Theory of phase-locking in generalized hybrid Josephson junction arrays

A recently proposed scheme for the analytical treatment of the dynamics of two-dimensional hybrid Josephson junction arrays is extended to a class of generalized hybrid arrays with ''horizontal'' shunts involving a capacitive as well as an inductive component. This class of arrays is of special interest, because the internal cell coupling has been shown numerically to favor in-phase synchronization for certain parameter values. As a result, we derive limits on the circuit design parameters for realizing this state. In addition, we obtain formulas for the flux-dependent frequency including flux-induced switching processes between the in-phase and anti-phase oscillation regime. The treatment covers unloaded arrays as well as arrays shunted via an external load.Comment: 24 pages, REVTeX, 5 Postscript figures, Subm. to Phys. Rev.

Full capacitance-matrix effects in driven Josephson-junction arrays

We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction (RCSJ) model, including full capacitance-matrix effects}. We define and study three different models of the capacitance matrix $C_{\vec{r},\vec{r}'}$: Model A includes only mutual capacitances; Model B includes mutual and self capacitances, leading to exponential screening of the electrostatic fields; Model C includes a dense matrix $C_{\vec{r},\vec{r}'}$ that is constructed approximately from superposition of an exact analytic solution for the capacitance between two disks of finite radius and thickness. In the latter case the electrostatic fields decay algebraically. For comparison, we have also evaluated the full capacitance matrix using the MIT fastcap algorithm, good for small lattices, as well as a corresponding continuum effective-medium analytic evaluation of a finite voltage disk inside a zero-potential plane. In all cases the effective $C_{\vec{r},\vec{r}'}$ decays algebraically with distance, with different powers. We have then calculated current voltage characteristics for DC+AC currents for all models. We find that there are novel giant capacitive fractional steps in the I-V's for Models B and C, strongly dependent on the amount of screening involved. We find that these fractional steps are quantized in units inversely proportional to the lattice sizes and depend on the properties of $C_{\vec{r},\vec{r}'}$. We also show that the capacitive steps are not related to vortex oscillations but to localized screened phase-locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed.Comment: 12 pages 18 Postscript figures, REVTEX style. Paper to appear in July 1, Vol. 58, Phys. Rev. B 1998 All PS figures include

27. New echocardiogram index alternatives to MAPSE and TAPSE z-scores in children

BackgroundMitral annular plane systolic excursion (MAPSE), and tricuspid annular plane systolic excursion (TAPSE) are relatively load independent longitudinal left ventricle (LV) and right ventricle (RV) measurement in both adults and children. Normal paediatric values of MAPSE and TAPSE unlike adults are based on inconvenient z-scores. We hypothesize novel indexes of (LSI) LV longitudinal systolic index and (RSI) RV longitudinal systolic index are BSA, age, gender independent and nullifies the need for MAPSE and TAPSE z-scores.MethodsNormal echocardiograms were retrospectively reviewed from 2009 to 2011. Ejection fraction, LV dimensions, MAPSE, and TAPSE were determined. LSI and RSI were calculated using MAPSE and TAPSE divided by LV length. Echocardiogram indices were correlated. Regression analysis was done for BSA, age, and gender.ResultsTwo hundred and one patients had normal ejection fractions (67.3;±5.1%). Mean MAPSE 10.4;±3.3mm, z-score −0.07;±1.2, and LSI 0.20;±0.03; Mean TAPSE 17.4;±5.4mm, z-score 0.74;±1.7, and RSI 0.34;±0.06. LSI and MAPSE z-scores correlated, r=0.73, p<0.001. Age, gender, and BSA did not correlate with LSI. RSI and TAPSE z-scores correlated with r=0.76, p<0.001. Age influences RSI, R2=0.58, p value <0.001, BSA and gender does not. RSI, with age stratification, is significantly decreased less than 2months.ConclusionLSI obviates need for-MAPSE z scores. RSI offers an additional non TAPSE z-score method to evaluate RV function, but does not nullify age effect. RSI, especially in the first two months is decreased

