Static Magnetic Flux Dynamics in One-Dimensional (1D) Josephson Lattices

We investigated static magnetic flux dynamical properties of one-dimensional lattices of Josephson junctions. The discretized wave equations of the Josephson junction lattice were solved using a generalized relaxation iteration algorithm. Numerical simulations indicated that transitions between periodic state and chaotic state will occur as the physical parameters and geometric parameters such as external current y _n, magnetic field h ₀, h, and the length of Josephson junction _n and d _n , varied. A shot length of the Josephson junction favors stable periodic states.     

A Problem of Ranking and Estimation With Poisson Processes

There are given k Poisson processes with parameters (rates of occurrence) λ₁, …, λ _k . Let λ₍₁₎ ≤ λ₍₂₎ ≤ … ≤ λ_(k) denote the ordered set of values of the parameters. A procedure is given for selecting the process corresponding to λ_(k) and estimating its parameter (λ_(k)). The given procedure controls the joint risk of improper selection and of large error in the estimate. Let θ > 1 and 0 < α, β < 1 be given numbers, and let δ denote the estimate of λ_(k). The joint probability that a correct selection is made and that |(δ/λ_(k)) ? 1| ≤ α is at least as large as β, for (λ_(k)/λ_(k?1)) ≥ θ. Two cases are considered, that is, when the processes are observed continuously in time, and when they are observed at successive intervals of time. Both the cases lead to the same theoretical results.     

Quantum effects and the resistive transition in superconducting granular films

Static and dynamic properties of an array of Josephson junctions shunted by Ohmic resistors are discussed within a quantum Ginzburg-Landau theory. The phase diagram at zero temperature is calculated in mean field approximation. It shows that global superconductivity atT=0 is possible only if the normal-state film resistanceR _n is smaller than a critical valueR _n ^c which depends only logarithmically on the Josephson coupling and charging energies. The particular valueR _n ^c =6.5 k found in recent experiments on granular films is in reasonable agreement with estimates for these parameters. A phenomenological order parameter relaxation mechanism is introduced and the associated fluctuation-induced conductivity and diamagnetic susceptibility aboveT _c are determined. The resulting precursor conductivity does not explain the observed exponential decrease withR _n-R _n ^c of the residual resistance at low temperature. However, a very simple model for the resistance due to vortex flow, generalizing the classical Kosterlitz-Thousless picture, is in good agreement with the experimental data.     

THE ENGINEERING FLAW ASSESSMENT METHOD (EFAM)

This communication gives an introduction to the Engineering Flaw Assessment Method (EFAM) presently being developed at GKSS. The EFAM consists of various documents describing experimental procedures for determining fracture properties under various conditions, as well as analytical procedures for estimating the crack tip opening displacement in terms of δ₅ , the rate of δ₅ , (dδ₅ /dt), and the J-integral as driving force parameters.     

Cross-Whisker Intrinsic Josephson Junction as a Probe of Symmetry of the Superconducting Order Parameter

As a test of the superconducting order parameter, we have developed an intrinsic Josephson junction by the name of cross-whisker junction. This junction was made using two Bi₂Sr₂CaCu₂O_8+d single crystal whiskers. Two whiskers were connected at their c planes with various cross-angles. Angular dependence of the critical current densities shows d-wave-like fourfold-symmetry. However, the angular dependence is much stronger than that of the conventional d_x ^{2-y 2} wave. The Jc shows its smallest value around 45 deg, which suggests that the Josephson penetration depth becomes longer. We have successfully observed a Fraunhofer pattern in the cross-whisker junction with cross-angle 45 deg.     

Sequential Optimum Procedures for Unbiased Estimation of a Binomial Parameter

Let x ₁, x ₂, … x _n, … be a sequence of independent random variables with a common density function P(x = 1) = p, P(x = 0) = 1 – p, 0 < p < 1. This paper considers the non-randomized sequential procedures δ's for estimating p and the following three problems on choice of δ. (i) Choose δ to minimize E _v (Z _δ – P)² subject to E _p N _δ ≤ m where m ≥ 1 and Z _δ is an unbiased estimate of p; (ii) Choose δ to minimize E_p N _δ subject to E _p (Z _δ – p)² ≤ α where α is a real positive number; (iii) choose δ to minimize C E_p N _δ + E _p (Z _δ – p)² where C is the cost of an observation. In each case the minimization is to be done uniformly in p if possible; otherwise the supremum over p of the risk in question is to be minimized. A procedure is constructed for problem (i) when m is not an integer. A fixed sample size procedure is shown to be admissible and minimax for problem (ii). A procedure is constructed which is asymptotically uniformly better than the fixed sample size for problem (ii). Furthermore, for problem (iii) some optimum procedures are constructed.     

