A self-consistent approach for the evaluation of the existing three-parameter corresponding states principles of non-polar fluids and the calculation of the corresponding states parameters is presented. This self consistent approach is based upon the assumption that the contribution of the third parameter to the thermophysical properties is much smaller than the contributions of the first two p...

We present shape-preserving self-accelerating beams of Maxwell's equations with optical nonlinearities. Such beams are exact solutions to Maxwell's equations with Kerr or saturable nonlinearity. The nonlinearity contributes to self-trapping and causes backscattering. Those effects, together with diffraction effects, work to maintain shape-preserving acceleration of the beam on a circular trajec...

Laplacian-based approximate consensus algorithms are an important and frequently used building block in many distributed applications, including formation control, sensor fusion, and synchronization. These algorithms, however, converge extremely slowly on networks that are more than a few hops in diameter and where values are spatially correlated. This paper presents a new algorithm, Power Law ...

Standard backpropagation and many procedures derived from it use the steepest-descent method to minimize a cost function. In this paper, we present a new genetic algorithm, dynamic self-adaptation, to accelerate steepest descent as it is used in iterative procedures. The underlying idea is to take the learning rate of the previous step, to increase and decrease it slightly, to evaluate the cost...

We find accelerating beams in a general periodic optical system, such as photonic crystal slabs, honeycomb lattices, and various metamaterials. These beams retain a shape-preserving profile while bending to highly non-paraxial angles along a circular-like trajectory. The properties of such beams depend on the crystal lattice structure: on a small-scale, the fine features of the beams profile ar...

We study linear and nonlinear self-accelerating beams propagating along circular trajectories beyond the paraxial approximation. Such nonparaxial accelerating beams are exact solutions of the Helmholtz equation, preserving their shapes during propagation even under nonlinearity. We generate experimentally and observe directly these large-angle bending beams in colloidal suspensions of polystyre...

We demonstrate both theoretically and experimentally nonparaxial Mathieu and Weber accelerating beams, generalizing the concept of previously found accelerating beams. We show that such beams bend into large angles along circular, elliptical, or parabolic trajectories but still retain nondiffracting and self-healing capabilities. The circular nonparaxial accelerating beams can be considered as ...

Scalar–tensor gravity is the simplest and best understood modification of general relativity, consisting of a real scalar field coupled directly to the Ricci scalar curvature. Models of this type have self-accelerating solutions. In an example inspired by string dilaton couplings, scalar–tensor gravity coupled to ordinary matter exhibits a de Sitter type expansion, even in the presence of a neg...

Pierre Gratia,1, ∗ Wayne Hu,2, † and Mark Wyman2, 3, ‡ Department of Physics, University of Chicago, Chicago, Illinois 60637, U.S.A. Kavli Institute for Cosmological Physics, Department of Astronomy & Astrophysics, Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, U.S.A. Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY, 10...