Probing polarization and dielectric function of molecules with higher order harmonics in scattering-near-field scanning optical microscopy

The idealized system of an atomically flat metallic surface [highly oriented pyrolytic graphite (HOPG)] and an organic monolayer (porphyrin) was used to determine whether the dielectric function and associated properties of thin films can be accessed with scanning-near-field scanning optical microscopy (s-NSOM). Here, we demonstrate the use of harmonics up to fourth order and the polarization dependence of incident light to probe dielectric properties on idealized samples of monolayers of organic molecules on atomically smooth substrates. An analytical treatment of light/sample interaction using the s-NSOM tip was developed in order to quantify the dielectric properties. The theoretical analysis and numerical modeling, as well as experimental data, demonstrate that higher order harmonic scattering can be used to extract the dielectric properties of materials with tens of nanometer spatial resolution. To date, the third harmonic provides the best lateral resolution (∼50 nm) and dielectric constant contrast for a porphyrin film on HOPG. © 2009 American Institute of Physics.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.

Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification

We propose and experimentally validate a first-principles based model for the nonlinear piezoelectric response of an electroelastic energy harvester. The analysis herein highlights the importance of modeling inherent piezoelectric nonlinearities that are not limited to higher order elastic effects but also include nonlinear coupling to a power harvesting circuit. Furthermore, a nonlinear damping mechanism is shown to accurately restrict the amplitude and bandwidth of the frequency response. The linear piezoelectric modeling framework widely accepted for theoretical investigations is demonstrated to be a weak presumption for near-resonant excitation amplitudes as low as 0.5 g in a prefabricated bimorph whose oscillation amplitudes remain geometrically linear for the full range of experimental tests performed (never exceeding 0.25% of the cantilever overhang length). Nonlinear coefficients are identified via a nonlinear least-squares optimization algorithm that utilizes an approximate analytic solution obtained by the method of harmonic balance. For lead zirconate titanate (PZT-5H), we obtained a fourth order elastic tensor component of c1111p =-3.6673× 1017 N/m2 and a fourth order electroelastic tensor value of e3111 =1.7212× 108 m/V. © 2010 American Institute of Physics.

Cysteine proteinase-1 and cut protein isoform control dendritic innervation of two distinct sensory fields by a single neuron.

Dendrites often exhibit structural changes in response to local inputs. Although mechanisms that pattern and maintain dendritic arbors are becoming clearer, processes regulating regrowth, during context-dependent plasticity or after injury, remain poorly understood. We found that a class of Drosophila sensory neurons, through complete pruning and regeneration, can elaborate two distinct dendritic trees, innervating independent sensory fields. An expression screen identified Cysteine proteinase-1 (Cp1) as a critical regulator of this process. Unlike known ecdysone effectors, Cp1-mutant ddaC neurons pruned larval dendrites normally but failed to regrow adult dendrites. Cp1 expression was upregulated/concentrated in the nucleus during metamorphosis, controlling production of a truncated Cut homeodomain transcription factor. This truncated Cut, but not the full-length protein, allowed Cp1-mutant ddaC neurons to regenerate higher-order adult dendrites. These results identify a molecular pathway needed for dendrite regrowth after pruning, which allows the same neuron to innervate distinct sensory fields.

The past, present, and future of human centromere genomics.

The centromere is the chromosomal locus essential for chromosome inheritance and genome stability. Human centromeres are located at repetitive alpha satellite DNA arrays that compose approximately 5% of the genome. Contiguous alpha satellite DNA sequence is absent from the assembled reference genome, limiting current understanding of centromere organization and function. Here, we review the progress in centromere genomics spanning the discovery of the sequence to its molecular characterization and the work done during the Human Genome Project era to elucidate alpha satellite structure and sequence variation. We discuss exciting recent advances in alpha satellite sequence assembly that have provided important insight into the abundance and complex organization of this sequence on human chromosomes. In light of these new findings, we offer perspectives for future studies of human centromere assembly and function.