Simulation of Josephson junction in a microwave field

The resistively shunted junction (RSJ) model of a Josephson junction in a microwave field is studied using both analog and digital simulators. A comparison of the two methods shows very good agreement. Voltage-current characteristics of the Josephson junction in the low-frequency limit and their transition to chaotic behavior due to the punchthrough effect are investigated. The inverse ac effect on high- _c junctions is simulated. Fractional inverse steps are found.     

Notices

This paper presents the small sample optimum choice of the k(≤ r ₂) order statistics for the best linear unbiased estimate (BLUE) of the parameters μ and σ or σ alone (μ known) when the sample is Type II censored on the right. For n = 2(1)10, k = 1(1)r ₂ and Tr ₂ = ([.504n]+1}(1)n, the optimum ranks, the coefficients of the BLUES have been presented in Table I.     

Controlling the Josephson contact parameters in a semiconductor-superconductor eutectic composition

The current-voltage (I–U) curve was studied for the Josephson contact in a GaSb-V₂Ga₅ eutectic composition comprising parallel whiskers of a superconducting V₂Ga₅ phase formed by oriented crystallization in a semiconducting GaSb matrix. It is established that the parameters of the I-U curve can be controlled by varying the angle between the direction of electric current and the axis of whisker orientation. Using the Josephson relation hω=2eV and considering the parallel connection of infinite Josephson clusters in the structure studied, a formula is derived, n ₀ Nhω=2eV, which can be used for estimating the electromagnetic radiation frequency ω of the Josephson weak links, the number N of infinite Josephson clusters, and the number n0N of Josephson weak links in the semiconductor-superconductor eutectic compositions obtained by means of oriented crystallization.     

A Numerical Treatment of the rf SQUID: I. General Properties and Noise Energy

We investigate the characteristics and noise performance of rf Superconducting Quantum Interference Devices (SQUIDs) by solving the corresponding Langevin equations numerically and optimizing the model parameters with respect to noise energy. After introducing the basic concepts of the numerical simulations, we give a detailed discussion of the performance of the SQUID as a function of all relevant parameters. The best performance is obtained in the crossover region between the dispersive and dissipative regimes, characterized by an inductance parameter β′ _L ≡2π LI ₀/Φ ₀≈1; L is the loop inductance, I ₀ the critical current of the Josephson junction, and Φ ₀ the flux quantum. In this regime, the lowest (intrinsic) values of noise energy are a factor of about 2 above previous estimates based on analytical approaches. However, several other analytical predictions, such as the inverse proportionality of the noise energy on the tank circuit quality factor and the square of the coupling coefficient between the tank circuit and the SQUID loop, could not be well reproduced. The optimized intrinsic noise energy of the rf SQUID is superior to that of the dc SQUID at all temperatures. Although for technologically achievable parameters this advantage shrinks, particularly at low thermal fluctuation levels, we give examples for realistic parameters that lead to a noise energy comparable to that of the dc SQUID even in this regime.      

