A flexible anatomical set of mechanical models for the organ of Corti.

We build a flexible platform to study the mechanical operation of the organ of Corti (OoC) in the transduction of basilar membrane (BM) vibrations to oscillations of an inner hair cell bundle (IHB). The anatomical components that we consider are the outer hair cells (OHCs), the outer hair cell bundles, Deiters cells, Hensen cells, the IHB and various sections of the reticular lamina. In each of the components we apply Newton's equations of motion. The components are coupled to each other and are further coupled to the endolymph fluid motion in the subtectorial gap. This allows us to obtain the forces acting on the IHB, and thus study its motion as a function of the parameters of the different components. Some of the components include a nonlinear mechanical response. We find that slight bending of the apical ends of the OHCs can have a significant impact on the passage of motion from the BM to the IHB, including critical oscillator behaviour. In particular, our model implies that the components of the OoC could cooperate to enhance frequency selectivity, amplitude compression and signal to noise ratio in the passage from the BM to the IHB. Since the model is modular, it is easy to modify the assumptions and parameters for each component.

Current-Induced Crossover of Flux Periodicity from h/2 e to h/e in a Superconducting Nb Nano-Ring.

Magnetoresistance measurements in a granular Nb nanoring reveal current-induced crossover between two distinct quantum coherence effects. At low bias currents, Cooper-pair coherence is manifested by Little-Parks oscillations with flux periodicity of h/2 e. At high bias currents, magnetoresistance oscillations with flux periods of h/ e are observed and interpreted as Aharonov-Bohm oscillations, reflecting the phase coherence of individual quasi-particles. The model explaining these data views the ring as a chain of superconducting grains weakly coupled by tunnel junctions. Low bias currents allow coherent tunneling of Cooper pairs between the grains. Increasing the current above the critical current of all the junctions creates a quasi-particles conduction channel along the ring, allowing for quantum interference of quasi-particles.

Stationary nano-SQUID: theoretical investigation and feasibility analysis.

The standard operation of a dc SQUID leads to oscillatory electric fields that emit electromagnetic radiation. We estimate the effect that this radiation could have on the measured sample. A stationary SQUID could be advantageous if the oscillation contribution to back action on the measured sample has to be avoided. We study a superconducting loop that encloses a magnetic flux, connected to a superconducting and to a normal electrode, when a fixed electric current between the electrodes flows across the loop. The considered circuit does not contain Josephson junctions. We find that in a very broad range of parameters the current flow converges to a stationary regime, i.e. the densities of normal current and of supercurrent become functions of position only, independent of time. The potential difference between the electrodes depends on the magnetic flux, so that measuring this voltage would provide information on the enclosed flux. The influence of thermal noise was estimated. The sizes of the voltage and of the power dissipation could be appropriate for the design of a practical fluxmeter. We found narrow ranges of flux at which the voltage varies sharply with the flux.

Current-induced SQUID behavior of superconducting Nb nano-rings.

The critical temperature in a superconducting ring changes periodically with the magnetic flux threading it, giving rise to the well-known Little-Parks magnetoresistance oscillations. Periodic changes of the critical current in a superconducting quantum interference device (SQUID), consisting of two Josephson junctions in a ring, lead to a different type of magnetoresistance oscillations utilized in detecting extremely small changes in magnetic fields. Here we demonstrate current-induced switching between Little-Parks and SQUID magnetoresistance oscillations in a superconducting nano-ring without Josephson junctions. Our measurements in Nb nano-rings show that as the bias current increases, the parabolic Little-Parks magnetoresistance oscillations become sinusoidal and eventually transform into oscillations typical of a SQUID. We associate this phenomenon with the flux-induced non-uniformity of the order parameter along a superconducting nano-ring, arising from the superconducting leads ('arms') attached to it. Current enhanced phase slip rates at the points with minimal order parameter create effective Josephson junctions in the ring, switching it into a SQUID.

Characterization of the spontaneous symmetry breaking due to quenching of a one-dimensional superconducting loop.

We study the final distribution of the winding numbers in a 1D superconducting ring that is quenched through its critical temperature in the absence of magnetic flux. The study is conducted using the stochastic time-dependent Ginzburg-Landau model, and the results are compared with the Kibble-Zurek mechanism (KZM). The assumptions of the KZM are formulated and checked as three separate propositions. We find characteristic lengths and characteristic times for the processes we study. Besides the case of uniform rings, we examined the case of rings with several weak links. For temperatures close to or below Tc, the Ginzburg-Landau coherence length ξ(0)|T/Tc-1|(-1/2) does not play the role of the correlation length. In order to regard the winding number as a conserved quantity, it is necessary to allow for a short lapse of time during which unstable configurations decay. We found criteria for the validity of the 1D treatment. There is no lower bound for the final temperatures that permit 1D treatment. For moderate quenching times τQ, the variance of the winding number obeys the scaling proportional variant τ(-1/4)Q, as predicted by the KZM in the case of mean field models; for τQ ≲ 10(5)h/kBTc, the dependence is weaker. We also studied the behavior of the system when fluctuations of the gauge field are suppressed, and obtained that the scaling proportional variant τ(-1/4)Q is obeyed over a wider range.

The influence of thermal fluctuations on uniform and nonuniform superconducting rings according to the Ginzburg-Landau and the Kramer-Watts-Tobin models.

We evaluate the influence of thermal fluctuations on superconducting rings that enclose a magnetic flux, using the time-dependent Ginzburg-Landau model (TDGL) or the Kramer-Watts-Tobin model (KWT), while thermal fluctuations are accounted for by means of Langevin terms. This method is applicable in situations where previous methods are not, such as for nonuniform loops, rings with large width to radius ratio and loops with large coherence length to perimeter ratio. We evaluate persistent currents, the position and statistical behavior of flux-induced vortices, and the lifetime of metastable fluxoid states. The influence of nonuniformity on the persistent current does not depend strongly on the details of the cross section profile; it depends mainly on its first harmonic, but not only on it. As a consequence of nonuniformity the maximum of the persistent current shifts to smaller fluxes and the passage between fluxoid states remains non-hysteretic down to lower temperatures than in the case of a uniform sample. Our results obtained using TDGL agree remarkably well with recent measurements of the persistent current in superconducting rings and with measurements of the position of a vortex that mediates between fluxoid states in an asymmetric disc with a hole; they could also provide a plausible explanation for the unexpectedly short measured lifetimes of metastable states. Comparison of TDGL and KWT indicates that they lead to the same results for the persistent current, whereas KWT leads to larger lifetimes than TDGL.