Formation of a pseudoknot in the conserved RNA core domain in the ribonucleoprotein human telomerase is required for function. In vitro experiments show that the pseudoknot (PK) is in equilibrium with an extended hairpin (HP) structure. We use molecular simulations of a coarse-grained model, which reproduces most of the salient features of the experimental melting profiles of PK and HP, to show that crowding enhances the stability of PK relative to HP in the wild type and in a mutant associated with dyskeratosis congenita. In monodisperse suspensions, small crowding particles increase the stability of compact structures to a greater extent than larger crowders. If the sizes of crowders in a binary mixture are smaller than the unfolded RNA, the increase in melting temperature due to the two components is additive. In a ternary mixture of crowders that are larger than the unfolded RNA, which mimics the composition of ribosome, large enzyme complexes and proteins in E. coli, the marginal increase in stability is entirely determined by the smallest component. We predict that crowding can restore partially telomerase activity in mutants, which dramatically decrease the PK stability.; Comment: File "JACS_MAIN_archive_PDF_from_DOC.pdf" (PDF created from DOC) contains the main text of the paper File JACS_SI_archive.tex + 7 figures are the supplementary info

To test the theoretical understanding that finding bright CO emission depends primarily on dust shielding, we investigate the relationship between CO emission ($I_{\rm CO}$) and the amount of dust (estimated from IR emission and expressed as "$A_V$") across the Large Magellanic Cloud, the Small Magellanic Cloud, and the Milky Way. We show that at our common resolution of 10 pc scales, $I_{\rm CO}$ given a fixed line-of-sight $A_V$ is similar across all three systems despite the difference in metallicity. We find some evidence for a secondary dependence of $I_{\rm CO}$ on radiation field; in the LMC, $I_{\rm CO}$ at a given $A_V$ is smaller in regions of high $T_{\rm dust}$, perhaps because of an increased photodissociating radiation field. We suggest a simple but useful picture in which the CO-to-H$_2$ conversion factor (\xco) depends on two separable factors: (1) the distribution of gas column densities, which maps to an extinction distribution via a dust-to-gas ratio; and (2) the dependence of $I_{\rm CO}$ on $A_V$. Assuming that the probability distribution function (PDF) of local Milky Way clouds is universal, this approach predicts a dependence of \xco\ on $Z$ between $Z^{-1}$ and $Z^{-2}$ above about a third solar metallicity. Below this metallicity...

We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations from exact log-normality. The proposed function provides an extraordinarily accurate description of the density PDFs in simulations with Mach numbers ~0.1-15 and dispersion in log(rho) from ~0.01-4 dex. Compared to a lognormal or lognormal-skew-kurtosis model, the fits are improved by orders of magnitude in the wings of the distribution (with fewer free parameters). This is true in simulations using distinct numerical methods, including or excluding magnetic fields. Deviations from lognormality are represented by a parameter T that increases with the compressive Mach number. The proposed distribution can be derived from intermittent cascade models of the longitudinal (compressive) velocity differences, which should be directly related to density fluctuations, and we provide a simple interpretation of the density PDF as the product of a continuous-time relaxation process. As such the parameter T is consistent with the same parameter needed to explain the (intermittent) velocity structure functions; its behavior is consistent with turbulence becoming more intermittent as it becomes more dominated by strong shocks. It provides a new and unique probe of the role of intermittency in the density (not just velocity) structure of turbulence. We show that this naturally explains some apparent contradictory results in the literature based on use of different moments of the density PDF...