Resonant-Cavity-Induced Phase Locking and Voltage Steps in a Josephson Array

We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that (i) current-voltage characteristics of the array have self-induced resonant steps (SIRS), (ii) at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and (iii) when $N_a$ active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with $N_a$. All three features are in agreement with a recent experiment [Barbara {\it et al}, Phys. Rev. Lett. {\bf 82}, 1963 (1999)]}.Comment: 4 pages, 3 eps figures included. Submitted to PRB Rapid Com

Superconducting states and depinning transitions of Josephson ladders

We present analytical and numerical studies of pinned superconducting states of open-ended Josephson ladder arrays, neglecting inductances but taking edge effects into account. Treating the edge effects perturbatively, we find analytical approximations for three of these superconducting states -- the no-vortex, fully-frustrated and single-vortex states -- as functions of the dc bias current $I$ and the frustration $f$. Bifurcation theory is used to derive formulas for the depinning currents and critical frustrations at which the superconducting states disappear or lose dynamical stability as $I$ and $f$ are varied. These results are combined to yield a zero-temperature stability diagram of the system with respect to $I$ and $f$. To highlight the effects of the edges, we compare this dynamical stability diagram to the thermodynamic phase diagram for the infinite system where edges have been neglected. We briefly indicate how to extend our methods to include self-inductances.Comment: RevTeX, 22 pages, 17 figures included; Errata added, 1 page, 1 corrected figur

Dynamics of a Josephson Array in a Resonant Cavity

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B {\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when $N_a$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in $N_a$, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.

Diagnostic accuracy of a three-gene Mycobacterium tuberculosis host response cartridge using fingerstick blood for childhood tuberculosis: a multicentre prospective study in low-income and middle-income countries

BACKGROUND: Childhood tuberculosis remains a major cause of morbidity and mortality in part due to missed diagnosis. Diagnostic methods with enhanced sensitivity using easy-to-obtain specimens are needed. We aimed to assess the diagnostic accuracy of the Cepheid Mycobacterium tuberculosis Host Response prototype cartridge (MTB-HR), a candidate test measuring a three-gene transcriptomic signature from fingerstick blood, in children with presumptive tuberculosis disease. METHODS: RaPaed-TB was a prospective diagnostic accuracy study conducted at four sites in African countries (Malawi, Mozambique, South Africa, and Tanzania) and one site in India. Children younger than 15 years with presumptive pulmonary or extrapulmonary tuberculosis were enrolled between Jan 21, 2019, and June 30, 2021. MTB-HR was performed at baseline and at 1 month in all children and was repeated at 3 months and 6 months in children on tuberculosis treatment. Accuracy was compared with tuberculosis status based on standardised microbiological, radiological, and clinical data. FINDINGS: 5313 potentially eligible children were screened, of whom 975 were eligible. 784 children had MTB-HR test results, of whom 639 had a diagnostic classification and were included in the analysis. MTB-HR differentiated children with culture-confirmed tuberculosis from those with unlikely tuberculosis with a sensitivity of 59·8% (95% CI 50·8–68·4). Using any microbiological confirmation (culture, Xpert MTB/RIF Ultra, or both), sensitivity was 41·6% (34·7–48·7), and using a composite clinical reference standard, sensitivity was 29·6% (25·4–34·2). Specificity for all three reference standards was 90·3% (95% CI 85·5–94·0). Performance was similar in different age groups and by malnutrition status. Among children living with HIV, accuracy against the strict reference standard tended to be lower (sensitivity 50·0%, 15·7–84·3) compared with those without HIV (61·0%, 51·6–69·9), although the difference did not reach statistical significance. Combining baseline MTB-HR result with one Ultra result identified 71·2% of children with microbiologically confirmed tuberculosis. INTERPRETATION: MTB-HR showed promising diagnostic accuracy for culture-confirmed tuberculosis in this large, geographically diverse, paediatric cohort and hard-to-diagnose subgroups. FUNDING: European and Developing Countries Clinical Trials Partnership, UK Medical Research Council, Swedish International Development Cooperation Agency, Bundesministerium für Bildung und Forschung; German Center for Infection Research (DZIF)