This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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The current-phase relation in Josephson junctions

Flame acceleration and transition to detonation in ducts

Exploration of new superconductors and functional materials, and fabrication of superconducting tapes and wires of iron pnictides

Gas in an unconsolidated sand reservoir encased in shale often results in a dramatic increase in amplitude of the seismic reflection from the shale/gas-sand interface. Unfortunately, reflection amplitude appears not to vary linearly with water (brine) saturation, and thus cannot be used to estimate gas quantity. Previously presented theoretical velocity computations for a Tertiary sedimentary section, which demonstrate that compressional-wave velocity in an unconsolidated gas sand varies nonlinearly with brine saturation, qualitatively agree with laboratory velocity measurements on a sand specimen composed of pure quartz grains. However, significant departure of measured and theoretical velocities at high brine saturation indicates that the technique for partially saturating the sand specimen by flowing a gas-brine mixture through the specimen does not provide a sufficiently uniform distribution. The gas preferentially seeks larger pores. In a subsequent experiment on a specimen composed of spherical glass beads of nearly uniform size, the previous, as well as a modified, fluid injection technique was used. For the latter, brine only was injected into the pore space previously filled with a mixture of gas and brine in nearly equal proportions. This resulted in a more uniform distribution of the gas-brine mixture. For approximately equal brine saturations, this modified technique more » resulted in a measured compressional-wave velocity approximately one-half of the velocity measured for the previously used fluid injection technique. This result implies that if the gas-brine mixture is uniformly distributed in a reservoir, the fluid compressibility is the weighted-by-volume average of the constituent compressibilities. « less

Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir. [Laboratory velocity measurements in unconsolidated sand at various brine saturations]

The failure mechanism of gaseous detonations: experiments in porous wall tubes

The resistance of thin-film lead-copper-lead junctions has been studied with the lead in the superconducting state. The junctions will sustain a supercurrent up to a certain critical value above which a voltage appears, rising smoothly from zero as the current is increased. The effect of a magnetic field upon the critical current has demonstrated that the sandwiches behave phenomenologically as Josephson junctions. The critical current rises rapidly as the temperature is lowered, decreases exponentially with increasing thickness of copper and mcreases with increase of the mean free path of the copper. A simplified version of the de Gennes theory of the proximity effect has been used to account quantitatively for this behaviour. The experiments show that the coherence length of the paired electrons in the copper increases as the temperature decreases, implying that thermal fluctuations govern the decay of the pairs. From the value of the decay length, the interaction parameter in copper is estimated to lie between +0$\cdot$06 and +0$\cdot$14. The properties of these junctions are compared with those of junctions with insulating barriers.

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Supercurrents in lead-copper-lead sandwiches

Two types of quasi-steady high-speed deflagration have been observed experimentally. In the first place they are reaction-waves created in, and propagating through, rough tubes and tubes that contain obstacles; in the second place they are deflagrations created from established detonations by eliminating the transverse waves from the latter’s structure. Changes in tube roughness, obstacle size and tube diameter have no significant influence on the speeds at which the deflagrations propagate. These speeds are close to sonic relative to product gases flowing out of the reaction-waves, and both classes of deflagration are observed to travel at about one-half of the corresponding Chapman-Jouguet (CJ) detonation speed. A theoretical analysis has been carried out on a configuration that consists of a plane precursor shock-wave driven by a plane CJ deflagration. Results agree very well with observations and support the idea that, at least for the duration of these observations, this combination of shock and deflagration is controlled by the energetics of the reacting mixture.

Chapman-Jouguet Deflagrations

It is assumed that energy is transferred at a rapid rate through a plane wall into a spatially uniform and initially stagnant combustible gas mixture. This action generates a shock wave, just as it does in an inert mixture, and also switches on a significant rate of chemical reaction. The Navier-Stokes equations for plane unsteady flow are integrated numerically in order to reveal the subsequent history of events. Four principal time domains are identified, namely ‘early’, ‘transitional’, ‘formation’ and ‘ZND’. The first contains a conduction-dominated explosion and formation of a shock wave; in the second interval the shock wave is responsible for the acceleration of chemical activity, which becomes intense during the ‘formation’ period. Finally a wave whose structure is in essence that of a ZND detonation wave emerges.

On the direct initiation of a plane detonation wave

An inert compressible gas, confined between infinite parallel planar walls, is in an equilibrium state initially. Subsequently energy is added at the boundary during a period that is short compared to the acoustic time of the slot $t'\_a$ (the wall spacing divided by the equilibrium sound speed), but larger than the mean time between molecular collisions. Conductive heating of a thin layer of gas adjacent to the wall induces a gas motion arising from thermal expansion. The small local Mach number at the layer edge has the effect of a piston on the gas beyond. A linear acoustic wave field is then generated in a thicker layer adjacent to the walls. Eventually nonlinear accumulation effects occur on a timescale that is longer than the initial heating time but short compared with $t'\_a$. A weak shock then appears at some well defined distance from the boundary. If the heating rate at the wall is maintained over the longer timescale, then a high temperature zone of conductively heated expanding gas develops. The low Mach number edge speed of this layer acts like a contact surface in a shock tube and supports the evolution of the weak shock propagating further from the boundary. One-dimensional, unsteady solutions to the complete Navier-Stokes equations for an inert gas are obtained by using perturbation methods based on the asymptotic limit $t'\_a$/$t'\_c \rightarrow$ 0, where $t'_c$, the conduction time of the region, is the ratio of the square of the wall spacing to the thermal diffusivity in the initial state. The shock strength is shown to be related directly to the duration of the initial boundary heating.

Shocks generated in a confined gas due to rapid heat addition at the boundary. II: Strong shock waves

Numerical solutions of the Navier–Stokes equations for the plane one-dimensional unsteady motion of a compressible, combustible gas mixture are used to follow the history of events that are initiated by addition of large heat power through a solid surface bounding an effectively semi­-infinite domain occupied by the gas. Plane Zel’dovich–von Neumann–Doring detonations eventually appear either at the precursor shock (which exists in every set of circumstances) or in the regions, occupied by an unsteady induction-domain and an initially quasi-steady fast-flame, that lie behind the precursor shock.

John Frederick Clarke

Papers

Supercurrents in lead-copper-lead sandwiches

Chapman-Jouguet Deflagrations

On the direct initiation of a plane detonation wave

Shocks generated in a confined gas due to rapid heat addition at the boundary. II: Strong shock waves

On the evolution of plane detonations