The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY model in its harmonic approximation. Numerical simulations and perturbative results have shown a Gumbel-like shape of the PDF, in spite of the fact that the average magnetization is not an extreme variable. Our analytical result allows to test both perturbative analytical expansions and also numerical computations performed previously. Perfect agreement is found for the first moments of the PDF. Also for large volume and in the high temperature limit the distribution becomes Gaussian, as it should be. In the low temperature regime its numerical evaluation is compatible with a Gumbel distribution.; Comment: 4 pages, 3 figures

In this paper we describe the predictions for the smoothed weak lensing shear and aperture-mass of two simple analytical models of the density field: the minimal tree-model and the stellar model. Both models give identical results for the statistics of the 3-d density contrast smoothed over spherical cells and only differ by the detailed angular dependence of the many-body density correlations. We have shown in previous work that they also yield almost identical results for the pdf of the smoothed convergence, $\kappa_s$. We find that both models give rather close results for both the shear and the positive tail of the aperture-mass. However, we note that at small angular scales ($\theta_s \la 2'$) the tail of the pdf $\cP(\Map)$ for negative $\Map$ shows a strong variation between the two models and the stellar model actually breaks down for $\theta_s \la 0.4'$ and $\Map<0$. This shows that the statistics of the aperture-mass provides a very precise probe of the detailed structure of the density field, as it is sensitive to both the amplitude and the detailed angular behaviour of the many-body correlations. On the other hand, the minimal tree-model shows good agreement with numerical simulations over all scales and redshifts of interest...

Generalized universality, as recently proposed, postulates a universal non-Gaussian form of the probability density function (PDF) of certain global observables for a wide class of highly correlated systems of finite volume N. Studying the 2D XY -model, we link its validity to renormalization group properties. It would be valid if there were a single dimension 0 operator, but the actual existence of several such operators leads to T-dependent corrections. The PDF is the Fourier transform of the partition function Z(q) of an auxiliary theory which differs by a dimension 0 perturbation with a very small imaginary coefficient iq/N from a theory which is asymptotically free in the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).; Comment: To be published in Phys. Rev. E

This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called stochastic density matrices in order to reflect an analogy with the quantum mechanical density matrices. The SDM approximation of a PDF satisfies the normalization condition and is nonnegative everywhere in contrast to the truncated Gram-Charlier and Edgeworth expansions. For bases with an algebraic structure, such as the Hermite polynomial and Fourier bases, the SDM approximation can be chosen so as to satisfy given moment specifications and can be optimized using a quadratic proximity criterion. We apply the SDM approach to the Fokker-Planck-Kolmogorov PDF dynamics of Markov diffusion processes governed by nonlinear stochastic differential equations. This leads to an ordinary differential equation for the SDM dynamics of the approximating PDF. As an example, we consider the Smoluchowski SDE on a multidimensional torus.; Comment: 12 pages, 3 figures. A brief version of this paper will appear in the proceedings of the IEEE Multi-Conference on Systems and Control, 21-23 September 2015, Sydney, Australia

We investigate the statistics of the gap, G_n, between the two rightmost positions of a Markovian one-dimensional random walker (RW) after n time steps and of the duration, L_n, which separates the occurrence of these two extremal positions. The distribution of the jumps \eta_i's of the RW, f(\eta), is symmetric and its Fourier transform has the small k behavior 1-\hat{f}(k)\sim| k|^\mu with 0 < \mu \leq 2. We compute the joint probability density function (pdf) P_n(g,l) of G_n and L_n and show that, when n \to \infty, it approaches a limiting pdf p(g,l). The corresponding marginal pdf of the gap, p_{\rm gap}(g), is found to behave like p_{\rm gap}(g) \sim g^{-1 - \mu} for g \gg 1 and 0<\mu < 2. We show that the limiting marginal distribution of L_n, p_{\rm time}(l), has an algebraic tail p_{\rm time}(l) \sim l^{-\gamma(\mu)} for l \gg 1 with \gamma(1<\mu \leq 2) = 1 + 1/\mu, and \gamma(0<\mu<1) = 2. For l, g \gg 1 with fixed l g^{-\mu}, p(g,l) takes the scaling form p(g,l) \sim g^{-1-2\mu} \tilde p_\mu(l g^{-\mu}) where \tilde p_\mu(y) is a (\mu-dependent) scaling function. We also present numerical simulations which verify our analytic results.; Comment: 5 pages, 3 figures

