Excitation of highly conjugated (porphinato)palladium(II) and (porphinato)platinum(II) oligomers produces long-lived, triplet states at unit quantum yield that absorb strongly over broad spectral domains of the NIR.

Transient dynamical studies of bis[(5,5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II)]ethyne (PPd(2)), 5,15-bis{[(5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II)]ethynyl}(10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II) (PPd(3)), bis[(5,5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II)]ethyne (PPt(2)), and 5,15-bis{[(5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II)]ethynyl}(10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II) (PPt(3)) show that the electronically excited triplet states of these highly conjugated supermolecular chromophores can be produced at unit quantum yield via fast S(1) → T(1) intersystem crossing dynamics (τ(isc): 5.2-49.4 ps). These species manifest high oscillator strength T(1) → T(n) transitions over broad NIR spectral windows. The facts that (i) the electronically excited triplet lifetimes of these PPd(n) and PPt(n) chromophores are long, ranging from 5 to 50 μs, and (ii) the ground and electronically excited absorptive manifolds of these multipigment ensembles can be extensively modulated over broad spectral domains indicate that these structures define a new precedent for conjugated materials featuring low-lying π-π* electronically excited states for NIR optical limiting and related long-wavelength nonlinear optical (NLO) applications.

Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

Role of DNA binding sites and slow unbinding kinetics in titration-based oscillators.

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators.

Localization in systems of non-identical oscillators

A singular perturbation method is applied to a non-conservative system of two weakly coupled strongly nonlinear non-identical oscillators. For certain parameters, localized solutions exist for which the amplitude of one oscillator is an order of magnitude smaller than the other. It is shown that these solutions are described by coupled equations for the phase difference and scaled amplitudes. Three types of localized solutions are obtained as solutions to these equations which correspond to phase locking, phase drift, and phase entrainment. Quantitative results for the phases and amplitudes of the oscillators and the stability of these phenomena are expressed in terms of the parameters of the model.

Numerical simulation of free surface behaviour of a molten liquid metal droplet with and without electromagnetic induction

Electromagnetic levitation of electrically conductive droplets by alternating magnetic fields is a technique used to measure the physical properties of liquid metallic alloys such as surface tension or viscosity. Experiments can be conducted under terrestrial conditions or in microgravity, to reduce electromagnetic stirring and shaping of the droplet. Under such conditions, the time-dependent behaviour of a point of the free surface is recorded. Then the signal is analysed considering the droplet as a harmonic damped oscillator. We use a spectral code, for fluid flow and free surface descriptions, to check the validity of this assumption for two cases. First when the motion inside the droplet is generated by its initial distortion only and second, when the droplet is located in a uniform magnetic field originating far from the droplet. It is found that some deviations exist which can lead to an overestimate of the value of viscosity.

Developing Single-Laser Sources for Multimodal Coherent Anti-Stokes Raman Scattering Microscopy

Coherent anti-Stokes Raman scattering (CARS) microscopy has developed rapidly and is opening the door to new types of experiments. This work describes the development of new laser sources for CARS microscopy and their use for different applications. It is specifically focused on multimodal nonlinear optical microscopy—the simultaneous combination of different imaging techniques. This allows us to address a diverse range of applications, such as the study of biomaterials, fluid inclusions, atherosclerosis, hepatitis C infection in cells, and ice formation in cells. For these applications new laser sources are developed that allow for practical multimodal imaging. For example, it is shown that using a single Ti:sapphire oscillator with a photonic crystal fiber, it is possible to develop a versatile multimodal imaging system using optimally chirped laser pulses. This system can perform simultaneous two photon excited fluorescence, second harmonic generation, and CARS microscopy. The versatility of the system is further demonstrated by showing that it is possible to probe different Raman modes using CARS microscopy simply by changing a time delay between the excitation beams. Using optimally chirped pulses also enables further simplification of the laser system required by using a single fiber laser combined with nonlinear optical fibers to perform effective multimodal imaging. While these sources are useful for practical multimodal imaging, it is believed that for further improvements in CARS microscopy sensitivity, new excitation schemes are necessary. This has led to the design of a new, high power, extended cavity oscillator that should be capable of implementing new excitation schemes for CARS microscopy as well as other techniques. Our interest in multimodal imaging has led us to other areas of research as well. For example, a fiber-coupling scheme for signal collection in the forward direction is demonstrated that allows for fluorescence lifetime imaging without significant temporal distortion. Also highlighted is an imaging artifact that is unique to CARS microscopy that can alter image interpretation, especially when using multimodal imaging. By combining expertise in nonlinear optics, laser development, fiber optics, and microscopy, we have developed systems and techniques that will be of benefit for multimodal CARS microscopy.

