395 research outputs found
A Nonlinear Analysis of the Averaged Euler Equations
This paper develops the geometry and analysis of the averaged Euler equations
for ideal incompressible flow in domains in Euclidean space and on Riemannian
manifolds, possibly with boundary. The averaged Euler equations involve a
parameter ; one interpretation is that they are obtained by ensemble
averaging the Euler equations in Lagrangian representation over rapid
fluctuations whose amplitudes are of order . The particle flows
associated with these equations are shown to be geodesics on a suitable group
of volume preserving diffeomorphisms, just as with the Euler equations
themselves (according to Arnold's theorem), but with respect to a right
invariant metric instead of the metric. The equations are also
equivalent to those for a certain second grade fluid. Additional properties of
the Euler equations, such as smoothness of the geodesic spray (the Ebin-Marsden
theorem) are also shown to hold. Using this nonlinear analysis framework, the
limit of zero viscosity for the corresponding viscous equations is shown to be
a regular limit, {\it even in the presence of boundaries}.Comment: 25 pages, no figures, Dedicated to Vladimir Arnold on the occasion of
his 60th birthday, Arnold Festschrift Volume 2 (in press
Comparative analysis of magnetic resonance in the polaron pair recombination and the triplet exciton-polaron quenching models
We present a comparative theoretical study of magnetic resonance within the polaron pair recombination (PPR) and the triplet exciton-polaron quenching (TPQ) models. Both models have been invoked to interpret the photoluminescence detected magnetic resonance (PLDMR) results in π -conjugated materials and devices. We show that resonance line shapes calculated within the two models differ dramatically in several regards. First, in the PPR model, the line shape exhibits unusual behavior upon increasing the microwave power: it evolves from fully positive at weak power to fully negative at strong power. In contrast, in the TPQ model, the PLDMR is completely positive, showing a monotonic saturation. Second, the two models predict different dependencies of the resonance signal on the photoexcitation power, P L . At low P L , the resonance amplitude Δ I / I is ∝ P L within the PPR model, while it is ∝ P 2 L crossing over to P 3 L within the TPQ model. On the physical level, the differences stem from different underlying spin dynamics. Most prominently, a negative resonance within the PPR model has its origin in the microwave-induced spin-Dicke effect, leading to the resonant quenching of photoluminescence. The spin-Dicke effect results from the spin-selective recombination, leading to a highly correlated precession of the on-resonance pair partners under the strong microwave power. This effect is not relevant for TPQ mechanism, where the strong zero-field splitting renders the majority of triplets off resonance. On the technical level, the analytical evaluation of the line shapes for the two models is enabled by the fact that these shapes can be expressed via the eigenvalues of a complex Hamiltonian. This bypasses the necessity of solving the much larger complex linear system of the stochastic Liouville equations. Our findings pave the way towards a reliable discrimination between the two mechanisms via cw PLDMR
Tunable perovskite-based photodetectors in optical sensing
Broad- and narrow-band, tunable perovskite photodetectors (PPDs) with size-dependent fast response times are demonstrated for the first time in optical sensing of analytes, including gas-phase and dissolved oxygen (DO), as well as glucose. The sensors included a LED excitation source and a polystyrene film with embedded oxygen-sensitive dyes, PtOEP or PdOEP. The analyte's dose-dependent photoluminescence (PL) intensity I and decay time τ were measured. Using the PPDs enabled monitoring gas-phase O2 at levels of 0 %–100 % with a sensitivity comparable to that of a Si photodiode. A broad dynamic range was similarly observed for DO monitoring and the limit of detection for glucose monitoring was ∼0.02 mM at an initial level of ∼0.26 mM DO. Importantly, the size-dependent fast response time of the PPDs enabled analyte monitoring via the preferred measurement of τ, rather than I, over a broad dynamic range, which was unattainable with organic photodetectors. The use of the narrow-band PPDs eliminated the need for optical filters, which leads to more compact device designs
Electronic Structure of Lanthanum Hydrides with Switchable Optical Properties
Recent dramatic changes in the optical properties of LaH_{2+x} and YH_{2+x}
films discovered by Huiberts et al. suggest their electronic structure is
described best by a local model. Electron correlation is important in H^-
-centers and in explaining the transparent insulating behavior of LaH_3. The
metal-insulator transition at takes place in a band of highly
localized states centered on the -vacancies in the LaH_3 structure.Comment: plain tex, 3 figure
Rules for biological regulation based on error minimization
The control of gene expression involves complex mechanisms that show large
variation in design. For example, genes can be turned on either by the binding
of an activator (positive control) or the unbinding of a repressor (negative
control). What determines the choice of mode of control for each gene? This
