the temperature and magnetic field dependence of complex AC susceptibility of 2D-JJA. We also demonstrate the use of the scanning SQUID microscope for imaging the local flux distribution within our unshunted arrays

Nano-porosity in GaSb induced by swift heavy ion irradiation

Nano-porous structures form in GaSb after ion irradiation with 185 MeV Au ions. The porous layer formation is governed by the dominant electronic energy loss at this energy regime. The porous layer morphology differs significantly from that previously reported for low-energy, ion-irradiated GaSb. Prior to the onset of porosity, positron annihilation lifetime spectroscopy indicates the formation of small vacancy clusters in single ion impacts, while transmission electron microscopy reveals fragmentation of the GaSb into nanocrystallites embedded in an amorphous matrix. Following this fragmentation process, macroscopic porosity forms, presumably within the amorphous phase.The authors thank the Australian Research Council for support and the staff at the ANU Heavy Ion Accelerator Facility for their continued technical assistance. R.C.E. acknowledges the support from the Office of Basic Energy Sciences of the U.S. DOE (Grant No. DE-FG02-97ER45656)

An Improved hybrid DC circuit breaker with self-adaptive fault current limiting capability

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe effective fault current limiting is very significant for the dc distribution system. However, the traditional dc fault current limiting method, i.e., directly installing dc reactor, may trigger negative impacts the system normal operation and fast isolation of the circuit breaker. Therefore, an improved hybrid dc circuit breaker with self-adaptive fault current limiting capability is proposed in this article. Not only can it realize fault current limitation in a quick and efficient manner, but also ensures the continuous operation of the converter and the fault ride-through of the healthy network after the dc fault. In this sense, the requirements on the protection and arrester capacity are reduced. Compared with other types of fault current limiting methods, the proposed topology has the merit of few negative effects on system stability and transient response. It can effectively perform fault current limiting and fault isolation, with low conduction loss and low implementation difficulty. The working principle and advantages of the proposed topology are verified by experimental tests and simulation cases.Peer ReviewedPostprint (author's final draft

Thermoelectrical Field Effects in Low Dimensional Structure Solar Cells

Taking into account the temperature gradients in solar cells, it is shown that their efficiency can be increased beyond the Shockley-Queisser limit (J. Appl. Phys. 32 (1961) 510). The driving force for this gain is the temperature gradient between this region and its surroundings. A quantitative theory is given. Though the effect is found to be weak in conventional solar cells, it is argued that it can be substantially increased by proper choice of materials and design of the device. In particular, it is shown that the insertion of a quantum well can enhance the efficiency beyond one of the single gap cell, due to the presence of temperature jumps at the heterojunctions.Comment: Published in Special issue Physica E 14 (1-2) on Nanostructures in Photovoltaic