Scaling and Universality in the Counterion-Condensation Transition at Charged Cylinders

We address the critical and universal aspects of counterion-condensation transition at a single charged cylinder in both two and three spatial dimensions using numerical and analytical methods. By introducing a novel Monte-Carlo sampling method in logarithmic radial scale, we are able to numerically simulate the critical limit of infinite system size (corresponding to infinite-dilution limit) within tractable equilibration times. The critical exponents are determined for the inverse moments of the counterionic density profile (which play the role of the order parameters and represent the inverse localization length of counterions) both within mean-field theory and within Monte-Carlo simulations. In three dimensions (3D), correlation effects (neglected within mean-field theory) lead to an excessive accumulation of counterions near the charged cylinder below the critical temperature (condensation phase), while surprisingly, the critical region exhibits universal critical exponents in accord with the mean-field theory. In two dimensions (2D), we demonstrate, using both numerical and analytical approaches, that the mean-field theory becomes exact at all temperatures (Manning parameters), when number of counterions tends to infinity. For finite particle number, however, the 2D problem displays a series of peculiar singular points (with diverging heat capacity), which reflect successive de-localization events of individual counterions from the central cylinder. In both 2D and 3D, the heat capacity shows a universal jump at the critical point, and the energy develops a pronounced peak. The asymptotic behavior of the energy peak location is used to locate the critical temperature, which is also found to be universal and in accordance with the mean-field prediction.Comment: 31 pages, 16 figure

The Search for Intergalactic Hydrogen Clouds in Voids

I present the results of a search for intergalactic hydrogen clouds in voids. Clouds are detected by their HI LyA absorption lines in the HST spectra of low-redshift AGN. The parameter with which the environments of clouds are characterized is the tidal field, which places a lower limit on the cloud mass-density which is dynamically stable against disruption. Galaxy redshift catalogs are used to sum the tidal fields along the lines of sight, sorting clouds according to tidal field upper, or lower limits. The analytical methodology employed is designed to detect gas clouds whose expansion following reionization is restrained by dark matter perturbations. End-products are the cloud equivalent width distribution functions (EWDF) of catalogs formed by sorting clouds according to various tidal field upper, or lower limits. Cumulative EWDFs are steep in voids (S ~ -1.5 \pm 0.2), but flatter in high tidal field zones (S ~ -0.5 \pm 0.1). Most probable cloud Doppler parameters are ~30 km/s in voids and ~60 km/s in proximity to galaxies. In voids, the cumulative line density at low EW (~ 15 mA) is ~ 500 per unit redshift. The void filling factor is found to be 0.87 <= f_v <= 0.94. The void EWDF is remarkably uniform over this volume, with a possible tendency for more massive clouds to be in void centers. The size and nature of the void cloud population suggested by this study is completely unanticipated by the results of published 3-D simulations, which predict that most clouds are in filamentary structures around galaxy concentrations, and that very few observable absorbers would lie in voids. Strategies for modeling this population are briefly discussed.Comment: 21 pages, 19 figures, apjemulate style, to appear in ApJ vol. 57

Ain\u27t Love Grand!

https://digitalcommons.library.umaine.edu/mmb-vp/1032/thumbnail.jp

Dynamics of Counterion Condensation

Using a generalization of the Poisson-Boltzmann equation, dynamics of counterion condensation is studied. For a single charged plate in the presence of counterions, it is shown that the approach to equilibrium is diffusive. In the far from equilibrium case of a moving charged plate, a dynamical counterion condensation transition occurs at a critical velocity. The complex dynamic behavior of the counterion cloud is shown to lead to a novel nonlinear force-velocity relation for the moving plate.Comment: 5 pages, 1 ps figure included using eps

Mechanical response of plectonemic DNA: an analytical solution

We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically and we derive formulas for the contact pressure, twisting moment and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque, and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner, and are found to be consistent with those available in the literature.Comment: 14 pages, 4 figure

Not all surveillance data are created equal—A multi‐method dynamic occupancy approach to determine rabies elimination from wildlife

1. A necessary component of elimination programmes for wildlife disease is effective surveillance. The ability to distinguish between disease freedom and non‐detection can mean the difference between a successful elimination campaign and new epizootics. Understanding the contribution of different surveillance methods helps to optimize and better allocate effort and develop more effective surveillance programmes. 2. We evaluated the probability of rabies virus elimination (disease freedom) in an enzootic area with active management using dynamic occupancy modelling of 10 years of raccoon rabies virus (RABV) surveillance data (2006–2015) collected from three states in the eastern United States. We estimated detection probability of RABV cases for each surveillance method (e.g. strange acting reports, roadkill, surveillance‐trapped animals, nuisance animals and public health samples) used by the USDA National Rabies Management Program. 3. Strange acting, found dead and public health animals were the most likely to detect RABV when it was present, and generally detectability was higher in fall– winter compared to spring–summer. Found dead animals in fall–winter had the highest detection at 0.33 (95% CI: 0.20, 0.48). Nuisance animals had the lowest detection probabilities (~0.02). 4. Areas with oral rabies vaccination (ORV) management had reduced occurrence probability compared to enzootic areas without ORV management. RABV occurrence was positively associated with deciduous and mixed forests and medium to high developed areas, which are also areas with higher raccoon (Procyon lotor) densities. By combining occupancy and detection estimates we can create a probability of elimination surface that can be updated seasonally to provide guidance on areas managed for wildlife disease. 5. Synthesis and applications. Wildlife disease surveillance is often comprised of a combination of targeted and convenience‐based methods. Using a multi‐method analytical approach allows us to compare the relative strengths of these methods, providing guidance on resource allocation for surveillance actions. Applying this multi‐method approach in conjunction with dynamic occupancy analyses better informs management decisions by understanding ecological drivers of disease occurrence

