Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces

Journal of Nonlinear Science - Transfer operators such as the Perron–Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The...     

Holography and Local Fields

This paper, which is a summary (in which considerable creative license has been taken) of the author’s talk at the sixth international conference on p-adic mathematical physics and its applications (CINVESTAV, Mexico City, October 2017), reviews some recent work connecting field theories defined on the p-adic numbers and ideas from the AdS/CFT correspondence. Some results are included, along with general discussion of the utility and interest of p-adic analogues of Lagrangian field theories, at least from the author’s perspective. A few challenges, shortcomings, and ideas for future work are also discussed.     

Fabrication of polymeric replicas of cell surfaces with nanoscale resolution

We report an approach for fabricating biomimetic surface replicas of cells with nanoscale resolution. Fixed cells serve as a template for a two-stage replica molding process. Cast from the template, the impression replica contains a reproduction of cellular topographical features indented into its surface, and cast from the impression replica, the relief replica contains a copy of these features protruding from its surface. Various polymers and cells can be utilized, and scanning electron microscopy, atomic force microscopy, and white light interferometry analyses confirm the replication of nanoscale features. These replicas are useful for investigating cellular function and for biomimetic tissue engineering.     

Measuring the momentum of a nanomechanical oscillator through the use of two tunnel junctions

We propose a way to measure the momentum p of a nanomechanical oscillator. The p detector is based on two tunnel junctions in an Aharonov-Bohm-type setup. One of the tunneling amplitudes depends on the motion of the oscillator, the other one not. Although the coupling between the detector and the oscillator is assumed to be linear in the position x of the oscillator, it turns out that the finite-frequency noise output of the detector will in general contain a term proportional to the momentum spectrum of the oscillator. This is a true quantum phenomenon, which can be realized in practice if the phase of the tunneling amplitude of the detector is tuned by the Aharonov-Bohm flux Phi to a p-sensitive value.     

Ruthenium complexes with diazadienes. I. Synthesis and crystal structure ofcis-Ru(dad)2Cl2 (dad = 2,7-dimethyl-3,6-diaza-3,5-octadiene)

Summary Reduction of RuCl₃ · 3 H₂O in the presence of the title diazadiene i-PrN=CH-CH=NPr-i (from the condensation of glyoxal and isopropylamine) gives the intensely colouredcis-Ru(dad)₂Cl₂ (2) in moderate yield. The crystal and molecular structure was determined by x-ray diffraction. Complex (2) crystallizes in space group P ¯1 witha = 1110.2(10),b = 1360.3(6) andc = 1427.6(8) pm;a = 85.05(4), = 79.07(6) and =82.65(6)° with four molecules in the unit cell.Electronic and¹H n.m.r. spectra are discussed. An abnormally small vicinal coupling of the azomethine protons is detected.     

Josephson effect in S<Subscript>F</Subscript>XS<Subscript>F</Subscript> junctions

We investigate the Josephson effect in S_FXS_F junctions, where S_F is a superconducting material with a ferromagnetic exchange field, and X is a weak link. The critical current I_c increases with the (antiparallel) exchange fields, if the distribution of transmission eigenvalues of the X layer has its maximum weight at small values. This exchange-field enhancement of the supercurrent does not exist if X is a diffusive normal metal. At low temperatures, there is a correspondence between the critical current in an S_FIS_F junction with collinear orientations of the two exchange fields, and the AC supercurrent amplitude in an SIS tunnel junction. The difference in the exchange fields h₁-h₂ in an S_FIS_F junction corresponds to the potential difference V₁-V₂ in an SIS junction; i.e., the singularity in I_c [in an S_FIS_F junction] at |h₁-h₂|=Δ₁+Δ₂ is the analogue of the Riedel peak. We also discuss the AC Josephson effect in S_FIS_F junctions.     

Full counting statistics of a superconducting beam splitter

We study the statistics of charge transport in a mesoscopic three-terminal device with one superconducting terminal and two normal-metal terminals. We calculate the full distribution of transmitted charges into the two symmetrically biased normal terminals. In a wide parameter range, we find large positive cross correlations between the currents in the two normal arms. We also determine the third cumulant that provides additional information on the statistics not contained in the current noise.     

Sorption Mechanisms of Eu(3+) on CSH Phases of Hydrated Cements

The sorption mechanisms of Eu(3+) on calcium silicate hydrate (CSH) phases of hydrated cement were investigated as a tool for the prediction of the behavior of trivalent radionuclides with aged/degraded cements in radioactive waste repositories. Four techniques were used: site-selective and time-resolved luminescence spectroscopy, XPS, high-resolution SEM coupled with EDX, and XRD. Results showed that europium is not precipitated in the solution despite its low solubility limit. It is strongly retained on CSH, resulting in a more than 99.8% sorption rate. Two main sorption sites were characterized by luminescence spectroscopy. One site, with a long lifetime, can be interpreted as Eu included in the framework of CSH. Another one, with a shorter lifetime, can be interpreted as a site with a hydrated environment that is high but is less than that of europium hydroxide. It corresponds to superficial complexation or precipitation. Copyright 2001 Academic Press.     

Nitrogen Alkylation of schiff bases and amidines as a route to N-alkyl amino acids

Schiff base and amidine ester $\text{3}$ are alkylated and then hydrolyzed to yield N-alkyl amino acids $\text{4}$ in 41–75% yield with high to complete retention of optical activity.