This chapter derives the properties of light from the properties of processing, including its ability to be both a wave and a particle, to respond to objects it doesn't physically touch, to take all paths to a destination, to choose a route after it arrives, and to spin both ways at once as it moves. Here a photon is an entity program spreading as a processing wave of instances. It becomes a "particle" if any part of it overloads the grid network that runs it, causing the photon program to reboot and restart at a new node. The "collapse of the wave function" is how quantum processing creates what we call a physical photon. This informational approach gives insights into issues like the law of least action, entanglement, superposition, counterfactuals, the holographic principle and the measurement problem. The conceptual cost is that physical reality is a quantum processing output, i.e. virtual.; Comment: This is the third in a series of papers, the previous ones are available at http://brianwhitworth.com/BW-VRT2.pdf and at http://brianwhitworth.com/BW-VRT1.pdf The latest version of this one is always available at http://brianwhitworth.com/BW-VRT3.pdf

The present paper deals with the numerical study of high pressure LOx/H2 or LOx/hydrocarbon combustion for propulsion systems. The present research effort is driven by the continued interest in achieving low cost, reliable access to space and more recently, by the renewed interest in hypersonic transportation systems capable of reducing time-to-destination. Moreover, combustion at high pressure has been assumed as a key issue to achieve better propulsive performance and lower environmental impact, as long as the replacement of hydrogen with a hydrocarbon, to reduce the costs related to ground operations and increase flexibility. The current work provides a model for the numerical simulation of high- pressure turbulent combustion employing detailed chemistry description, embedded in a RANS equations solver with a Low Reynolds number k-omega turbulence model. The model used to study such a combustion phenomenon is an extension of the standard flamelet-progress-variable (FPV) turbulent combustion model combined with a Reynolds Averaged Navier-Stokes equation Solver (RANS). In the FPV model, all of the thermo-chemical quantities are evaluated by evolving the mixture fraction Z and a progress variable C. When using a turbulence model in conjunction with FPV model...

The weak lensing surveys have the potential to probe directly the clustering statistics of dark matter in the universe. Recent studies have shown that it is possible to predict analytically the whole probability distribution function (pdf) and the bias associated with the collapsed objects in the highly non-linear regime using the hierarchical ansatz. We extend such studies to the quasi-linear regime where the hierarchical ansatz is replaced by the tree-level perturbative calculations to an arbitrary order. It is shown how the generating function techniques can be coupled with the perturbative calculations to compute the complete pdf and the bias in the quasi-linear regime for the weak-lensing convergence field. We study how these quantities depend on the smoothing angle and the source red-shift in different realistic cosmological scenarios. We show that it is possible to define a reduced convergence whose statistics is similar to underlying 3D mass distribution for small smoothing angle but it resembles projected mass distribution for large smoothing angles. We have also compared our peturbative results with log-normal model for pdf and bias and found a good agreement between the two analytical results.; Comment: 10 pages, 4 figures...

Statistical properties of the interplanetary magnetic field fluctuations can provide an important insight into the solar wind turbulent cascade. Recently, analysis of the Probability Density Functions (PDF) of the velocity and magnetic field fluctuations has shown that these exhibit non-Gaussian properties on small time scales while large scale features appear to be uncorrelated. Here we apply the finite size scaling technique to explore the scaling of the magnetic field energy density fluctuations as seen by WIND. We find a single scaling sufficient to collapse the curves over the entire investigated range. The rescaled PDF follow a non Gaussian distribution with asymptotic behavior well described by the Gamma distribution arising from a finite range Levy walk. Such mono scaling suggests that a Fokker-Planck approach can be applied to study the PDF dynamics. These results strongly suggest the existence of a common, nonlinear process onthe time scale up to ~26 hours.; Comment: 4 pages, 5 figures. In press, Geophysical Research Letters

