Temperature time traces are obtained in turbulent thermal convection at high Rayleigh numbers. Measurements are made in the midplane of the apparatus, near the sidewall but outside the boundary layer. A telegraph approximation for temperature traces is generated by setting the fluctuation amplitude to 1 or 0 depending on whether or not it exceeds the mean value. Unlike the standard diagnostics of intermittency, the telegraph approximation allows one to distinguish the tendency of events to cluster (clusterization) from their large-scale variability in amplitude. A qualitative conclusion is that amplitude intermittency might mitigate clusterization effects.
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http://dx.doi.org/10.1103/PhysRevE.69.056314 | DOI Listing |
J Chem Phys
August 2024
Department of Pure and Applied Chemistry, Faculty of Science and Technology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan.
For both dielectric spectroscopy and light scattering spectra, the relaxation modes in the microwave region have been characterized by the Debye relaxation model, which is determined by the peak frequency, or by an empirically extended model (e.g., Cole-Davidson and Kohlrausch-Williams-Watts), which has the appropriate line shape.
View Article and Find Full Text PDFMath Biosci
July 2024
School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3BF, UK. Electronic address:
We introduce a biologically detailed, stochastic model of gene expression describing the multiple rate-limiting steps of transcription, nuclear pre-mRNA processing, nuclear mRNA export, cytoplasmic mRNA degradation and translation of mRNA into protein. The processes in sub-cellular compartments are described by an arbitrary number of processing stages, thus accounting for a significantly finer molecular description of gene expression than conventional models such as the telegraph, two-stage and three-stage models of gene expression. We use two distinct tools, queueing theory and model reduction using the slow-scale linear-noise approximation, to derive exact or approximate analytic expressions for the moments or distributions of nuclear mRNA, cytoplasmic mRNA and protein fluctuations, as well as lower bounds for their Fano factors in steady-state conditions.
View Article and Find Full Text PDFBiophys J
January 2024
Biology Department, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France.
The snapshot distribution of mRNA counts per cell can be measured using single-molecule fluorescence in situ hybridization or single-cell RNA sequencing. These distributions are often fit to the steady-state distribution of the two-state telegraph model to estimate the three transcriptional parameters for a gene of interest: mRNA synthesis rate, the switching on rate (the on state being the active transcriptional state), and the switching off rate. This model assumes no extrinsic noise, i.
View Article and Find Full Text PDFR Soc Open Sci
April 2023
Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, Guangdong Province 510275, People's Republic of China.
Gene expression has inherent stochasticity resulting from transcription's burst manners. Single-cell snapshot data can be exploited to rigorously infer transcriptional burst kinetics, using mathematical models as blueprints. The classical telegraph model (CTM) has been widely used to explain transcriptional bursting with Markovian assumptions.
View Article and Find Full Text PDFSci Rep
March 2023
Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research, RIKEN, Wakoshi, Saitama, 351-0198, Japan.
The approach by Ettore Majorana for non-adiabatic transitions between two quasi-crossing levels is revisited and significantly extended. We rederive the transition probability, known as the Landau-Zener-Stückelberg-Majorana formula, and introduce Majorana's approach to modern readers. This result, typically referred as the Landau-Zener formula, was published by Majorana before Landau, Zener and Stückelberg.
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