Self-accelerating self-trapped optical beams

We present self-accelerating self-trapped beams in nonlinear optical media, exhibiting self-focusing and self-defocusing Kerr and saturable nonlinearities, as well as a quadratic response. In Kerr and saturable media such beams are stable under self-defocusing and weak self-focusing, whereas for strong self-focusing the beams off-shoot solitons while their main lobe continues to accelerate. Self-accelerating self-trapped wave packets are universal, and can also be found in matter waves, plasma, etc.     

Real-time quantification of protein expression and translocation at individual cell resolution using imaging-dish-based live cell array

Cell populations represent intrinsically heterogeneous systems with a high level of spatiotemporal complexity. Monitoring and understanding cell-to-cell diversity is essential for the research and application of intra- and interpopulation variations. Optical analysis of live cells is challenging since both adherent and nonadherent cells change their spatial location. However, most currently available single-cell techniques do not facilitate treatment and monitoring of the same live cells over time throughout multistep experiments. An imaging-dish-based live cell array (ID-LCA) has been developed and produced for cell handling, culturing, and imaging of numerous live cells. The dish is composed of an array of pico scale cavities—pico wells (PWs) embossed on its glass bottom. Cells are seeded, cultured, treated, and spatiotemporally measured on the ID-LCA, while each cell or small group of cells are locally constrained in the PWs. Finally, predefined cells can be retrieved for further evaluation. Various types of ID-LCAs were used in this proof-of-principle work, to demonstrate on-ID-LCA transfection of fluorescently tagged chimeric proteins, as well as the detection and kinetic analysis of their induced translocation. High variability was evident within cell populations with regard to protein expression levels as well as the extent and dynamics of protein redistribution. The association of these parameters with cell morphology and functional parameters was examined. Both the new methodology and the device facilitate research of the translocation process at individual cell resolution within large populations and thus, can potentially be used in high-throughput fashion. Graphical Abstract

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Brownian motion of a nonlinear oscillator

Starting with the Langevin equation for a nonlinear oscillator (the Duffing oscillator) undergoing ordinary Brownian motion, we derive linear transport laws for the motion of the average position and velocity of the oscillator. The resulting linear equations are valid for only small deviations of average values from thermal equilibrium. They contain a renormalized oscillator frequency and a renormalized and non-Markovian friction coefficient, both depending on the nonlinear part of the original equation of motion. Numerical computations of the position correlation function and its spectral density are presented. The spectral density compares favorably with experimental results obtained by Morton using an analog computer method.Technical Note BN-674. Research supported in part by NSF grant GP-12591, and in part by PHS Research Grant No. MG16426-02 from the National Institute of General Medical Sciences.     

Study of 71, 73, 75, 77As with Ge(3He,d) reactions

Studies of ^{71, 73, 75, 77}As isotopes using Ge(³He, d) reactions have enabled the identification of many previously unreported levels together with new spin-parity assignments. A comparison of the results with the predictions of the model of Scholz and Malik shows good agreement for both positive- and negative-parity states.     

On powers of nonnegative matrices

We investigate the structure of powers of nonnegative matrices A, and in particular characterize those A for which some power is (essentially) triangular. We also show how the number of irreducible components of A can be determined from its powers.     

Pattern projection for subpixel resolved imaging in microscopy

In this paper, we present a new approach providing super resolved images exceeding the geometrical limitation given by the detector pixel size of the imaging camera. The concept involves the projection of periodic patterns on top of the sample, which are then investigated under a microscope. Combining spatial scanning together with proper digital post-processing algorithm yields the improved geometrical resolution enhancement. This new method is especially interesting for microscopic imaging when the resolution of the detector is lower than the resolution due to diffraction.     

Magnetic resonance studies of the properties of water in cellulose acetate membranes

The properties of water in various cellulose acetate (CA) membranes have been investigated by magnetic resonance techniques. It has been observed that the longitudinal (T₁) relaxation time of ¹⁷O in CA membranes containing H₂ ¹⁷O is considerably shorter (by a factor of 5 to 6) than the corresponding value in pure water. The T₁ values of ²³Na ions contained in these membranes were, however, shorter than the corresponding values observed in measurements of the aqueous mother solution by a factor smaller than 2. The EPR spectra of Mn²⁺ and of Cr³⁺ contained in CA membranes were practically identical to the spectra of the pure aqueous solution.

The data suggest the existence, in the CA membrane, of two “types” of water; a small fraction of highly immobilized “bound” water and the remaining large fraction of “free” water displaying properties almost identical to those of pure bulk water. This model is supported by measurements of the longitudinal relaxation rates of H₂ ¹⁷O in CA membranes which were gradually dehydrated from their water.