Electron collisions with Fe-peak elements: Forbidden transitions between the low lying valence states 3d6, 3d54s, and 3d54p of Fe III:

Effective collision strengths are presented for the Fe-peak element Fe III at electron temperatures (Te in degrees Kelvin) in the range 2 × 103 to 1 × 106. Forbidden transitions results are given between the 3d6, 3d54s, and the 3d54p manifolds applicable to the modeling of laboratory and astrophysical plasmas.

Electron impact excitation of Ar XVII

Energies for the lowest 49 levels among the 1s(2) and 1snl (n = 2-5) configurations of Ar XVII have been calculated using the GRASP code of Dyall et al. (1989, Comput. Phys. Comm., 55, 424). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Furthermore, collision strengths have also been calculated for all the 1176 transitions among the above 49 levels using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2005, Comput. Phys. Commun., in preparation), over a wide energy range up to 580 Ryd. Resonances have been resolved in the threshold region, and effective collision strengths have been obtained over a wide temperature range up to log T-e = 7.2 K. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 0.1%, whereas results for other parameters are probably accurate to better than 20%.

Radiative rates for E1, E2, M1 and M2 transitions in Fe X

Energies of the 54 levels belonging to the (1s(2)2s(2)2p(6)) 3s(2)3p(5), 3s3p(6), 3s(2)3p(4)3d and 3s3p(5)3d configurations of Fe X have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 3%, whereas results for other parameters are probably accurate to better than 20%. Additionally, the agreement between measured and calculated lifetimes is better than 10%.

Electron impact excitation of Fe XIII

Energy levels and radiative rates for transitions among the lowest 97 fine-structure levels belonging to the (1s(2) 2s(2) 2p(6)) 3 s(2) 3p(2), 3s3p(3), 3s(2) 3p3d, 3p(4), 3s3p(2) 3d and 3s(2) 3d(2) configurations of Fe XIII have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed using the Dirac Atomic R-matrix Code (DARC) of Norrington & Grant (2004). Radiative rates and oscillator strengths are tabulated for all allowed transitions among the 97 fine-structure levels, while collision strengths are reported for some transitions at a few energies above thresholds. Comparisons are made with the available results, and the accuracy of the data is assessed.

Radiative rates for transitions in Fe XVII

Energies of the lowest 157 levels belonging to the (1s(2)) 2s(2)2p(6), 2s(2)p(5)3l, 2s(2)2p(5)4l, 2s(2)2p(5)4l, 2s2p(5)5l, 2s2p(6)4l and 2s2p(6)5l configurations of Fe XVII have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E I), magnetic dipole (M I), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the results already available in the literature, and the accuracy of the data is assessed. Our energy levels are expected to be accurate to better than M whereas results for other parameters are probably accurate to better than 20%.

Radiative rates, collision strengths and effective collision strengths for transitions in Gd XXXVII

Energy levels and radiative rates for transitions among 107 fine-structure levels belonging to the (1s(2)2S(2)p(6)) 3S(2)3p(6)3d(10), 3S(2)3p(6)3d(9)4e. 3S(2)3p(5)3d(10)4e. and 3s3p(6)3d(10)4e configurations of Ni-like Gd XXXVII have been calculated using the fully relativistic GRASP code. Radiative rates and oscillator strengths are tabulated for all allowed transitions among these levels. Additionally. collision strengths for transitions among the lowest 59 levels have been computed using the Dirac Atomic R-matrix Code. Resonances in the threshold region have been delineated, but results for collision strengths are tabulated only at energies above thresholds in the range 120

Energy levels and radiative rates for transitions in Ni XIII-Ni XVI

Energy levels and radiative rates for fine-structure transitions in nickel ions (Ni XIII-XVI) have been calculated using the GRASP code. Configuration interaction and relativistic effects have been included, and comparisons are made with available data. Energy levels and radiative rates are tabulated for transitions among the 48, 43, 32, and 84 levels of Ni XIII, Ni XIV, Ni XV, and Ni XVI, respectively. The energy levels are assessed to be accurate to better than 5% for a majority of levels, while oscillator strengths for all strong transitions are accurate to better than 20%. (C) 2003 Published by Elsevier Inc.

Energy levels and radiative rates for transitions in Ar XIII, Ar XIV and Ar XV

Energies for 524 levels of Ar XIII, 460 levels of Ar XIV and 156 levels of Ar XV have been calculated using the GRASP code of Dyall et al. (1989). Additionally, radiative rates, oscillator strengths, and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among these levels. Comparisons are made with the limited results available in the literature, and the accuracy of the data is assessed. Our energy levels are estimated to be accurate to better than 1%, whereas results for other parameters are probably accurate to better than 20%. Additionally, the level lifetimes derived from our radiative rates are in excellent agreement with measured values.