We introduce to astrophysics the threshold probability functions S_2, C_2, and D_2 first derived by \citet{torq+88}, which effectively samples the flux probability distribution (PDF) of the Lya forest at different spatial scales. These statistics are tested on mock Lya forest spectra based on various toy models for HeII reionization, with homogeneous models with various temperature-density relations as well as models with temperature inhomogeneities. These mock samples have systematics and noise added to simulate the latest Sloan Digital Sky Survey Data Release 7 (SDSS DR7) data. We find that the flux PDF from SDSS DR7 can be used to constrain the temperature-density relation $\gamma$ (where $T \propto (1 + \Delta)^{\gamma-1}$) of the intergalactic medium (IGM) at z=2.5 to a precision of $\Delta \gamma = 0.2$ at $\sim 4\sigma$ confidence. The flux PDF is degenerate to temperature inhomogeneities in the IGM arising from HeII reionization, but we find S_2 can detect these inhomogeneities at $\sim 3 \sigma$, with the assumption that the flux continuum of the Lya forest can be determined to 9% accuracy, approximately the error from current fitting methods. If the quasar continuum can be determined to 3% accuracy, then S_2 is capable of constraining the characteristic scale of temperature inhomogeneities...

We present experimental results on statistics of polymer orientation angles relatively to shear plane and tumbling times in shear flow with thermal noise. Strong deviation of probability distribution functions (PDF) of these parameters from Gaussian was observed and a good accord with theory was found. The scaling relations of PDF widths for both angles as a function of the control parameter $Wi$ are verified and compared with numerics. An universal exponential PDF tail for the tumbling times and its predicted scaling with $Wi$ are also tested experimentally against numerics.; Comment: 4 pages, 6 figures, submitted to PRL, see the following paper

We further characterize the structures tentatively identified on thermal and chemical grounds as the sites of dissipation of turbulence in molecular clouds (Papers I and II). Our study is based on two-point statistics of line centroid velocities (CV), computed from three large 12CO maps of two fields. Probability density functions (PDF) of the CO line centroid velocity increments (CVI) over lags varying by an order of magnitude and structure functions of the line CV, up to the 6th order, are computed. We show that the line CV bear the three signatures of intermittency in a turbulent velocity field: (1) the non-Gaussian tails in the CVI PDF grow as the lag decreases, (2) the departure from Kolmogorov scaling of the high-order structure functions is more pronounced in the more turbulent field, (3) the positions contributing to the CVI PDF tails delineate narrow filamentary structures (thickness ~ 0.02 pc), uncorrelated to dense gas structures and spatially coherent with thicker ones (~0.18 pc) observed on larger scales. The confrontation with theoretical predictions leads us to identify these small-scale filamentary structures with extrema of velocity-shears associated with gas warmer than the bulk. Last, their average direction is parallel (or close) to that of the local magnetic field projection. Turbulence in these translucent fields exhibits the statistical and structural signatures of small-scale and inertial-range intermittency. The more turbulent field on the 30 pc-scale is also the more intermittent on small scales. The small-scale intermittent structures coincide with those formerly identified as sites of enhanced dissipation. They are organized into parsec-scale coherent structures...

The diffusion process of N hard rods in a 1D interval of length L (--> inf) is studied using scaling arguments and an asymptotic analysis of the exact N-particle probability density function (PDF). In the class of such systems, the universal scaling law of the tagged particle's mean absolute displacement reads, <|r|>~ <|r|>_{free}/n^mu, where <|r|>_{free} is the result for a free particle in the studied system and n is the number of particles in the covered length. The exponent mu is given by, mu=1/(1+a), where a is associated with the particles' density law of the system, rho~rho_0*L^(-a), 0<= a <=1. The scaling law for <|r|> leads to, <|r|>~rho_0^((a-1)/2) (<|r| >_{free})^((1+a)/2), an equation that predicts a smooth interpolation between single file diffusion and free particle diffusion depending on the particles' density law, and holds for any underlying dynamics. In particular, <|r|>~t^((1+a)/2) for normal diffusion, with a Gaussian PDF in space for any value of a (deduced by a complementary analysis), and, <|r|>~t^((beta(1+a))/2), for anomalous diffusion in which the system's particles all have the same power-law waiting time PDF for individual events, psi~t^(-1-beta), 0~t^(1/2) in a 'standard' single file is a direct result of the fixed particles' density condition imposed on the system...

