1,501 research outputs found
Simultaneous stabilization and simultaneous pole placement by nonswitching dynamic compensation
The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed
Inhomogeneous non-Gaussianity
We propose a method to probe higher-order correlators of the primordial
density field through the inhomogeneity of local non-Gaussian parameters, such
as f_NL, measured within smaller patches of the sky. Correlators between
n-point functions measured in one patch of the sky and k-point functions
measured in another patch depend upon the (n+k)-point functions over the entire
sky. The inhomogeneity of non-Gaussian parameters may be a feasible way to
detect or constrain higher-order correlators in local models of
non-Gaussianity, as well as to distinguish between single and multiple-source
scenarios for generating the primordial density perturbation, and more
generally to probe the details of inflationary physics.Comment: 16 pages, 2 figures; v2: Minor changes and references added. Matches
the published versio
Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems
The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined
Local non-Gaussianity from inflation
The non-Gaussian distribution of primordial perturbations has the potential
to reveal the physical processes at work in the very early Universe. Local
models provide a well-defined class of non-Gaussian distributions that arise
naturally from the non-linear evolution of density perturbations on
super-Hubble scales starting from Gaussian field fluctuations during inflation.
I describe the delta-N formalism used to calculate the primordial density
perturbation on large scales and then review several models for the origin of
local primordial non-Gaussianity, including the cuvaton, modulated reheating
and ekpyrotic scenarios. I include an appendix with a table of sign conventions
used in specific papers.Comment: 21 pages, 1 figure, invited review to appear in Classical and Quantum
Gravity special issue on non-linear and non-Gaussian cosmological
perturbation
Interactions between sea urchin grazing and prey diversity on temperate rocky reef communities
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116948/1/ecy20139471636.pd
Large non-Gaussianity from two-component hybrid inflation
We study the generation of non-Gaussianity in models of hybrid inflation with
two inflaton fields, (2-brid inflation). We analyse the region in the parameter
and the initial condition space where a large non-Gaussianity may be generated
during slow-roll inflation which is generally characterised by a large f_NL,
tau_NL and a small g_NL. For certain parameter values we can satisfy
tau_NL>>f_NL^2. The bispectrum is of the local type but may have a significant
scale dependence. We show that the loop corrections to the power spectrum and
bispectrum are suppressed during inflation, if one assume that the fields
follow a classical background trajectory. We also include the effect of the
waterfall field, which can lead to a significant change in the observables
after the waterfall field is destabilised, depending on the couplings between
the waterfall and inflaton fields.Comment: 16 pages, 6 figures; v2: comments and references added, typos
corrected, matches published versio
Generation of helical magnetic fields from inflation
The generation of helical magnetic fields during single field inflation due
to an axial coupling of the electromagnetic field to the inflaton is discussed.
We find that such a coupling always leads to a blue spectrum of magnetic fields
during slow roll inflation. Though the helical magnetic fields further evolve
during the inverse cascade in the radiation era after inflation, we conclude
that the magnetic fields generated by such an axial coupling can not lead to
observed field strength on cosmologically relevant scales.Comment: 4 pages, 1 figure; Contribution to the proceedings of the
International Conference on Gravitation and Cosmology (ICGC), Goa, India,
December, 201
Scale-Dependent Non-Gaussianity as a Generalization of the Local Model
We generalize the local model of primordial non-Gaussianity by promoting the
parameter fNL to a general scale-dependent function fNL(k). We calculate the
resulting bispectrum and the effect on the bias of dark matter halos, and thus
the extent to which fNL(k) can be measured from the large-scale structure
observations. By calculating the principal components of fNL(k), we identify
scales where this form of non-Gaussianity is best constrained and estimate the
overlap with previously studied local and equilateral non-Gaussian models.Comment: Accepted to JCAP. 22 pages, 4 figure
Scale-dependent non-Gaussianity and the CMB power asymmetry
We introduce an alternative parametrisation for the scale dependence of the non–linearity parameter fNL in quasi-local models of non–Gaussianity. Our parametrisation remains valid when fNL changes sign, unlike the commonly adopted power law ansatz fNL(k) ∝ knfNL. We motivate our alternative parametrisation by appealing to the self-interacting curvaton scenario, and as an application, we apply it to the CMB power asymmetry. Explaining the power asymmetry requires a strongly scale dependent non-Gaussianity. We show that regimes of model parameter space where fNL is strongly scale dependent are typically associated with a large gNL and quadrupolar power asymmetry, which can be ruled out by existing observational constraints
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