19,545 research outputs found
Constraining auto-interaction terms in α-attractor supergravity models of inflation
The inflationary mechanism has become the paradigm of modern cosmology over the last thirty years. However, there are several aspects of inflationary physics that are still to be addressed, like the shape of the inflationary potential. Regarding this, the so-called α-attractor models show interesting properties. In this work, the reconstruction of the effective potential around the global minimum of these particular potentials is provided, assuming a detection of permille-order for the tensor-to-scalar-ratio by forthcoming cosmic microwave background or gravitational waves experiments
Reconstruction of -attractor supergravity models of inflation
In this paper, we apply reconstruction techniques to recover the potential
parameters for a particular class of single-field models, the
-attractor (supergravity) models of inflation. This also allows to
derive the inflaton vacuum expectation value at horizon crossing. We show how
to use this value as one of the input variables to constrain the
postaccelerated inflationary phase. We assume that the tensor-to-scalar ratio
is of the order of , a level reachable by the expected
sensitivity of the next-generation CMB experiments.Comment: 10 pages, LaTeX, some typos correcte
Lot-sizing with stock upper bounds and fixed charges
Here we study the discrete lot-sizing problem with an initial stock variable and an associated variable upper bound constraint. This problem is of interest in its own right, and is also a natural relaxation of the constant capacity lot-sizing problem with upper bounds and fixed charges on the stock variables. We show that the convex hull of solutions of the discrete lot-sizing problem is obtained as the intersection of two simpler sets, one involving just 0-1 variables and the second a mixing set with a variable upper bound constraint. For these two sets we derive both inequality descriptions and polynomial-size extended formulations of their respective convex hulls. Finally we carry out some limited computational tests on single-item constant capacity lot-sizing problems with upper bounds and fixed charges on the stock variables in which we use the extended formulations derived above to strengthen the initial mixed integer programming formulations.mixed integer programming, discrete lot-sizing, stock fixed costs, mixing sets
Condensation phenomena in nonlinear drift equations
We study nonnegative, measure-valued solutions to nonlinear drift type
equations modelling concentration phenomena related to Bose-Einstein particles.
In one spatial dimension, we prove existence and uniqueness for measure
solutions. Moreover, we prove that all solutions blow up in finite time leading
to a concentration of mass only at the origin, and the concentrated mass
absorbs increasingly the mass converging to the total mass as time goes to
infinity. Our analysis makes a substantial use of independent variable scalings
and pseudo-inverse functions techniques
Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D
We prove the equivalence between the notion of Wasserstein gradient flow for
a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian
potential on one side, and the notion of entropy solution of a Burgers-type
scalar conservation law on the other. The solution of the former is obtained by
spatially differentiating the solution of the latter. The proof uses an
intermediate step, namely the gradient flow of the pseudo-inverse
distribution function of the gradient flow solution. We use this equivalence to
provide a rigorous particle-system approximation to the Wasserstein gradient
flow, avoiding the regularization effect due to the singularity in the
repulsive kernel. The abstract particle method relies on the so-called
wave-front-tracking algorithm for scalar conservation laws. Finally, we provide
a characterization of the sub-differential of the functional involved in the
Wasserstein gradient flow
Slow-roll Inflation for Generalized Two-Field Lagrangians
We study the slow-roll regime of two field inflation, in which the two fields
are also coupled through their kinetic terms. Such Lagrangians are motivated by
particle physics and by scalar-tensor theories studied in the Einstein frame.
We compute the power spectra of adiabatic and isocurvature perturbations on
large scales to first order in the slow-roll parameters. We discuss the
relevance of the extra coupling terms for the amplitude and indexes of the
power spectra. Beyond the consistency condition which involves the amplitude of
gravitational waves, additional relations may be found in particular models
based on such Lagrangians: as an example, we find an additional general
consistency condition in implicit form for Brans-Dicke theory in the Einstein
frame.Comment: 17 pages, 1 figure, accepted for publication in Phys. Rev.
A homogeneous limit methodology and refinements of computationally efficient zigzag theory for homogeneous, laminated composite, and sandwich plates
The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multiscale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear-deformation theory, whereas the fine displacement field has a piecewise-linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct variants of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elastostatic deformations are used to identify the best-performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous-plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. This theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient, C0 a continuous function of (x1,x2) coordinates whose first-order derivatives are discontinuous along finite element interfaces and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures
Robust Unconditionally Secure Quantum Key Distribution with Two Nonorthogonal and Uninformative States
We introduce a novel form of decoy-state technique to make the single-photon
Bennett 1992 protocol robust against losses and noise of a communication
channel. Two uninformative states are prepared by the transmitter in order to
prevent the unambiguous state discrimination attack and improve the phase-error
rate estimation. The presented method does not require strong reference pulses,
additional electronics or extra detectors for its implementation.Comment: 7 pages, 2 figure
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