14,613 research outputs found
Generic Schemes for Single Molecule Kinetics 2: Information Content of the Poisson Indicator
Recently, we described a pathway analysis technique (paper 1) for analyzing
generic schemes for single-molecule kinetics based upon the first-passage time
distribution. Here, we employ this method to derive expressions for the Poisson
indicator, a measure of stochastic variation (essentially equivalent to the
Fano factor and Mandel's Q parameter), for various renewal (memoryless)
enzymatic reactions. We examine its dependence on substrate concentration,
without assuming all steps follow Poissonian kinetics. Based upon fitting to
the functional forms of the first two waiting time moments, we show that, to
second order, the non-Poissonian kinetics are generally underdetermined but can
be specified in certain scenarios. For an enzymatic reaction with an arbitrary
intermediate topology, we identify a generic minimum of the Poisson indicator
as a function of substrate concentration, which can be used to tune substrate
concentration to the stochastic fluctuations and estimate the largest number of
underlying consecutive links in a turnover cycle. We identify a local maximum
of the Poisson indicator (with respect to substrate concentration) for a
renewal process as a signature of competitive binding, either between a
substrate and an inhibitor or between multiple substrates. Our analysis
explores the rich connections between Poisson indicator measurements and
microscopic kinetic mechanisms
A Case Study: An Investigation on Influences Affecting the Reading Levels of Bilingual Students
This study examines the reading of native Spanish-speaking Hispanic students, focusing on any influences or factors that might impede their ability to gain competence in their target language—English. It focuses on eight students from a middle school in Rochester, NY. Four students scoring in the lower half of the Pupil Evaluation Program (PEP) test and four students scoring in the upper half were selected for examination. Each student participated in a personal interview to determine whether there are any influences that impact them in the affective domain. The study reveals four primary concerns that may impact student success, including parent/school miscommunication about the bilingual program, code-mixing in the home, parental modeling and reading instruction, and the lack of adequate Spanish reading material available to the bilingual students. In addition, the author notes that using bilingual programs to transition multi-lingual students into an exclusively English environment seems counterproductive, given the emphasis on foreign language acquisition in secondary school
Linear response formula for piecewise expanding unimodal maps
The average R(t) of a smooth function with respect to the SRB measure of a
smooth one-parameter family f_t of piecewise expanding interval maps is not
always Lipschitz. We prove that if f_t is tangent to the topological class of
f_0, then R(t) is differentiable at zero, and the derivative coincides with the
resummation previously proposed by the first named author of the (a priori
divergent) series given by Ruelle's conjecture.Comment: We added Theorem 7.1 which shows that the horizontality condition is
necessary. The paper "Smooth deformations..." containing Thm 2.8 is now
available on the arxiv; see also Corrigendum arXiv:1205.5468 (to appear
Nonlinearity 2012
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Numerical investigation of high-speed droplet impact using a multiscale two-fluid approach
A single droplet impact onto solid surfaces remains a fundamental and challenging topic in both experimental and numerical studies with significant importance in a plethora of industrial applications, ranging from printing technologies to fuel injection in internal combustion engines. Under high-speed impact conditions, additional complexities arise as a result of the prompt droplet splashing and the subsequent violent fragmentation; thus, different flow regimes and a vast spectrum of sizes for the produced secondary flow structures coexist in the flow field. The present work introduces a numerical methodology to capture the multiscale processes involved with respect to local topological characteristics. The proposed methodology concerns a compressible Σ-Υ two-fluid model with dynamic interface sharpening based on an advanced flow topology detection algorithm. The model has been developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of droplet splashing, by switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively. An additional transport equation for the interface surface area density (Σ) introduces important information for the sub-grid scale phenomena, which is exploited in the dispersed flow regions to provide an insight into the extended cloud of secondary droplets after impact on the target. A high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at velocity as high as 150m/s, which corresponds to a Weber number of ~7.6×10^5. At the investigated impact conditions compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. The proposed numerical approach is found to capture relatively accurately the phenomena and provide significant information regarding the produced flow structure dimensions, which is not available from the experiment
Statistical properties of quadratic polynomials with a neutral fixed point
We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2\pi a i} z+z^2 on the complex plane, with a of high return times. In particular, we show that these maps are uniquely ergodic on their measure theoretic attractors, and the unique invariant probability is a physical measure describing the statistical behavior of typical orbits in the Julia set. This confirms a conjecture of Perez-Marco on the unique ergodicity of hedgehog dynamics, in this class of maps
The rise of fully turbulent flow
Over a century of research into the origin of turbulence in wallbounded shear
flows has resulted in a puzzling picture in which turbulence appears in a
variety of different states competing with laminar background flow. At slightly
higher speeds the situation changes distinctly and the entire flow is
turbulent. Neither the origin of the different states encountered during
transition, nor their front dynamics, let alone the transformation to full
turbulence could be explained to date. Combining experiments, theory and
computer simulations here we uncover the bifurcation scenario organising the
route to fully turbulent pipe flow and explain the front dynamics of the
different states encountered in the process. Key to resolving this problem is
the interpretation of the flow as a bistable system with nonlinear propagation
(advection) of turbulent fronts. These findings bridge the gap between our
understanding of the onset of turbulence and fully turbulent flows.Comment: 31 pages, 9 figure
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