Despite the simplicity of theoretical models of supersonically turbulent, isothermal media, their predictions successfully match the observed gas structure and star formation activity within low-pressure (P/k < 10^5 K cm^-3) molecular clouds in the solar neighbourhood. However, it is unknown if these theories extend to clouds in high-pressure (P/k > 10^7 K cm^-3) environments, like those in the Galaxy's inner 200 pc Central Molecular Zone (CMZ) and in the early Universe. Here we present ALMA 3mm dust continuum emission within a cloud, G0.253+0.016, which is immersed in the high-pressure environment of the CMZ. While the log-normal shape and dispersion of its column density PDF is strikingly similar to those of solar neighbourhood clouds, there is one important quantitative difference: its mean column density is 1--2 orders of magnitude higher. Both the similarity and difference in the PDF compared to those derived from solar neighbourhood clouds match predictions of turbulent cloud models given the high-pressure environment of the CMZ. The PDF shows a small deviation from log-normal at high column densities confirming the youth of G0.253+0.016. Its lack of star formation is consistent with the theoretically predicted, environmentally dependent volume density threshold for star formation which is orders of magnitude higher than that derived for solar neighbourhood clouds. Our results provide the first empirical evidence that the current theoretical understanding of molecular cloud structure derived from the solar neighbourhood also holds in high-pressure environments. We therefore suggest that these theories may be applicable to understand star formation in the early Universe.; Comment: 17 pages...

We study the Photon statistics in the superpositions of coherent states $|\alpha\rangle$ and $|\alpha^*\rangle$ named ``Schr\"odinger real and imaginary cat states''. The oscillatory character of photon distribution function (PDF) emerging due to the quantum interference between the two components is shown, and the phenomenon of the quadrature squeezing is observed for the moderate values of $|\alpha|\sim 1$. Despite the quantity ${\langle\triangle n^2\rangle}/{\langle n\rangle}$ tends to the unit value (like in the Poissonian PDF) at $|\alpha|\gg 1$, the photon statistics is essentially non-Poissonian for all values of $|\alpha|$. The factorial moments and cumulants of the PDF are calculated, and the oscillations of their ratio are demonstrated.; Comment: 13 pages, LaTEX

We conduct a comprehensive theoretical and numerical investigation of the pollution of pristine gas in turbulent flows, designed to provide new tools for modeling the evolution of the first generation of stars. The properties of such Population III (Pop III) stars are thought to be very different than later generations, because cooling is dramatically different in gas with a metallicity below a critical value Z_c, which lies between ~10^-6 and 10^-3 solar value. Z_c is much smaller than the typical average metallicity, , and thus the mixing efficiency of the pristine gas in the interstellar medium plays a crucial role in the transition from Pop III to normal star formation. The small critical value, Z_c, corresponds to the far left tail of the probability distribution function (PDF) of the metallicity. Based on closure models for the PDF formulation of turbulent mixing, we derive equations for the fraction of gas, P, lying below Z_c, in compressible turbulence. Our simulation data shows that the evolution of the fraction P can be well approximated by a generalized self-convolution model, which predicts dP/dt = -n/tau_con P (1-P^(1/n)), where n is a measure of the locality of the PDF convolution and the timescale tau_con is determined by the rate at which turbulence stretches the pollutants. Using a suite of simulations with Mach numbers ranging from M = 0.9 to 6.2...

The control of open quantum systems has a fundamental relevance for fields ranging from quantum information processing to nanotechnology. Typically, the system whose coherent dynamics one wants to manipulate, interacts with an environment that smoothly degrades its quantum dynamics. Thus, a precise understanding of the inner mechanisms of this process, called "decoherence", is critical to develop strategies to control the quantum dynamics. In this thesis we solved the generalized Liouville-von Neumann quantum master equation to obtain the dynamics of many-spin systems interacting with a spin bath. We also solve the spin dynamics within the Keldysh formalism. Both methods lead to identical solutions and together gave us the possibility to obtain numerous physical predictions that contrast well with Nuclear Magnetic Resonance experiments. We applied these tools for molecular characterizations, development of new numerical methodologies and the control of quantum dynamics in experimental implementations. But, more important, these results contributed to fundamental physical interpretations of how quantum dynamics behaves in open systems. In particular, we found a manifestation of an environmentally induced quantum dynamical phase transition.; Comment: PhD Thesis...