Transition state theory: variational formulation, dynamical corrections, and error estimates

Transition state theory (TST) is revisited, as well as evolutions upon TST such as variational TST in which the TST dividing surface is optimized so as to minimize the rate of recrossing through this surface and methods which aim at computing dynamical corrections to the TST transition rate constant. The theory is discussed from an original viewpoint. It is shown how to compute exactly the mean frequency of transition between two predefined sets which either partition phase space (as in TST) or are taken to be well-separated metastable sets corresponding to long-lived conformation states (as necessary to obtain the actual transition rate constants between these states). Exact and approximate criterions for the optimal TST dividing surface with minimum recrossing rate are derived. Some issues about the definition and meaning of the free energy in the context of TST are also discussed. Finally precise error estimates for the numerical procedure to evaluate the transmission coefficient kappaS of the TST dividing surface are given, and it is shown that the relative error on kappaS scales as 1/square root(kappaS) when kappaS is small. This implies that dynamical corrections to the TST rate constant can be computed efficiently if and only if the TST dividing surface has a transmission coefficient kappaS which is not too small. In particular, the TST dividing surface must be optimized upon (for otherwise kappaS is generally very small), but this may not be sufficient to make the procedure numerically efficient (because the optimal dividing surface has maximum kappaS, but this coefficient may still be very small).     

Transport Properties of H+-Selective Membranes Containing Amine-Derivative Ionophores and Mobile Sites

Transport processes in plasticized PVC membranes containing the H⁺ chromoionophore ETH 5294 and additional tetraphenylborate-type mobile sites were analyzed by employing the potential-step method. Using chronoamperometry, impedance spectroscopy, and UV/VIS absorbance measurements, it is shown that the ionophore behaves as a carrier for protons, when the membranes are immersed between two aqueous solutions. It was possible to document the changes in the concentration profiles of both free ionophores and ionic species in some of the membranes. There is no evidence of proton hopping between the ionophores.     

Femtosecond pulse-shape modulation at nanosecond rates

We report high-rate, computer-controlled femtosecond pulse shaping by use of an electro-optical gallium arsenide optical phased-array modulator with 2304 controlled waveguides. It provides fast modulation speed of both spectral phases and amplitudes. Limited by the driving electronics of our current setup, we were able to update a pulse shape in approximately 30 ns. This technique paves the way toward individual shaping of every single pulse of typical femtosecond mode-locked oscillators.     

Monitoring Dissociation Kinetics during Electrophoretic Focusing to Enable High‐Specificity Nucleic Acid Detection

A wide range of medical conditions can be diagnosed through sequence‐specific analysis of nucleic acids. However, a major challenge remains in detecting a specific target in samples containing a high concentration of mismatching sequences. A single‐step kinetic homogenous (free solution) assay is presented in which free sequence‐specific probes are continuously separated from probe–target hybrids during electrophoretic sample focusing, allowing monitoring of dissociation kinetics. Under these conditions, the different kinetics of targets versus mismatches result in distinct patterns of the signal (for example, linear increase for target versus exponential decay for mismatch), allowing the detection of desired sequences even in the presence of high background nucleic acid content. Additionally, an analytical model provides insight into the underlying dynamics, and allows design of assays based on this mechanism.     

Hardy Spaces on ? n with Pointwise Variable Anisotropy

In this work we develop highly geometric Hardy spaces, for the full range 0<p≤1. These spaces are constructed over multi-level ellipsoid covers of ℝ ⁿ that are highly anisotropic in the sense that the ellipsoids can change shape rapidly from point to point and from level to level. This generalizes previous work on anisotropic Hardy spaces where the geometry of the space was ‘fixed’ over ℝ ⁿ and extends Hardy spaces over spaces of homogeneous type, where the theory holds for p values that are ‘close’ to 1.     

Talbot solitons

We propose a new type of scalar wave-mixing optical solitons, Talbot solitons. The soliton consists of sinusoidal and uniform components that are mutually coherent and jointly trapped in one direction. The intensity structure of the soliton oscillates in the propagation direction as a result of the linear Talbot effect and periodic nonlinear energy exchange between the components. Talbot solitons induce a 1D waveguide and a 2D photonic lattice within the waveguide that may be used for quasi-phase matching of frequency conversion and as a tunable waveguide filter.     

Students' Understanding of the Particulate Nature of Matter

The particulate nature of matter is identified in science education standards as one of the fundamental concepts that students should understand at the middle school level. However, science education research in indicates that secondary school students have difficulties understanding the structure of matter. The purpose of the study is to describe how engaging in an extended project‐based unit developed urban middle school students' understanding of the particulate nature of matter. Multiple sources of data were collected, including pre‐ and posttests, interviews, students' drawings, and video recordings of classroom activities. One teacher and her five classes were chosen for an indepth study. Analyses of data show that after experiencing a series of learning activities the majority of students acquired substantial content knowledge. Additionally, the finding indicates that students' understanding of the particulate nature of matter improved over time and that they retained and even reinforced their understanding after applying the concept. Discussions of the design features of curriculum and the teacher's use of multiple representations might provide insights into the effectiveness of learning activities in the unit.     

Mode conversion in quadratic nonlinear crystals

We propose a novel all-optical, nonlinear mode-conversion scheme based on cascaded three-wave-mixing phase-matched interactions in quadratic nonlinear crystals. We demonstrate the method experimentally by performing all-optical mode conversion of an input 1636 nm Hermite-Gaussian mode from the zeroth order to the first order using two periodically poled LiNbO(3) crystals. Nonlinear mode conversion of an input beam into a higher order, orthogonally polarized output beam can be realized using only one quasiperiodic nonlinear structure. Moreover, it can be enhanced for conversion of complex modes, e.g., Laguerre-Gaussian or Bessel modes.