Suppressing the large scale curvature perturbation by interacting fluids

In brane-world cosmologies of Randall-Sundrum type, we show that evolution of large-scale curvature perturbations may be determined on the brane, without solving the bulk perturbation equations. The influence of the bulk gravitational field on the brane is felt through a projected Weyl tensor which behaves effectively like an imperfect radiation fluid with anisotropic stress. We define curvature perturbations on uniform density surfaces for both the matter and Weyl fluids, and show that their evolution on large scales follows directly from the energy conservation equations for each fluid. The total curvature perturbation is not necessarily constant for adiabatic matter perturbations, but can change due to the Weyl entropy perturbation. To relate this curvature perturbation to the longitudinal gauge metric potentials requires knowledge of the Weyl anisotropic stress which is not determined by the equations on the brane. We discuss the implications for large-angle anisotropies on the cosmic microwave background sky.

The curvature perturbation in power law (e.g. extended) inflation

Several scenarios have been proposed in which primordial perturbations could originate from quantum vacuum fluctuations in a phase corresponding to a collapse phase (in an Einstein frame) preceding the Big Bang. I briefly review three models which could produce scale-invariant spectra during collapse: (1) curvature perturbations during pressureless collapse, (2) axion field perturbations in a pre big bang scenario, and (3) tachyonic fields during multiple-field ekpyrotic collapse. In the separate universes picture one can derive generalised perturbation equations to describe the evolution of large scale perturbations through a semi-classical bounce, assuming a large-scale limit in which inhomogeneous perturbations can be described by locally homogeneous patches. For adiabatic perturbations there exists a conserved curvature perturbation on large scales, but isocurvature perturbations can change the curvature perturbation through the non-adiabatic pressure perturbation on large scales. Different models for the origin of large scale structure lead to different observational predictions, including gravitational waves and non-Gaussianity.

We discuss the residual isocurvature perturbations, fully correlated with the curvature perturbation, that are automatic in the curvaton scenario if curvaton decay is sufficiently late. We contrast these residual isocurvature perturbations with the generally uncorrelated ``intrinsic'' isocurvature perturbation generated by an additional field such as the axion. We present a general formula for the residual isocurvature perturbations, referring only to the generation of the relevant quantity [cold dark matter (CDM), baryon number or lepton number] in an unperturbed universe. Specific formulas for the residual isocurvature CDM perturbation are given for most of the commonly considered CDM candidates.

Molecular energy calculations employing actual and approximate multicenter angular dependent integral evaluations are compared. Individual integral values for three-center integrals used in calculations for the triangular H3+ ion as computed by exact methods and by the approximate formulas of Mulliken and of Rudenberg are given. The results indicate that angular and distance relations of the nuclear skeleton of this polyatomic ion are determinable at almost the identical ``best'' value found using the much more laborious exact integral calculations. The energies of the approximate evaluations, however, indicate that once these ``best'' parametric values are determined the more exact calculations must be used. The approximate evaluations of second angular derivatives of integrals that are dependent on the angular and distance relations of component molecular nuclei are also computed and compared. Use of such derivatives in determination of approximate zero point energies, vibrational frequencies, and force constants is indicated.

We study the interplay of clumping at small scales with the collapse and\nrelaxation of perturbations at much larger scales. We present results of our\nanalysis when the large scale perturbation is modelled as a plane wave. We find\nthat in absence of substructure, collapse leads to formation of a pancake with\nmulti-stream regions. Dynamical relaxation of plane wave is faster in presence\nof substructure. Scattering of substructures and the resulting enhancement of\ntransverse motions of haloes in the multi-stream region lead to a thinner\npancake. In turn, collapse of the plane wave leads to formation of more massive\ncollapsed haloes as compared to the collapse of substructure in absence of the\nplane wave. The formation of more massive haloes happens without any increase\nin the total mass in collapsed haloes. A comparison with the Burgers' equation\napproach in absence of any substructure suggests that the preferred value of\neffective viscosity depends primarily on the number of streams in a region.\n

We have examined, in Part I, the propagation mechanism and geostrophic property of classical Rossby waves in a non-divergent barotropic atmosphere. As we found that the non-divergent Rossby waves do not propagate in a hydrostatically equilibrium atmosphere, and do not manifest a good geostrophic property, an alternative large scale circulation pattern of geostrophic waves has been proposed (McHall, 1991a). The propagation mechanism and geostrophic property of these waves are examined in the present study.

We study the effect of the dynamical degrees of freedom resulting from the lattice structure of an antiferromagnet on pattern forming bifurcations. They are examined in a one-dimensional chain of damped and driven classical spin oscillators. In addition to stationary states where all spins are parallel (quasiferromagnetic state), it exhibits states where the spins are lined up on two sublattices (noncollinear state). Besides showing instabilities against large scale perturbations, short wavelengths of the order of the lattice constant become critical even for weak driving fields. A general formalism admitting a dynamical description of discrete oscillator chains in the weakly nonlinear regime beyond the instabilities is developed. The ensuing amplitude equation allows the examination of the formation of patterns in this domain. Special emphasis is laid on instabilities of higher codimension. A codimension-3 bifurcation where all wave numbers become critical simultaneously implies a direct transition to turbulence.

In the model where Primordial Black Holes (PBHs) form from large primordial curvature (C) perturbations, i.e., CPBHs, constraints on PBH abundance provide in principle constraints on the primordial curvature power spectrum. This connection however depends necessarily on the details of PBH formation mechanism. In this paper we provide, for the first time, constraints on the primordial curvature power spectrum from the latest limits on PBH abundance, taking into account all the steps from gravitational collapse in real space to PBH formation. In particular, we use results from numerical relativity simulations and peak theory to study the conditions for PBH formation for a range of perturbation shapes, including non-linearities, perturbation profile and a careful treatment of smoothing and filtering scales. We then obtain updated PBH formation conditions and translate that into primordial spectrum constraints for a wide range of shapes and abundances. These updated constraints cover a range of scales not probed by other cosmological observables. Our results show that the correct and accurate modelling of non-linearities, filtering and typical perturbation profile, is crucial for deriving meaningful cosmological implications.