Potential flow along a wavy wall and transonic controversy

Summary The flow of an inviscid, compressible, perfect gas along a sinus-shaped wall is used as a model to shed light into the long-standing transonic controversy. The solution of the small-disturbance approximation for the velocity potential is developed as a formal series in the similarity parameterk. Forty terms ink were obtained, delegating the computational work to a computer. The coefficients of the maximal-speed series turn out to be moments with positive weight on a finite interval of support. This implies % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWraaSqabe% aacaWG1baaaGqacOGaa8xBaiaa-fgacaWF4bGaeyypa0ZaaabCaeaa% caWGHbWaaSbaaSqaaiaad6gaaeqaaOGaam4AamaaCaaaleqabaGaam% OBaaaakiabg2da9maapedabaWaaSaaaeaacaWGKbGaam4DaiaacIca% caWG4bGaaiykaaqaaiaaigdacqGHsislcaWGRbGaamiEaaaaaSqaai% aadggaaeaacaWGIbaaniabgUIiYdaaleaacaWGUbGaeyypa0JaaGim% aaqaaiabg6HiLcqdcqGHris5aaaa!5264!\[{}^umax = \sum\limits_{n = 0}^\infty {a_n k^n = \int_a^b {\frac{{dw(x)}}{{1 - kx}}} } \]The solution of the classical moment problem, i.e. the recovering of the weight distribution, shows that-a=b=1/k _c, withk _c as the critical value of the parameter, at which the flow first becomes sonic.k _chas been determined as 0.8253, the four digits being regarded as definite. It follows thatu _max as a function ofk is analytic on (-k _c, k_c) and has exactly two singularities located on the real axis atk=–k _c andk=k _c. It is known from the theory of moments that there does not exist an analytic continuation on the real axis exceeding the interval. This means that the velocity depends analytically on the parameter as long as the local velocity of sound is nowhere reached, but that the exceeding of it is marked by termination of analyticity and, to this degree, is critical. Thus, the view that there will not exist a transonic potential flow having neighbour solutions is supported. The smallness of the weight distribution at the interval ends (at least atk=–k _c it is even exponentially small, giving an exponentially small singularity ofu _max) is the key to explaining, within the scope of the inviscid model, the shockless exceeding of the critical value by some per cent seen in numerical calculations and experiments.     

The modulation instability of dispersed electromagnetic waves in the Josephson junction with nonlocal interaction

The modulation instability of dispersed electromagnetic waves propagating in the Josephson junction between massive superconductors has been studied. A dispersion equation for the increment of small perturbations of the wave amplitude is obtained. It is shown that the spatial nonlocality produces a stabilizing influence with respect to the development of modulation instability in a long-wavelength region of the perturbation wavevectors 0≤Q≤Q _B1(k). The region of modulation instability Q _B1(k)<Q<Q _B2(k, A, L) can be controlled by the dispersion parameter—the wavevector k (or the frequency ω(k)) of the carrier wave in the linear approximation.     

Partition of solute elements during solidification of iron-carbon-chromium alloys

The partition coefficients of chromium between austenite and liquid iron,k _Cr ^A/L , were determined from the experiment of rapid cooling of iron-carbon hypo-eutectic alloys containing a small amount of chromium from coexisting solid—liquid states; the partition coefficients between eutectic and its liquid,k _0,Cr, andk _0,Cr, for the stable and metastable eutectic solidifications were obtained from the zone-melting experiment of iron—carbon eutectic alloys containing a small amount of chromium. Chromium was rejected to liquid iron on the crystallization of primary austenite,k _Cr ^A/L <1. On the eutectic solidification, chromium was enriched in eutectic liquid for the stable system,k _0,Cr<1, and was conversely diluted in the liquid for the metastable system,k _0,Cr>1. The relationship between effective and equilibrium partition coefficients given by Burtonet al. was observed for the results of the zone melting experiment and, from the relationship, the thickness of boundary layer in the liquid ahead of the solid—liquid interface was found to be 0.17 mm for the stable system and 0.11 mm for the metastable system. Thermodynamic calculation of the partition coefficients of chromium and carbon proved to represent the observed partition coefficients well.     

Chaotic Dynamics of Externally Shunted Josephson Junction with Unharmonic CPR

The current–phase relation (CPR) of Josephson junctions based on high-T _c superconductors and other types of superconducting structures contain second harmonics. In this work, the influence of second harmonics of CPR on an externally shunted Josephson junction circuit model with nonzero inductance has been studied to analyze the chaotic dynamics of the system. Having constructed the circuit model, the time dependent simulations are carried out for a variety of control parameters. It is shown that the presence of second harmonics leads to a change in the boundary of the chaotic region in bifurcation diagram.     

