Quantum Phase Slips in one-dimensional Josephson Junction Chains

We have studied quantum phase-slip (QPS) phenomena in long one-dimensional Josephson junction series arrays with tunable Josephson coupling. These chains were fabricated with as many as 2888 junctions, where one sample had a tunable weak link in the middle. Measurements were made of the zero-bias resistance, $R_0$, as well as current-voltage characteristics (IVC). The finite $R_0$ is explained by QPS and shows an exponential dependence on $\sqrt{E_J/E_C}$ with a distinct change in the exponent at $R_0=R_Q=h/4e^2$. When $R_0 > R_Q$ the IVC clearly shows a remnant of the Coulomb blockade, which evolves to a zero-current state with a sharp critical voltage as $E_J$ is tuned to a smaller value. The zero-current state below the critical voltage is due to coherent QPS and we show that these are enhanced at the central weak link. Above the critical voltage a negative differential resistance is observed which nearly restores the zero-current state

The effect of combined torsional and bending loads on a channel beam with one end restrained from warping

Channel beams have been designed with the main purpose of giving large resistance to bending while the torsional strengths are known to be relatively small. In this experiment, a cantilevered channel beam was loaded with a concentrated load at the free end, first through the experimentally determined shear center and then through the centroid of the cross section. For each loading condition, the strains were measured with the aid of SR-4 strain gages placed at intervals along the length of the beam. With the aid of a computer, the strains were converted into longitudinal stresses and these stresses were compared to the theoretically predicted values of longitudinal stresses. The derivation of the torsional stress equation as shown in the text Advanced Mechanics of Materials by Seely and Smith is briefly compared to the derivation of the torsional stress equation as shown in the text Strength of Materials by Timoshenko. The two derivations are discussed and, even though the derivations are completely different, the values of longitudinal stress obtained by the use of each equation agree very well with each other. The longitudinal stresses calculated from the experimentally obtained values or strain agree very closely with the theoretically predicted values of longitudinal stress --Abstract, page iii

Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps

Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed response is studied using normal forms based on the most general assumptions of iterated maps. Such an analysis provides a theoretical footing for previous experimental and numerical observations, such as the failure of linear analysis and the saturation of the gain. Qualitative as well as quantitative features of the gain are exhibited using selected models of cardiac dynamics.Comment: 12 pages, 7 figure

Theoretical considerations on a 2D compliant tensegrity joint in context of a biomedical application

In this paper, a two-dimensional compliant tensegrity joint was investigated for potential biomedical applications such as orthotics or exoskeletons. The structure consists of two compressed members connected by five compliant tensioned members. The concept is based on the tensegrity principle, which allows the realization of dynamic orthoses without conventional hinge joints. Another advantage is the adaptability to the individual needs of the patient through a suitable design of the structure and the careful selection of the characteristics of the elements. Using geometric nonlinear analysis, the mechanical behavior of the structure was investigated, focusing on mechanical compliance. The main objective was to determine the influence of the initial length and stiffness of the tensioned members and the influence of the magnitude of external forces on the overall stiffness of the movable member of the structure. The results highlight the significant impact of member parameters on the structure's stiffness and movability under varying load magnitudes. The research laid the foundation for future development of dynamic orthoses based on this structure

Well-posed continuum equations for granular flow with compressibility and μ(I)-rheology

Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent $\mu(I)$-rheology is ill-posed when the non-dimensional strain-rate $I$ is too high or too low. Here, incorporating ideas from Critical-State Soil Mechanics, we derive conditions for well-posedness of PDEs that combine compressibility with $I$-dependent rheology. When the $I$-dependence comes from a specific friction coefficient $\mu(I)$, our results show that, with compressibility, the equations are well-posed for all deformation rates provided that $\mu(I)$ satisfies certain minimal, physically natural, inequalities