On Hilberg's Law and Its Links with Guiraud's Law

Hilberg (1990) supposed that finite-order excess entropy of a random human text is proportional to the square root of the text length. Assuming that Hilberg's hypothesis is true, we derive Guiraud's law, which states that the number of word types in a text is greater than proportional to the square root of the text length. Our derivation is based on some mathematical conjecture in coding theory and on several experiments suggesting that words can be defined approximately as the nonterminals of the shortest context-free grammar for the text. Such operational definition of words can be applied even to texts deprived of spaces, which do not allow for Mandelbrot's ``intermittent silence'' explanation of Zipf's and Guiraud's laws. In contrast to Mandelbrot's, our model assumes some probabilistic long-memory effects in human narration and might be capable of explaining Menzerath's law.Comment: To appear in Journal of Quantitative Linguistic

A SQUAMOSA MADS-box gene involved in the regulation of anthocyanin accumulation in bilberry fruits

Anthocyanins are important health promoting phytochemicals that are abundant in many fleshy fruits. Bilberry (Vaccinium myrtillus L.) is one of the best sources of these compounds. Here we report on the expression pattern and functional analysis of a SQUAMOSA (SQUA) class MADS-box transcription factor, VmTDR4, associated with anthocyanin biosynthesis in bilberry. Levels of VmTDR4 expression were spatially and temporally linked with colour development and anthocyanin-related gene expression. Virus induced gene silencing (VIGS) was used to suppress VmTDR4 expression in bilberry resulting in substantial reduction in anthocyanin levels in fully ripe fruits. Chalcone synthase was used a positive control in the VIGS experiments. Additionally, in sectors of fruit tissue in which the expression of the VmTDR4 gene was silenced, the expression of R2R3 MYB family transcription factors related to the biosynthesis of flavonoids were also altered. We conclude that VmTDR4 plays an important role in the accumulation of anthocyanins during normal ripening in bilberry; probably through direct or indirect control of transcription factors belonging to the R2R3 MYB family

Highly optimized tolerance and power laws in dense and sparse resource regimes

Power law cumulative frequency $(P)$ vs. event size $(l)$ distributions $P(\geq l)\sim l^{-\alpha}$ are frequently cited as evidence for complexity and serve as a starting point for linking theoretical models and mechanisms with observed data. Systems exhibiting this behavior present fundamental mathematical challenges in probability and statistics. The broad span of length and time scales associated with heavy tailed processes often require special sensitivity to distinctions between discrete and continuous phenomena. A discrete Highly Optimized Tolerance (HOT) model, referred to as the Probability, Loss, Resource (PLR) model, gives the exponent $\alpha=1/d$ as a function of the dimension $d$ of the underlying substrate in the sparse resource regime. This agrees well with data for wildfires, web file sizes, and electric power outages. However, another HOT model, based on a continuous (dense) distribution of resources, predicts $\alpha= 1+ 1/d$. In this paper we describe and analyze a third model, the cuts model, which exhibits both behaviors but in different regimes. We use the cuts model to show all three models agree in the dense resource limit. In the sparse resource regime, the continuum model breaks down, but in this case, the cuts and PLR models are described by the same exponent.Comment: 19 pages, 13 figure

On the importance of hydrodynamic interactions in polyelectrolyte electrophoresis

The effect of hydrodynamic interactions on the free-solution electrophoresis of polyelectrolytes is investigated with coarse-grained molecular dynamics simulations. By comparing the results to simulations with switched-off hydrodynamic interactions, we demonstrate their importance in modelling the experimentally observed behaviour. In order to quantify the hydrodynamic interactions between the polyelectrolyte and the solution, we present a novel way to estimate its effective charge. We obtain an effective friction that is different from the hydrodynamic friction obtained from diffusion measurements. This effective friction is used to explain the constant electrophoretic mobility for longer chains. To further emphasize the importance of hydrodynamic interactions, we apply the model to end-labeled free-solution electrophoresis.Comment: 15 pages, 7 figures; accepted for publication in J. Phys.: Condens. Matte