We study the vertex-cover problem, which is a nondeterministic polynomial-time hard optimization problem and a prototypical model exhibiting phase transitions on random graphs, such as Erdős-Rényi (ER) random graphs. These phase transitions coincide with changes of the solution space structure, e.g., for the ER ensemble at connectivity c=e≈2.7183 from replica symmetric to replica-symmetry broke...

The alpha-beta magnetostructural phase transition in MnAs/GaAs(111) epilayers is investigated by elastic neutron scattering. The in-plane parameter of MnAs remains almost constant with temperature from 100 to 420 K, following the thermal evolution of the GaAs substrate. This induces a temperature dependent biaxial strain that is responsible for an alpha-beta phase coexistence and, more importan...

We study the effect of nonparaxiality in a folded resonator by accurate measurements of the Gouy phase, as function of the mode number for mode numbers up to 1500. Our experimental method is based upon tuning the resonator close to a frequency-degenerate point. The Gouy phase shows a nonparaxial behavior that is much stronger in the folding-plane than in the perpendicular plane. Agreement with ...

We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that energy conversion and pulse propagation known from three-wave interaction is reproduced in the lattice and that exact phase matching of parametr...

This represents a circle in the phase plane. Its plot is given in Fig. 2.1.b. __________________________________________________________________________________________ The nature of the system response corresponding to various initial conditions is directly displayed on the phase plane. In the above example, we can easily see that the system trajectories neither converge to the origin nor dive...

In this note we present a novel stability analysis method for DC to DC series resonant converters which relies on the phase plane technique. This method gives more insight into the rationale behind the stability conditions because these are obtained from geometrical considerations instead of eigenvalues of linear discrete time approximations as presented in previous works. The proposed method a...

In this paper, the problem of one-dimensional (1-D) velocity estimation is addressed, using two-dimensional (2D) spatiotemporal orientation estimation. A new frequency estimator based on a least square plane fitting of the estimated autocorrelation phase has been previously developed and is applied here to random textured images for the problem of velocity estimation. This algorithm requires th...

The aim of this paper is to study a predator-prey population model which takes into account the uncertainty that arises when determining the initial populations of predator and prey . This model is solved numerically by means of a 4-order Runge-Kutta method. Simulations are made and a graphical representation is also provided to show the evolution of both populations over time. In addition to t...

Combustion oscillation in a rocket combustor was analyzed using Variational Auto-Encoder (VAE). Dimension reductions were conducted on various physical quantities (p′, ˙q′, etc.) the combustor. Orthogonal modes obtained proper orthogonal decomposition for output of VAE. Pumping and damping regions identified distribution Rayleigh Index each mode. Three characteristic that supply energy to oscil...

Temporal and spatial phase shifting in electronic speckle-pattern interferometry are compared quantitatively with respect to the quality of the resultant deformation phase maps. On the basis of an analysis of the noise in sawtooth fringes a figure of merit is defined and measured for various in-plane and out-of-plane sensitive electronic speckle-pattern interferometry configurations. Varying qu...