A technique for studying collisionless dynamics of a homogeneous superconducting system is developed which is based on Riccati parametrization of the Wigner distribution function. The quantum evolution of the superconducting order parameter, initially deviating from the equilibrium value, is calculated using this technique. The effect of a time-dependent BCS paring interaction on the dynamics of the order parameter is also studied.

A temperature-dependent Schrödinger equation is proposed for the study of quantum dynamics in systems which interact with an external bath. The derivation is based on a time-dependent self consistent field (TDSCF) approximation for a system-bath wave function. As previously shown by Miller, this approximation leads to a quantum mechanical analog to the classical generalized Langevin equation. By replacing the time-evolution of the quantum mechanical bath observables with the corresponding classical trajectories, the fluctuating force and the nonlinear friction kernel in the Langevin-Schrödinger equation become temperature-dependent where the fluctuations intensity is proportional to T. Application of the new equation to the spin-boson model shows agreement with numerically exact path integral calculations for T>0. We relate the success of the TDSCF approximation in this case to the bath-induced noise which diminishes the importance of quantum mechanical system-bath correlations.

Three-dimensional upper bound limit analysis of underground cavities using nonlinear Baker failure criterion

We study adiabatic ~curvature! and entropy ~isocurvature! perturbations produced during a period of cosmological inflation that is driven by multiple scalar fields with an arbitrary interaction potential. A local rotation in field space is performed to separate out the adiabatic and entropy modes. The resulting field equations show explicitly how on large scales entropy perturbations can source adiabatic perturbations if the background solution follows a curved trajectory in field space, and how adiabatic perturbations cannot source entropy perturbations in the long-wavelength limit. It is the effective mass of the entropy field that determines the amplitude of entropy perturbations during inflation. We present two applications of the equations. First, we show why one in general expects the adiabatic and entropy perturbations to be correlated at the end of inflation, and calculate the cross correlation in the context of a double inflation model with two non-interacting fields. Second, we consider two-field preheating after inflation, examining conditions under which entropy perturbations can alter the large-scale curvature perturbation and showing how our new formalism has advantages in numerical stability when the background solution follows a non-trivial trajectory in field space.

<p>The Met Office hourly 4D-Var was introduced operationally to its convective-scale limited area model (UKV) in summer 2017, improving forecast skill for nowcasting and short-range purposes. However, in recent tests a downscaler run from a global analysis tends to be better than hourly 4D-Var, especially for some variables (e.g. screen temperature). This is probably due to a poor representation of large-scale dynamics in the LAM DA system, which is now integrated on an extended domain, whilst the global model has improved to a 10km resolution and with better DA (hybrid 4D-Var). Therefore, the MO recognises the necessity of coupling large scale dynamics with convective systems using the better estimation of these motions from the global model.<br>We opted for a solution similar to spectral nudging, which uses large scale increments derived from a model with a better representation of these scales. At the same time, the short scales from UKV are maintained. We call this method ‘Background Increments’ (BGInc), as it updates the UKV background fields using a spectrally filtered increment derived from a different (global) model. This update is calculated just prior to computing the analysis increments from the hourly DA cycle. We investigated different set-ups for the implementation, changing the cut-off wavelength, the vertical weights, the frequency of updates of BGInc and other set-up features.<br>This novel system is now in a testing phase for operational purposes. From preliminary results, the forecast is improved for about the first 12 hours for different variables. We also notice a reduction in the gravity wave activity generated when new lateral boundary conditions are introduced to the LAM from the latest global forecast. This research shows the benefits of a better representation of large-scale motions for LAM forecasts. <br>In the short term, future development involves the computation of new static covariances using a better representation of the large-scale error. In the longer term, this technique could be useful in a hybrid 4D-Var scheme while enabling the use of large-scale ensemble perturbations in the analysis without causing large adjustments at the lateral boundaries.</p>

For evaluation of capacitance-voltage measurements on an abrupt pn semiconductor junction with reverse-biased depletion layer an approximation equation for the quantity Ue is presented, where Ue is the value at the intercept of the extrapolated plot C−2 to the applied voltage axis. The approximation formula is compared with an exact calculation. The maximum error in the approximate relationship for Ue is less than 3% in a wide range of impurity density and applied reverse voltage, therefore the discrepancy in the space-charge layer capacitance Cs is less than 1.5%. Cs is given by the relationship, which follows from Shockley's theory, if (U + UD) is replaced by (U + Ue). Für die Auswertung von Kapazitätsmessungen an abrupten pn-Übergängen, die in Sperrich-tung belastet sind, wird eine Näherungsbeziehung für die Größe Ue entwickelt, wobei Ue die Spannung am Schnittpunkt der extrapolierten Kurve C−2 mit der Spannungsabszisse U darstellt. Die Näherungslösung wird mit den Werten einer exakten numerischen Rechnung verglichen. Der maximale Fehler bei der approximierten Größe Ue liegt in einem weiten Dotierungsbereich und Sperrspannungsbereich unter 3%, so daß die Abweichungen bei der Sperrschichtkapazität Cs kleiner als 1,5% sind. Man kann Cs durch die Beziehung nach der Shockleyschen Theorie beschreiben, wenn man (U - UD) durch (U + Ue) ersetzt.