Local Expansion Rate Research Articles

Self-regulation in tip-growth: The role of cell wall ageing

We develop a model to describe the effect of cell wall ageing on the local expansion rate of tip-growing cells. Starting from an exact equation for the stationary age-distribution of the wall material, we propose a generic measure for the local expansion propensity of the wall if the ageing process is described by a constant rate Poissonian decay process. This ageing process may be either interpreted as biochemical in nature describing the finite lifetime of regulatory proteins, or as mechanical in nature describing the gradual “hardening” of the wall through cross-linking or gelation of the wall polymers. In this way we can construct models for tip-growth in which material deposition, evolving wall properties and surface expansion are self-consistently intertwined. As a proof of principle, we implement our ageing approach in two different idealised models of tip-growth, obtaining the stationary tip shapes as a function of the ageing parameter. In the first, the spatial distribution of delivery of growth material is determined by the local curvature of the cell and the growth mode is orthogonal. In the second, the growth material originates from a Vesicle Supply Center, a point-like representation of the Spitzenkörper as found in fungal hyphae, and the growth mode is isometric.

Hiding dark energy transitions at low redshift

We show that it is both observationally allowable and theoretically possible to have large fluctuations in the dark energy equation of state as long as they occur at ultra-low redshifts z<0.02. These fluctuations would masquerade as a local transition in the Hubble rate of a few percent or less and escape even future, high precision, high redshift measurements of the expansion history and structure. Scalar field models that exhibit this behavior have a sharp feature in the potential that the field traverses within a fraction of an e-fold of the present. The equation of state parameter can become arbitrarily large if a sharp dip or bump in the potential causes the kinetic and potential energy of the field to both be large and have opposite sign. While canonical scalar field models can decrease the expansion rate at low redshift, increasing the local expansion rate requires a non-canonical kinetic term for the scalar field.

Volume averaging in the quasispherical Szekeres model

This paper considers volume averaging in the quasispherical Szekeres model. The volume averaging became of considerable interest after it was shown that the volume acceleration calculated within the averaging framework can be positive even when the local expansion rate decelerates. This issue was intensively studied within spherically symmetric models. However, since our Universe is not spherically symmetric similar analysis is needed in non-symmetrical models. This papers presents the averaging analysis within the quasispherical Szekeres model which is a non-symmetrical generalisation of the spherically symmetric Lemaître–Tolman family of models. In the quasispherical Szekeres model the distribution of mass over a surface of constant t and r has the form of a mass-dipole superposed on a monopole. This paper shows that when calculating the volume acceleration, ä, within the Szekeres model, the dipole does not contribute to the final result, hence ä only depends on a monopole configuration. Thus, the volume averaging within the Szekeres model leads to literally the same solutions as those obtained within the Lemaître–Tolman model.

Dynamical freeze-out condition in ultrarelativistic heavy ion collisions

We determine the decoupling surfaces for the hydrodynamic description of heavy ion collisions at RHIC and LHC by comparing the local hydrodynamic expansion rate with the microscopic pion-pion scattering rate. The pion ${p}_{T}$ spectra for nuclear collisions at BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) are computed by applying the Cooper-Frye procedure on the dynamical-decoupling surfaces and compared with those obtained from the constant-temperature freeze-out surfaces. Comparison with RHIC data shows that the system indeed decouples when the expansion rate becomes comparable with the pion scattering rate. The dynamical decoupling based on the rates comparison also suggests that the effective decoupling temperature in central heavy ion collisions remains practically unchanged from RHIC to LHC.

Can infrared gravitons screenΛ?

It has been suggested that infrared gravitons in de Sitter space may lead to a secular screening of the effective cosmological constant. This seems to clash with the naive expectation that the curvature scalar should stay constant due to the Heisenberg equation of motion. Here, we show that the tadpole correction to the local expansion rate, which has been used in earlier analyses as an indicator of a decaying effective $\ensuremath{\Lambda}$, is not gauge invariant. On the other hand, we construct a gauge-invariant operator which measures the renormalized curvature scalar smeared over an arbitrary window function, and we find that there is no secular screening of this quantity (to any given order in perturbation theory).

Cosmological matching conditions

We investigate the evolution of scalar metric perturbations across a sudden cosmologicaltransition, allowing for an inhomogeneous surface stress at the transition leading to adiscontinuity in the local expansion rate, such as might be expected in a big crunch/bigbang event. We assume that the transition occurs when some function of localmatter variables reaches a critical value, and that the surface stress is also afunction of local matter variables. In particular we consider the case of a singlescalar field and show that a necessary condition for the surface stress tensor tobe perturbed at the transition is the presence of a non-zero intrinsic entropyperturbation of the scalar field. We present the matching conditions in terms ofgauge-invariant variables assuming a sudden transition to a fluid-dominated universe withbarotropic equation of state. For adiabatic perturbations the comoving curvatureperturbation is continuous at the transition, while the Newtonian potential may bediscontinuous if there is a discontinuity in the background Hubble expansion.

