Icosahedron designs

It is known from the work of Adams and Bryant that icosahedron designs of order v exist for v ≡ 1 (mod 60) as well as for v = 16. Here we prove that icosahedron designs exist if and only if v ≡ 1, 16, 21 or 36 (mod 60), wit

Designs for graphs with six vertices and nine edges

The design spectrum has been determined for eleven of the 21 graphs with six vertices and nine edges. In this paper we completely solve the design spectrum problem for the remaining ten graphs

Spontaneous thermal runaway as an ultimate failure mechanism of materials

The first theoretical estimate of the shear strength of a perfect crystal was given by Frenkel [Z. Phys. 37, 572 (1926)]. He assumed that as slip occurred, two rigid atomic rows in the crystal would move over each other along a slip plane. Based on this simple model, Frenkel derived the ultimate shear strength to be about one tenth of the shear modulus. Here we present a theoretical study showing that catastrophic material failure may occur below Frenkel's ultimate limit as a result of thermal runaway. We demonstrate that the condition for thermal runaway to occur is controlled by only two dimensionless variables and, based on the thermal runaway failure mechanism, we calculate the maximum shear strength $\sigma_c$ of viscoelastic materials. Moreover, during the thermal runaway process, the magnitude of strain and temperature progressively localize in space producing a narrow region of highly deformed material, i.e. a shear band. We then demonstrate the relevance of this new concept for material failure known to occur at scales ranging from nanometers to kilometers.Comment: 4 pages, 3 figures. Eq. (6) and Fig. 2a corrected; added references; improved quality of figure

Spontaneous dissipation of elastic energy by self-localizing thermal runaway

Thermal runaway instability induced by material softening due to shear heating represents a potential mechanism for mechanical failure of viscoelastic solids. In this work we present a model based on a continuum formulation of a viscoelastic material with Arrhenius dependence of viscosity on temperature, and investigate the behavior of the thermal runaway phenomenon by analytical and numerical methods. Approximate analytical descriptions of the problem reveal that onset of thermal runaway instability is controlled by only two dimensionless combinations of physical parameters. Numerical simulations of the model independently verify these analytical results and allow a quantitative examination of the complete time evolutions of the shear stress and the spatial distributions of temperature and displacement during runaway instability. Thus we find that thermal runaway processes may well develop under nonadiabatic conditions. Moreover, nonadiabaticity of the unstable runaway mode leads to continuous and extreme localization of the strain and temperature profiles in space, demonstrating that the thermal runaway process can cause shear banding. Examples of time evolutions of the spatial distribution of the shear displacement between the interior of the shear band and the essentially nondeforming material outside are presented. Finally, a simple relation between evolution of shear stress, displacement, shear-band width and temperature rise during runaway instability is given.Comment: 16 pages, 7 figures. Extended conclusion; added reference

In-hospital extracorporeal cardiopulmonary resuscitation for patients with an out-of-hospital cardiac arrest in a semi-rural setting:An observational study on the implementation of a helicopter emergency medical services pathway

AIM: In this study, we aimed to investigate the efficacy of a helicopter emergency medical service (HEMS) facilitated pathway for in-hospital extracorporeal cardiopulmonary resuscitation (ECPR) for patients with an out of hospital cardiac arrest (OHCA) in a semi-rural setting. METHODS: We retrospectively reviewed all patients with an OHCA attended by a UK HEMS service between 1 January 2018 and 20 September 2021, when a dedicated ECPR pathway was in effect to facilitate transport of eligible patients to the nearest ECLS centre. The primary endpoint was the number of patients meeting ECPR eligibility criteria at three pre-defined time points: at HEMS dispatch, during on-scene evaluation and upon arrival in hospital. RESULTS: During the study period, 162 patients attended met ECPR pathway dispatch criteria. After on-scene evaluation, 74 patients (45%) had a return of spontaneously circulation before arrival of HEMS, 60 (37%) did not meet eligibility criteria regarding initial rhythm or etiology of the OHCA, and 15 (9%) had deteriorated (mainly into asystole) and were no longer suitable candidates upon arrival of HEMS. Eleven patients were eligible for ECPR and transported to hospital in arrest, and a further two patients were transported for post-ROSC ECLS. Nine patients deteriorated during transport and were no longer suitable ECPR candidates upon arrival. ECLS was successfully initiated in two patients (one intra-arrest, and one post-ROSC). CONCLUSION: In-hospital ECPR is of limited value for patients with refractory OHCA in a semi-rural setting, even when a dedicated pathway is in place. Potentially eligible patients often cannot be transported within an appropriate timeframe and/or deteriorate before arrival in hospital