On the Thermal Dynamics of Metallic and Superconducting Wires. Bifurcations, Quench, the Destruction of Bistability and Temperature Blowup

In the present study, a numerical bifurcation analysis is carried out in order to investigate the multiplicity and the thermal runaway features of metallic and superconducting wires in a unified framework. The analysis reveals that the electrical resistance, combined with the boiling curve, are the dominant factors shaping the conditions of bistability—which result in a quenching process—and the conditions of multistability—which may lead to a temperature blowup in the wire. An interesting finding of the theoretical analysis is that, for the case of multistability, there are two ways that a thermal runaway may be triggered. One is associated with a high current value (“normal” runaway) whereas the other one is associated with a lower current value (“premature” runaway), as has been experimentally observed with certain types of superconducting magnets. Moreover, the results of the bifurcation analysis suggest that a static criterion of a warm or a cold thermal wave propagation may be established based on the limit points obtained.

Relativistic modeling of stellar objects using embedded class one spacetime continuum

In this paper, we explore a family of exact solutions to the Einstein field equations (EFEs) describing a spherically symmetric, static distribution of fluid spheres with pressure anisotropy in the setting of embedding class one spacetime continuum. A detailed theoretical analysis of this class of solutions for compact stars PSR J16142230, Her X-1, LMC X-4 and 4U 1538-52 is carried out. The solutions are verified by examining various physical aspects, viz., anisotropy, gravitational redshift, causality condition, equilibrium (TOV-equation), stable static criterion and energy conditions, in connection to their cogency. Due to the well-behaved nature of the solutions for a large range of positive real [Formula: see text] values, we develop models of above stellar objects and discuss their behavior with graphical representations of the class of solutions of the first two objects extensively. The solutions studied by Fuloria [Astrophys. Space Sci. 362, 217 (2017)] for [Formula: see text] and Tamta and Fuloria [Mod. Phys. Lett. A 34, 2050001 (2019), https://doi.org/10.1142/S0217732320500017 ] for [Formula: see text] are particular cases of our generalized solution.

Approach to insect wing shape and deformation field measurement

Summary StatementA fine shape and deformation field measurement of insect wing is achieved by a self-developed setup. This measurement could foster investigation of insect wing stiffness distribution.AbstractFor measuring the shape and deformation of insect wing, a scanning setup adopting line laser and coaxial LED light is developed. Wing shape can be directly acquired from the line laser images by triangulation. Yet the wing deformation field can also be obtained by a self-devised algorithm that processes the images from line laser and coaxial LED simultaneously. During the experiment, three wing samples from termite and mosquito under concentrated force are scanned. The venation and corrugation could be significantly identified from shape measurement result. The deformation field is sufficiently accurate to demonstrate its variation from wing base to tip. The load conditions in experiments are also be discussed. For softer wings, local deformation is apparent if pinhead is employed to impose force. The similarity analysis is better than 5% deformation ratio as a static criterion, if the wing is simplified as a cantilever beam. The setup is proved to be effective and versatile. The shape and deformation fields would give enough details for the measurement of wing stiffness distribution.

A Nonlinear Catastrophic Model of Isolated Rock Pillar Instability and its Chaotic Behaviour Based on Material Properties

A cusp catastrophic model of rock pillar instability was developed under uniaxial stress conditions, based on the assumptive softening constitutive relations under static mechanics. The static criterion of rock pillar instability is derived. The dynamical nonlinear differential equation under nonequilibrium state followed by the cusp catastrophic model is introduced. The characteristics of rock pillars chaotic evaluation are studied under the change of linear stiffness. The results show that the rock pillars motion is chaotic when the linear stiffness is in a certain interval, which are proved by the calculated max Lyapunov exponent.

Static and Dynamic Experimental Analysis of the Galloping Stability of Porous H-Section Beams

The phenomenon of self-induced vibrations of prismatic beams in a cross-flow has been studied for decades, but it is still of great interest due to their important effects in many different industrial applications. This paper presents the experimental study developed on a prismatic beam with H-section. The aim of this analysis is to add some additional insight into the behaviour of the flow around this type of bodies, in order to reduce galloping and even to avoid it. The influence of some relevant geometrical parameters that define the H-section on the translational galloping behaviour of these beams has been analysed. Wind loads coefficients have been measured through static wind tunnel tests and the Den Hartog criterion applied to elucidate the influence of geometrical parameters on the galloping properties of the bodies under consideration. These results have been completed with surface pressure distribution measurements and, besides, dynamic tests have been also performed to verify the static criterion. Finally, the morphology of the flow past the tested bodies has been visualised by using smoke visualization techniques. Since the rectangular section beam is a limiting case of the H-section configuration, the results here obtained are compared with the ones published in the literature concerning rectangular configurations; the agreement is satisfactory.

Minimality of the correctness criterion for multiplicative proof nets

Almost a decade ago, Girard invented linear logic with the notion of a proof-net. Proof-nets are special graphs built from formulas, links and boxes. However, not all nets are proof-nets. First, they must be well constructed (we say that such graphs are proof-structures). Second, a proof-net is a proof-structure that corresponds to a sequential proof. It must satisfy a correctness criterion. One may wonder what this static criterion means for cut-elimination. We prove that every incorrect proof-structure (without cut) can be put in an environment where reductions lead to two kinds of basically wrong configurations: deadlocks and disconnected proof-structures. Thus, this proof says that there does not exist a bigger class of proof-structures than proof-nets where normalization does not lead to obviously bad configurations.

Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions

In this paper we consider the equilibrium configurations of a homogeneous, incompressible, isotropic elastic body subjected to a uniform dead load surface traction of magnitude T whose direction is normal to the surface of the body in the reference configuration, and to no other forces. We concentrate on homogeneous equilibrium solutions, that is those for which the deformation gradient F is constant, and we study their bifurcations and stability (with respect to an appropriate static criterion) as T varies. Since it turns out that the equations for homogeneous equilibrium solutions, and the stability properties that we consider of these solutions, are independent of the shape of the body in the reference configuration, we can suppose if desired that this shape is a cube. (See Fig. 1.1.)

Active Sites in Boiling

Effects of cavity size, shape, and their population on nucleation characteristics of a surface were investigated. A theoretical model has been developed for the stability of a cylindrical cavity in boiling considering the wetting characteristics of the fluid and the transient inertial, viscous, and heat transfer effects. For cavities having small depth/diameter ratio and boiling with organics (low contact angle) the model predicts higher superheats than those predicted by the static equilibrium criterion, and as depth/diameter ratio becomes large, the static criterion successfully predicts the required superheat. The predictions of the model are consistent with the experimental observations made on the natural and artificial cavities made by laser. A qualitative theoretical approach has been presented to predict the population of active sites at different superheats for a given fluid and surface.