COSMOLOGICAL ACCELERATION FROM STRUCTURE FORMATION

We discuss the Buchert equations, which describe the average expansion of an inhomogeneous dust universe. In the limit of small perturbations, they reduce to the Friedmann–Robertson–Walker equations. However, when the universe is very inhomogeneous, the behavior can be qualitatively different from the FRW case. In particular, the average expansion rate can accelerate even though the local expansion rate decelerates everywhere. We clarify the physical meaning of this paradoxical feature with a simple toy model, and demonstrate how acceleration is intimately connected with gravitational collapse. This provides a link to structure formation, which in turn has a preferred time around the era when acceleration has been observed to start.

COSMOLOGICAL INFLUENCE OF SUPER-HUBBLE PERTURBATIONS

The existence of cosmological perturbations of wavelength larger than the Hubble radius is a generic prediction of the inflationary paradigm. We provide the derivation beyond perturbation theory of a conserved quantity which generalizes the linear comoving curvature perturbation. As a by-product, we show that super-Hubble-radius (super-Hubble) perturbations have no physical influence on local observables (e.g. the local expansion rate) if cosmological perturbations are of the adiabatic type.

Back-reaction of perturbations in two scalar field inflationary models

We calculate the back-reaction of long wavelength cosmological perturbations on a generalrelativistic measure of the local expansion rate of the universe. Specifically, we considera cosmological model in which matter is described by two scalar matter fields,one being the inflaton and the other one representing a matter field which isused as a clock. We analyse back-reaction in a phase of inflaton-driven slow-rollinflation, and find that the leading infrared back-reaction terms contributingto the evolution of the expansion rate do not vanish when measured at a fixedvalue of the clock field. We also analyse the back-reaction of entropy modes in aspecific cosmological model with negative square mass for the entropy field and findthat back-reaction can become significant. Our work provides evidence that, ingeneral, the back-reaction of infrared fluctuations could be locally observable.

Extragalactic water masers, geometric estimation of H0, and characterization of dark energy

High precision estimation of the equation of state of dark energy depends on constraints external to analyses of Cosmic Microwave Background fluctuations. A geometric estimation of the local expansion rate, H 0, would provide the most direct and robust constraint. Traditional techniques to estimate H 0 have depended on observations of standard candles for which systematic effects can be 10% or more. Observations of water maser sources in the accretion disks that feed the central engines of active galaxies enable simplified, robust, and largely geometric analyses. Many thousand maser sources will be discovered in studies with the SKA, owing to its great sensitivity. Spectroscopic monitoring and interferometric mapping – with intercontinental baselines – will allow estimation of H 0 to ∼1% and possibly better.

Noise-induced enhancement of fluctuation and spurious synchronization in uncoupled type-I intermittent chaotic systems.

We study the dynamics of a pair of two uncoupled identical type-I intermittent chaotic systems driven by common random forcing. We first observe that the degree of the fluctuation of the local expansion rate of orbits to perturbations of a single system as a function of the noise intensity shows a convex curve and takes its maximum value at a certain noise intensity, whereas the Liapunov exponent itself monotonically increases in this range. Furthermore, it is numerically demonstrated that this nontrivial enhancement of fluctuation causes that two orbits with different initial conditions may synchronize each other after a finite interval of time. As pointed out by Pikovsky [Phys. Lett. A 165, 33 (1992)], since the Liapunov exponent of the present system is positive, the synchronization that we observed is a numerical artifact due to the finite precision of calculations. The spurious noise-induced synchronization in an ensemble of uncoupled type-I intermittent chaotic systems are numerically characterized and the relations between these features and the fluctuation properties of the local expansion rate are also discussed.

Multidimensional simulations of type Ia supernova explosions and nucleosynthesis

Because calibrated light curves of type Ia supernovae have become a major tool to determine the local expansion rate of the Universe, considerable attention has been given to models of these events over the past couple of years. It is now common believe that perhaps most type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, M Chan, ≈ 1.39 M⊙, and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling type Ia supernovae as well as several of the still open questions are addressed in this article. Although the main emphasis will be on studies of the explosion mechanism itself and on the related physical processes, including the physics and nuclear physics of turbulent nuclear combustion in degenerate stars, observational implications and constraints will also be discussed.

Back reaction and the local cosmological expansion rate

We calculate the back reaction of cosmological perturbations on a general relativistic variable which measures the local expansion rate of the Universe. Specifically, we consider a cosmological model in which matter is described by a single field. We analyze back reaction both in a matter-dominated Universe and in a phase of scalar field-driven chaotic inflation. In both cases, we find that the leading infrared terms contributing to the back reaction vanish when the local expansion rate is measured at a fixed value of the matter field which is used as a clock, whereas they do not appear to vanish if the expansion rate is evaluated at a fixed value of the background time. We discuss possible implications for more realistic models with a more complicated matter sector.

