Assessing T cell clonal size distribution: a non-parametric approach

Clonal structure of the human peripheral T-cell repertoire is shaped by a number of homeostatic mechanisms, including antigen presentation, cytokine and cell regulation. Its accurate tuning leads to a remarkable ability to combat pathogens in all their variety, while systemic failures may lead to severe consequences like autoimmune diseases. Here we develop and make use of a non-parametric statistical approach to assess T cell clonal size distributions from recent next generation sequencing data. For 41 healthy individuals and a patient with ankylosing spondylitis, who undergone treatment, we invariably find power law scaling over several decades and for the first time calculate quantitatively meaningful values of decay exponent. It has proved to be much the same among healthy donors, significantly different for an autoimmune patient before the therapy, and converging towards a typical value afterwards. We discuss implications of the findings for theoretical understanding and mathematical modeling of adaptive immunity.Comment: 13 pages, 3 figures, 2 table

Gate-controlled superconductivity in diffusive multiwalled carbon nanotube

We have investigated electrical transport in a diffusive multiwalled carbon nanotube contacted using superconducting leads made of Al/Ti sandwich structure. We find proximity-induced superconductivity with measured critical currents up to I_cm = 1.3 nA, tunable by gate voltage down to 10 pA. The supercurrent branch displays a finite zero bias resistance which varies as R_0 proportional to I_cm^-alpha with alpha=0.74. Using IV-characteristics of junctions with phase diffusion, a good agreement is obtained with Josephson coupling energy in the long, diffusive junction model of A.D Zaikin and G.F. Zharkov (Sov. J. Low Temp. Phys. 7, 184 (1981)).Comment: 5 pages, 4 figure

Supercurrent fluctuations in short filaments

We evaluate the average and the standard deviation of the supercurrent in superconducting nanobridges, as functions of the temperature and the phase difference, in an equilibrium situation. We also evaluate the autocorrelation of the supercurrent as a function of the elapsed time. The behavior of supercurrent fluctuations is qualitatively different from from that of the normal current: they depend on the phase difference, have a different temperature dependence, and for appropriate range their standard deviation is independent of the probing time. We considered two radically different filaments and obtained very similar results for both. Fluctuations of the supercurrent can in principle be measured

Operation of a superconducting nanowire quantum interference device with mesoscopic leads

A theory describing the operation of a superconducting nanowire quantum interference device (NQUID) is presented. The device consists of a pair of thin-film superconducting leads connected by a pair of topologically parallel ultra-narrow superconducting wires. It exhibits intrinsic electrical resistance, due to thermally-activated dissipative fluctuations of the superconducting order parameter. Attention is given to the dependence of this resistance on the strength of an externally applied magnetic field aligned perpendicular to the leads, for lead dimensions such that there is essentially complete and uniform penetration of the leads by the magnetic field. This regime, in which at least one of the lead dimensions lies between the superconducting coherence and penetration lengths, is referred to as the mesoscopic regime. The magnetic field causes a pronounced oscillation of the device resistance, with a period not dominated by the Aharonov-Bohm effect through the area enclosed by the wires and the film edges but, rather, in terms of the geometry of the leads, in contrast to the well-known Little-Parks resistance of thin-walled superconducting cylinders. A theory, encompassing this phenomenology, is developed through extensions, to the setting of parallel superconducting wires, of the Ivanchenko-Zil'berman-Ambegaokar-Halperin theory for the case of short wires and the Langer-Ambegaokar-McCumber-Halperin theory for the case of longer wires. It is demonstrated that the NQUID acts as a probe of spatial variations in the superconducting order parameter.Comment: 20 pages, 18 figure

Fractional Fokker-Planck dynamics: Numerical algorithm and simulations

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.Comment: 10 pages, 9 figure

Phase diffusion and charging effects in Josephson junctions

The supercurrent of a Josephson junction is reduced by phase diffusion. For ultrasmall capacitance junctions the current may be further decreased by Coulomb blockade effects. We calculate the Cooper pair current by means of time-dependent perturbation theory to all orders in the Josephson coupling energy and obtain the current-voltage characteristic in closed form in a range of parameters of experimental interest. The results comprehend phase diffusion of the coherent Josephson current in the classical regime as well as the supercurrent peak due to incoherent Cooper pair tunneling in the strong Coulomb blockade regime.Comment: 4 pages, 3 figures, RevTe

Current and universal scaling in anomalous transport

Anomalous transport in tilted periodic potentials is investigated within the framework of the fractional Fokker-Planck dynamics and the underlying continuous time random walk. The analytical solution for the stationary, anomalous current is obtained in closed form. We derive a universal scaling law for anomalous diffusion occurring in tilted periodic potentials. This scaling relation is corroborated with precise numerical studies covering wide parameter regimes and different shapes for the periodic potential, being either symmetric or ratchet-like ones

Manipulation and Generation of Supercurrent in Out-of-Equilibrium Josephson Tunnel Nanojunctions

We demonstrate experimentally manipulation of supercurrent in Al-AlO_x-Ti Josephson tunnel junctions by injecting quasiparticles in a Ti island from two additional tunnel-coupled Al superconducting reservoirs. Both supercurrent enhancement and quenching with respect to equilibrium are achieved. We demonstrate cooling of the Ti line by quasiparticle injection from the normal state deep into the superconducting phase. A model based on heat transport and non-monotonic current-voltage characteristic of a Josephson junction satisfactorily accounts for our findings.Comment: 4 pages, 4 colour figures, published versio

Quantum charge diffusion in underdamped Josephson junctions and superconducting nanowires

The effect of quantum fluctuations on the current-voltage characteristics of Josephson junctions and superconducting nanowires is studied in the underdamped limit. Quantum fluctuations induce transitions between a Coulomb--blockade and a supercurrent branch, and can significantly modify the shape of current-voltage characteristics in the case of a highly resistive environment. Owing to the phase-charge duality, our results can be directly extended to the opposite overdamped limit.Comment: 6 pages, 2 figures, replaced with published versio

Macroscopic quantum tunneling in "small" Josephson junctions in magnetic field

We study the phenomenon of macroscopic quantum tunneling (MQT) in small Josephson junctions (JJ) with an externally applied magnetic field. The latter results in the appearance of the Fraunhofer type modulation of the current density along the barrier. The problem of MQT for a point-like JJ is reduced to the motion of the quantum particle in the washboard potential. In the case of a finite size JJ under consideration, this problem corresponds to a MQT in potential which itself, besides the phase, depends on space variables. Finally, the general expression for the crossover temperature T_0 between thermally activated and macroscopic quantum tunneling regimes and the escaping time tau_esc have been calculated