Quantum Gravity Phenomenology from the Thermodynamics of Spacetime

This work is based on the formalism developed in the study of the thermodynamics of spacetime used to derive Einstein equations from the proportionality of entropy within an area. When low-energy quantum gravity effects are considered, an extra logarithmic term in the area is added to the entropy expression. Here, we present the derivation of the quantum modified gravitational dynamics from this modified entropy expression and discuss its main features. Furthermore, we outline the application of the modified dynamics to cosmology, suggesting the replacement of the Big Bang singularity with a regular bounce.

Some Properties of Chaotic Modified of Bogdanov Map

In this research to the modified dynamics of Bogdanov's map studied, and the found sensitivity to the initial conditions of the modified map found as well as the Lyapunov exponent .the general characteristics of the map by the diffeomorpism. Finally we boosted my research with matlab to find chaotic areas

Measuring Granger-causal effects in multivariate time series by system editing

1.AbstractWhat is the role of each node in a system of many interconnected nodes? This can be quantified by comparing the dynamics of the nodes in the intact system, with their modified dynamics in the edited system, where one node is deleted. In detail, the spectra are calculated from a causal multivariate autoregressive model for the intact system. Next, without re-estimation, one node is deleted from the model and the modified spectra at all other nodes are re-calculated. The change in spectra from the edited system to the intact system quantifies the role of the deleted node, giving a measure of its Granger-causal effects (CFX) on the system. A generalization of this novel measure is available for networks (i.e. for groups of nodes), which quantifies the role of each network in a system of many networks. For the sake of reproducible research, program codes (PASCAL), executable file, and toy data in human readable format are included in the supplementary material.

Design and Analysis of a Pose Estimator for Quadrotor MAVs With Modified Dynamics and Range Measurements

This paper presents the design and analysis of a pose estimator for quadrotor micro aerial vehicles (MAVs). The proposed design uses the dynamic model of the quadrotor with aerodynamic effects and uses the extended Kalman filter (EKF) formulation for state estimation. Range measurements to known locations, inertial measurements and height measurements are used for the estimation task. The purpose of the study is to evaluate the performance of the estimator when navigating through a changing indoor setting. The study investigates the effect of changing number of rannge measurements, different geometrical arrangements of range sensors and changing availability of confident height information on the performance of the estimator. Performance of the estimator for each scenario is numerically analyzed. Finally a criteria is proposed for selecting the sensors, number of range measurements, geometric location of sensors which facilitates accurate position estimation using the proposed method.

Dynamics of wide binary stars: A case study for testing Newtonian dynamics in the low acceleration regime

Extremely wide binary stars represent ideal systems to probe Newtonian dynamics in the low acceleration regimes ([Formula: see text][Formula: see text]ms[Formula: see text]) typical of the external regions of galaxies. Here, we present a study of 60 alleged wide binary stars with projected separation ranging from 0.004[Formula: see text]pc to 1[Formula: see text]pc, probing gravitational accelerations well below the limit where dark matter or modified dynamics theories set in. Radial velocities with accuracy [Formula: see text][Formula: see text]m/s were obtained for each star, in order to constrain their orbital velocity, that, together with proper motion data, can distinguish bound from unbound systems. It was found that about half of the observed pairs do have velocity in the expected range for bound systems, out of the largest separations probed here. In particular, we identified five pairs with projected separation [Formula: see text][Formula: see text]pc that are useful for the proposed test. While it would be premature to draw any conclusion about the validity of Newtonian dynamics at these low accelerations, our main result is that very wide binary stars seem to exist in the harsh environment of the solar neighborhood. This could provide a tool to test Newtonian dynamics versus modified dynamics theories in the low acceleration conditions typical of galaxies. In the near future the GAIA satellite will provide data to increase significantly the number of wide pairs that, with the appropriate follow-up spectroscopic observations, will allow the implementation of this experiment with unprecedented accuracy.