Statistics of phase turbulence II

The system described by the Kuramoto–Sivashinsky equation (SKSE) is shown to have a short- and a long-time regimes. The probability distribution function (PDF) for the absolute value of the solution is subjected to different scaling laws in the two time regimes. The local expansion rate (LER) and its two-time correlation function are calculated. The time regime where the correlation for the LER remains is shorter than the one for the absolute value of the solution for the SKSE. The fluctuation in the LER becomes small as the damping constant is increased. The PDF for the LER is also given in this paper.

Bifurcations and intermittent chaos observed in a ring of four‐coupled PLLs

AbstractIn this paper, we study various types of bifurcations of attractors observed in computer simulation and electronic circuit experiment of the ring of four‐coupled PLLs when coupling coefficient σ is increased and the route to chaos is made clear. In particular, for intermittent chaos that is observed when σ becomes large, we study the laminar distribution, time variation of local expansion rate, and Lyapunov exponent. We have shown the existence of several kinds of intermittent chaos with different properties. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 85(12): 56–64, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1128

Dynamics of phase turbulence

The state vector is defined for the phase turbulence described by the Kuramoto–Sivashinsky equation. Then the two-time correlation function (TTCF) for the state vector is calculated numerically. In the case when the damping constant is zero, the TTCF decays like Lorentzian. The TTCF changes its shape as we increase the value of the damping constant from zero. In addition, the local expansion rate is calculated and it is shown that the local expansion rate fluctuates around at zero.

No one loop back reaction in chaotic inflation

We use an invariant operator to study the quantum gravitational back reaction to scalar perturbations during chaotic inflation. Our operator is the inverse covariant d'Alembertian expressed as a function of the local value of the inflaton. In the slow roll approximation this observable gives $\ensuremath{-}{1/(2H}^{2})$ for an arbitrary homogeneous and isotropic geometry; hence it is a good candidate for measuring the local expansion rate even when the spacetime is not perfectly homogeneous and isotropic. Corrections quadratic in the scalar creation and annihilation operators of the initial value surface are included using the slow-roll and long wavelength approximations. The result is that all terms which could produce a significant secular back reaction cancel from the operator, before one even takes its expectation value. Although it is not relevant to the current study, we also develop a formalism for using stochastic samples to study back reaction.

Scalar measure of the local expansion rate

We define a scalar measure of the local expansion rate based on how astronomers determine the Hubble constant. Our observable is the inverse conformal d'Alembertian acting on a unit ``standard candle.'' Because this quantity is an integral over the past light cone of the observation point it provides a manifestly causal and covariant technique for averaging over small fluctuations. For an exactly homogeneous and isotropic spacetime our scalar gives minus one-half times the inverse square of the Hubble parameter. Our proposal is that it be assigned this meaning generally and that it be employed to decide the issue of whether or not there is a significant quantum gravitational back reaction on inflation. Several techniques are discussed for promoting the scalar to a full invariant by giving a geometrical description for the point of observation. We work out an explicit formalism for evaluating the invariant in perturbation theory. The results for two simple models are presented in subsequent papers.

Fast and accurate inclusion of steam properties in two- and three-dimensional steam turbine flow calculations

The Denton time-marching method for turbomachinery flow calculation has been modified for rapid and accurate access to the properties of steam in equilibrium dry and wet states and in the metastable dry region. Transition between metastable dry and equilibrium wet states is accomplished either at the stable equilibrium boundary or by allowing metastable equilibrium expansion followed by a condensation shock whose location depends on the local degree of subcooling of the metastable vapour and the local expansion rate. Steam properties and their derivatives are obtained from a wide-ranging Helmholtz representation of equilibrium (stable and metastable) thermodynamic properties and stored for use in an accurate Taylor series representation. Comparisons have been made of flow development in a low-pressure steam turbine blade row for three expansion assumptions: equilibrium stable and metastable dry, stable equilibrium, dry and wet, and dry expansion prior to a condensation ‘shock’ which is followed by equilibrium wet expansion. Inclusion of real steam properties extends calculation time for one iteration cycle by about 5 per cent and has little effect on the number of cycles required for convergence in the absence of a condensation shock; however, inclusion of the shock may double the time required for convergence.

Type Ia Supernova Explosion Models

▪ Abstract Because calibrated light curves of type Ia supernovae have become a major tool to determine the local expansion rate of the universe and also its geometrical structure, considerable attention has been given to models of these events over the past couple of years. There are good reasons to believe that perhaps most type Ia supernovae are the explosions of white dwarfs that have approached the Chandrasekhar mass, [Formula: see text], and are disrupted by thermonuclear fusion of carbon and oxygen. However, the mechanism whereby such accreting carbon-oxygen white dwarfs explode continues to be uncertain. Recent progress in modeling type Ia supernovae as well as several of the still open questions are addressed in this review. Although the main emphasis is on studies of the explosion mechanism itself and on the related physical processes, including the physics of turbulent nuclear combustion in degenerate stars, we also discuss observational constraints.