We have used electron-beam lithography to fabricate superconducting "wire" arrays in a variety of patterns ranging from periodic to random and including the intermediate quasicrystalline and incommensurate configurations.Sweeping an applied magnetic field while observing the critical temperature reveals which fields are favorable or commensurate with the pattern. We find sharp dips in the T, (H) curve for periodic, incommensurate (quasiperiodic), and quasicrystalline arrays reflecting a lock-in of the flux lattice with the underlying network. We find no similar fine structure for random arrays. This allows us to generalize the concept of commensurability to nonperiodic structures.

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We have measured the superconducting transition temperature T C (H) as a function of magnetic field for a network of thin aluminum wires arranged in two quasicrystalline arrays, a Fibonacci sequence and the eightfold-symmetric version of a Penrose tiling. The quasicrystals have two periods whose ratio cr is irrational and are constructed of two tiles with irrationally related areas. We find a series of dips in §T C {H) corresponding to favorable arrangements of the flux lattice on the quasicrystalline substrate. The largest dips are found at cr n and the dips approach the zero-field transition temperature as n increases.PACS numbers: 74.60.Ge, 64.70.Rh Flux-quantization experiments on periodic arrays of superconducting elements have shown a wealth of interesting and complex structure. 1 ' 2 When the magnetic field is such that there is an integral number of flux quanta per unit cell, the superconducting transition temperature returns to its zero-field value since at these fields each and every cell satisfies fluxoid quantization 3 with no current through the filaments. For fields less than one flux quantum per cell there are cusps on the phase-boundary curve T C (H) at every rational field (that is, every rational fraction p/q of a flux quantum, 0 = hc/2e, per unit cell). This is indicative of the flux lattice's finding a commensurate configuration on the array. 4 Using cells or tiles with relatively irrational areas will preclude the system from satisfying quantization in all cells simultaneously. If the system possesses quasiperiodic translational order, two or more incommensurate periods, this will greatly change the ability of the flux lattice to find a favorable "commensurate" configuration. Quasicrystalline arrays, 5,6 herein taken as quasiperiodic networks with a finite number of elementary tiles, should therefore exhibit phase boundaries which differ greatly from those of periodic (crystalline) arrays. However, quasicrystals are highly ordered structures, and so we would expect considerably more structure in the phase boundary than for a random network.In this Letter we report on experiments on two patterns that we have generated at the National Research and Resource Facility for Submicron Structures at Cornell. One pattern, Fig. 1 inset, consists of 400 parallel lines equally spaced (2 /utm) in the y direction crossed by 400 parallel lines arranged in a Fibonacci sequence 6 in the x direction [the small spacing is 1.45 fim and the large spacing is 2.34 /xm, larger by a factor of r = (V5 +1)/2, the golden mean]. The quasiperiodicity of the Fibonacci sequence and the ratio of the number of large to small intervals is also characterized by the number T. The thickness of the aluminum wires is 500 A and their width is 0.30 fxm. The resistance of the samples is measured with a four-probe ac technique. Typically the width of the superconducting transition as a function of temperature in zero field is 2.5 mK. The sample resistance is stabilized at a fixed fraction of the normal-state value by use of a feedba...

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Fluorescence tomography (FT) is depth-resolved three-dimensional (3D) localization and quantification of fluorescence distribution in biological tissue and entails a highly ill-conditioned problem as depth information must be extracted from boundary measurements. Conventionally, L2 regularization schemes that penalize the euclidean norm of the solution and possess smoothing effects are used for FT reconstruction. Oversmooth, continuous reconstructions lack high-frequency edge-type features of the original distribution and yield poor resolution. We propose an alternative regularization method for FT that penalizes the total variation (TV) norm of the solution to preserve sharp transitions in the reconstructed fluorescence map while overcoming ill-posedness. We have developed two iterative methods for fast 3D reconstruction in FT based on TV regularization inspired by Rudin-Osher-Fatemi and split Bregman algorithms. The performance of the proposed method is studied in a phantom-based experiment using a noncontact constant-wave trans-illumination FT system. It is observed that the proposed method performs better in resolving fluorescence inclusions at different depths.