All Cubic-Phase δ-TAGS Thermoelectrics Over the Entire Mid-Temperature Range

GeTe-based pseudo-binary (GeTe)_x(AgSbTe₂)_100−x (TAGS–x) is recognized as a promising p-type mid-temperature thermoelectric material with outstanding thermoelectric performance; nevertheless, its intrinsic structural transition and metastable microstructure (due to Ag/Sb/Ge localization) restrict the long-time application of TAGS-x in practical thermoelectric devices. In this work, a series of non-stoichiometric (GeTe)_x(Ag_1-δSb_1+δTe_2+δ)_100−x (x = 85∼50; δ = ≈0.20–0.23), referred to as δ-TAGS-x, with all cubic phase over the entire testing temperature range (300-773 K), is synthesized. Through optimization of crystal symmetry and microstructure, a state-of-the-art ZT_max of 1.86 at 673 K and average ZT_avg of 1.43 at ≈323–773 K are realized in δ-TAGS-75 (δ = 0.21), which is the highest value among all reported cubic-phase GeTe-based thermoelectric systems so far. As compared with stoichiometric TAGS-x, the remarkable thermoelectric achieved in cubic δ-TAGS-x can be attributed to the alleviation of highly (electrical and thermal) resistive grain boundary Ag₈GeTe₆ phase. Moreover, δ-TAGS-x exhibits much better mechanical properties than stoichiometric TAGS-x, together with the outstanding thermoelectric performance, leading to a robust single-leg thermoelectric module with η_max of ≈10.2% and P_max of ≈0.191 W. The finding in this work indicates the great application potential of non-stoichiometric δ-TAGS-x in the field of mid-temperature waste heat harvesting.     

Effects of oxygen stoichiometry on electrochromic properties in amorphous tungsten oxide films

We have investigated the electrochromic properties of amorphous granular tungsten oxide (WO_3 + δ) thin films with over-stoichiometric oxygen content (δ), using LiClO₄ with propylene carbonate as an electrolyte. Different optical and electrochromic characteristics are observed with increasing δ. All the devices are electrochemically stable for more than 5000 color/bleach cycles without apparent degradation, and they have a faster response to coloration than to bleaching. WO_3 + δ films with an optimized δ value show an optical modulation of 86% at a wavelength of 630 nm and the highest coloration efficiency ever reported of ~ 213 cm²/C. The δ-dependent coloration mechanism is discussed using the site saturation model. It is proposed that WO_3 + δ films with the optimal δ value have favorable thickness and stoichiometry for the generation of Li⁺W⁺⁵ states.     

Estimation of the Parameters of the Gamma Distribution by Sample Quantiles

This paper deals with large sample estimation of the location parameter (α₁ and the scale parameter α₂ in the gamma distribution with known shape parameter. Best linear unbiased estimates based on k sample quantiles are used. For a given k, the optimum spacings of the sample quantiles can be replaced by simpler “nearly optimum” spacings at virtually no loss of asymptotic efficiency. The theory behind the nearly optimum spacings is briefly reviewed. The major part of the paper concerns estimation of α₂ when α₂ is known. Nearly optimum spacings together with the coefficients to be used in computing the estimates are presented in a number of tables for k = 1(1) 10, and various values of the shape parameter. The paper also contains brief discussions of estimation of α₁, when α₂ is known, and simultaneous estimation of α₁ and α₂.     

Radiation amplification with help of the intrinsic Josephson effect

The use of the intrinsic Josephson effect in layered high-T_c superconductors for amplification of a signal in the presence of a strong pump radiation is investigated. Calculations are done both for thin films and massive material with a surface parallel to the c-direction, assuming normal incidence of the radiation with electric field parallel to the c-direction for parameter values relevant for high-T_c materials. In both cases high signal gain is obtained in a limited range of frequencies and pump power.     

Highly Sensitive Electrometers Based on Single Cooper Pair Tunneling

A superconducting transistor structure comprising two Josephson tunnel junctions connected in series and a small island in between, which is capacitively coupled to a gate, is considered. When self-capacitances of the junctions are sufficiently small that the corresponding charging energy E _c is of the order of magnitude of the Josephson coupling strength E _J (and both are k _B T), the interplay of the charging and Josephson effects in the circuit becomes essential. This leads to a characteristic IV curve which can be effectively modulated by the gate in two limit cases of external electrodynamic impedance Z _s (): (a) Z _s = R _s R _Q 6.5 k and (b) R _s R _Q . Both circuits can serve as electrometers which are competitive with traditional single-electron devices. Preliminary experimental results are discussed.     

Quantum travelling-wave analysis of a quasi-phase-matched parametric amplifier

The paper describes a phase-mismatched Fokker–Planck equation formulation for parametric amplification in periodically inverted nonlinear media. An analytical solution of the phase-mismatched Fokker–Planck equation and the amplitude quantum fluctuation after passing through the quasi-phase-matched (QPM) device are obtained. The calculated results for the QPM device conform to that of the Langevin equation in the case of no loss k=0, and give a general solution for k≠0. From this one can derive knowledge of the dependence of squeezing on the loss coefficient k and make a comparison between the QPM device and a phase matched device at the threshold k=ε₀.