Science in the Third Dimension of R&D

We study a Schumpeterian model of long-run growth with endogenous fertility and with three interacting dimensions of innovation. Scientific research is the fundamental dimension of innovation that creates new technological knowledge. This is allocated over new working prototypes in the horizontal dimension. New firms finance scientific research by obtaining the property rights of new working prototypes, and existing firms invest in developing the blueprint mode of working prototypes into the more productive modes of production in the vertical dimension. Balanced growth in the standards of living is fully endogenous without scale effects, and a new parameter, i.e., the elasticity of scientific knowledge with respect to existing collective scientific knowledge, nonlinearly accelerates long-run growth. With exogenous population growth, the model generates a semi-endogenous result due to the endogenously determined bound on technological opportunity.Science; Technology; Blueprints; R&D; Endogenous Fertility

Quantifying Diachronic Variability: The 'Ain Difla rockshelter (Jordan) and the Evolution of Levantine Mousterian Technology

Condette Jean-François. RAYNAL Pierre, voir CHAUDRU de RAYNAL Pierre. In: , . Les recteurs d'académie en France de 1808 à 1940. Tome II, Dictionnaire biographique. Paris : Institut national de recherche pédagogique, 2006. p. 327. (Histoire biographique de l'enseignement, 12

Relativistic dark matter at the Galactic center

In a large region of the supersymmetry parameter space, the annihilation cross section for neutralino dark matter is strongly dependent on the relative velocity of the incoming particles. We explore the consequences of this velocity dependence in the context of indirect detection of dark matter from the galactic center. We find that the increase in the annihilation cross section at high velocities leads to a flattening of the halo density profile near the galactic center and an enhancement of the annihilation signal.Comment: 13 pages, 9 figure

Prethermalization Production of Dark Matter

At the end of inflation, the inflaton field decays into an initially nonthermal population of relativistic particles which eventually thermalize. We consider the production of dark matter from this relativistic plasma, focusing on the prethermal phase. We find that for a production cross section $\sigma(E)\sim E^n$ with $n> 2$, the present dark matter abundance is produced during the prethermal phase of its progenitors. For $n\le 2$, entropy production during reheating makes the nonthermal contribution to the present dark matter abundance subdominant compared to that produced thermally. As specific examples, we verify that the nonthermal contribution is irrelevant for gravitino production in low scale supersymmetric models ($n=0$) and is dominant for gravitino production in high scale supersymmetry models ($n=6$).Comment: 12 pages, 4 figure

Gravitational perturbations from oscillons and transients after inflation

We study the scalar and tensor perturbations generated by the fragmentation of the inflaton condensate into oscillons or transients after inflation, using nonlinear classical lattice simulations. Without including the backreaction of metric perturbations, we find that the magnitude of scalar metric perturbations never exceeds a few $\times 10^{-3}$, whereas the maximal strength of the gravitational wave signal today is $\mathcal{O}(10^{-9})$ for standard post-inflationary expansion histories. We provide parameter scalings for the $\alpha$-attractor models of inflation, which can be easily applied to other models. We also discuss the likelihood of primordial black hole formation, as well as conditions under which the gravitational wave signal can be at observationally interesting frequencies and amplitudes. Finally, we provide an upper bound on the frequency of the peak of the gravitational wave signal, which applies to all preheating scenarios.Comment: 18 pages, 8 figure

A sequential sampling strategy for extreme event statistics in nonlinear dynamical systems

We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the 'next-best' data point (set of parameters) that when evaluated results in improved estimates of the probability density function (pdf) for a scalar quantity of interest. The approach utilizes Gaussian process regression to perform Bayesian inference on the parameter-to-observation map describing the quantity of interest. We then approximate the desired pdf along with uncertainty bounds utilizing the posterior distribution of the inferred map. The 'next-best' design point is sequentially determined through an optimization procedure that selects the point in parameter space that maximally reduces uncertainty between the estimated bounds of the pdf prediction. Since the optimization process utilizes only information from the inferred map it has minimal computational cost. Moreover, the special form of the metric emphasizes the tails of the pdf. The method is practical for systems where the dimensionality of the parameter space is of moderate size, i.e. order O(10). We apply the method to estimate the extreme event statistics for a very high-dimensional system with millions of degrees of freedom: an offshore platform subjected to three-dimensional irregular waves. It is demonstrated that the developed approach can accurately determine the extreme event statistics using limited number of samples

The charged inflaton and its gauge fields: preheating and initial conditions for reheating

We calculate particle production during inflation and in the early stages of reheating after inflation in models with a charged scalar field coupled to Abelian and non-Abelian gauge fields. A detailed analysis of the power spectra of primordial electric fields, magnetic fields and charge fluctuations at the end of inflation and preheating is provided. We carefully account for the Gauss constraints during inflation and preheating, and clarify the role of the longitudinal components of the electric field. We calculate the timescale for the back-reaction of the produced gauge fields on the inflaton condensate, marking the onset of non-linear evolution of the fields. We provide a prescription for initial conditions for lattice simulations necessary to capture the subsequent nonlinear dynamics. On the observational side, we find that the primordial magnetic fields generated are too small to explain the origin of magnetic fields on galactic scales and the charge fluctuations are well within observational bounds for the models considered in this paper.Comment: 48 pages, 6 figures, 2 appendices, v3: references added, minor changes to text, to appear in JCA