study proposes rules for gene regulation based on the assumption that free
regulatory sites are exposed to nonspecific binding errors, whereas sites bound
to their cognate regulators are protected from errors. Hence, the selected
mechanisms keep the sites bound to their designated regulators for most of the
time, thus minimizing fitness-reducing errors. This offers an explanation of
the empirically demonstrated Savageau demand rule: Genes that are needed often
in the natural environment tend to be regulated by activators, and rarely
needed genes tend to be regulated by repressors; in both cases, sites are bound
for most of the time, and errors are minimized. The fitness advantage of error
minimization appears to be readily selectable. The present approach can also
generate rules for multi-regulator systems. The error-minimization framework
raises several experimentally testable hypotheses. It may also apply to other
biological regulation systems, such as those involving protein-protein
interactions.Comment: biological physics, complex networks, systems biology,
transcriptional regulation
http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf
http://www.pnas.org/content/103/11/3999.ful
Robustness in Glyoxylate Bypass Regulation
The glyoxylate bypass allows Escherichia coli to grow on carbon sources with only two carbons by bypassing the loss of carbons as CO2 in the tricarboxylic acid cycle. The flux toward this bypass is regulated by the phosphorylation of the enzyme isocitrate dehydrogenase (IDH) by a bifunctional kinase–phosphatase called IDHKP. In this system, IDH activity has been found to be remarkably robust with respect to wide variations in the total IDH protein concentration. Here, we examine possible mechanisms to explain this robustness. Explanations in which IDHKP works simultaneously as a first-order kinase and as a zero-order phosphatase with a single IDH binding site are found to be inconsistent with robustness. Instead, we suggest a robust mechanism where both substrates bind the bifunctional enzyme to form a ternary complex
Theory for Metal Hydrides with Switchable Optical Properties
Recently it has been discovered that lanthanum, yttrium, and other metal
hydride films show dramatic changes in the optical properties at the
metal-insulator transition. Such changes on a high energy scale suggest the
electronic structure is best described by a local model based on negatively
charged hydrogen (H) ions. We develop a many-body theory for the strong
correlation in a H ion lattice. The metal hydride is described by a large
-limit of an Anderson lattice model. We use lanthanum hydride as a prototype
of these compounds, and find LaH is an insulator with a substantial gap
consistent with experiments. It may be viewed either as a Kondo insulator or a
band insulator due to strong electron correlation. A H vacancy state in LaH
is found to be highly localized due to the strong bonding between the electron
orbitals of hydrogen and metal atoms. Unlike the impurity states in the usual
semiconductors, there is only weak internal optical transitions within the
vacancy. The metal-insulator transition takes place in a band of these vacancy
states.Comment: 18 pages, 16 figures and 6 tables. Submitted to PR
Strong negative self regulation of Prokaryotic transcription factors increases the intrinsic noise of protein expression
Background
Many prokaryotic transcription factors repress their own transcription. It is often asserted that such regulation enables a cell to homeostatically maintain protein abundance. We explore the role of negative self regulation of transcription in regulating the variability of protein abundance using a variety of stochastic modeling techniques.
Results
We undertake a novel analysis of a classic model for negative self regulation. We demonstrate that, with standard approximations, protein variance relative to its mean should be independent of repressor strength in a physiological range. Consequently, in that range, the coefficient of variation would increase with repressor strength. However, stochastic computer simulations demonstrate that there is a greater increase in noise associated with strong repressors than predicted by theory. The discrepancies between the mathematical analysis and computer simulations arise because with strong repressors the approximation that leads to Michaelis-Menten-like hyperbolic repression terms ceases to be valid. Because we observe that strong negative feedback increases variability and so is unlikely to be a mechanism for noise control, we suggest instead that negative feedback is evolutionarily favoured because it allows the cell to minimize mRNA usage. To test this, we used in silico evolution to demonstrate that while negative feedback can achieve only a modest improvement in protein noise reduction compared with the unregulated system, it can achieve good improvement in protein response times and very substantial improvement in reducing mRNA levels.
Conclusions
Strong negative self regulation of transcription may not always be a mechanism for homeostatic control of protein abundance, but instead might be evolutionarily favoured as a mechanism to limit the use of mRNA. The use of hyperbolic terms derived from quasi-steady-state approximation should also be avoided in the analysis of stochastic models with strong repressors
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