An embedded 5(4) explicit Runge-Kutta-Nyström method with dissipation of high order

A new 5(4) embedded explicit Runge-Kutta-Nystrom (RKN) method with dissipation of high order is developed to solve integration of initial-value problems for second-order ordinary differential equations possessing oscillating solutions. The fifth order formula has dispersive order eight and dissipative order nine. The fourth-order embedded formula is obtained to control the local truncation errors. Numerical experiments indicate that the new method is more efficient than the existing embedded explicit RKN methods

Sharp estimation of local convergence radius for the Picard iteration

We investigate the local convergence radius of a general Picard iteration in the frame of a real Hilbert space. We propose a new algorithm to estimate the local convergence radius. Numerical experiments show that the proposed procedure gives sharp estimation (i.e., close to or even identical with the best one) for several well known or recent iterative methods and for various nonlinear mappings. Particularly, we applied the proposed algorithm for classical Newton method, for multi-step Newton method (in particular for third-order Potra-Ptak method) and for fifth-order "M5" method. We present also a new formula to estimate the local convergence radius for multi-step Newton method

Fifth order two derivative Runge-Kutta method with reduced function evaluations for solving IVPs

In this paper, the First Same As Last (FSAL) technique is implemented to Two Derivative Runge-Kutta method (TDRK) for the numerical integration of first order Initial Value Problems (IVPs). Using the FSAL property, a four stages fifth algebraic order TDRK method is constructed. Hence, the new method has three effective stages meaning that it has three function evaluations per step. It has two stages less compared with the classical Runge-Kutta for the same order. The stability of the method derived is analyzed. The numerical experiments are carried out to show the accuracy and efficiency of the method by comparing the derived method with other existing Runge-Kutta methods (RK)

Probing Modified Gravity with Atom-Interferometry: a Numerical Approach

Refined constraints on chameleon theories are calculated for atom-interferometry experiments, using a numerical approach consisting in solving for a four-region model the static and spherically symmetric Klein-Gordon equation for the chameleon field. By modeling not only the test mass and the vacuum chamber but also its walls and the exterior environment, the method allows to probe new effects on the scalar field profile and the induced acceleration of atoms. In the case of a weakly perturbing test mass, the effect of the wall is to enhance the field profile and to lower the acceleration inside the chamber by up to one order of magnitude. In the thin-shell regime, results are found to be in good agreement with the analytical estimations, when measurements are realized in the immediate vicinity of the test mass. Close to the vacuum chamber wall, the acceleration becomes negative and potentially measurable. This prediction could be used to discriminate between fifth-force effects and systematic experimental uncertainties, by doing the experiment at several key positions inside the vacuum chamber. For the chameleon potential $V(\phi) = \Lambda^{4+\alpha} / \phi^\alpha$ and a coupling function $A(\phi) = \exp(\phi /M)$, one finds $M \gtrsim 7 \times 10^{16} \mathrm{GeV}$, independently of the power-law index. For $V(\phi) = \Lambda^4 (1+ \Lambda/ \phi)$, one finds $M \gtrsim 10^{14} \mathrm{GeV}$. A sensitivity of $a\sim 10^{-11} \mathrm{m/s^2}$ would probe the model up to the Planck scale. Finally, a proposal for a second experimental set-up, in a vacuum room, is presented. In this case, Planckian values of $M$ could be probed provided that $a \sim 10^{-10} \mathrm{m/s^2}$, a limit reachable by future experiments. Our method can easily be extended to constrain other models with a screening mechanism, such as symmetron, dilaton and f(R) theories.Comment: 13 pages, 12 figures, version accepted by PR

Spatio-Velocity CSF as a Function of Retinal Velocity Using Unstabilized Stimuli

LCD televisions have LC response times and hold-type data cycles that contribute to the appearance of blur when objects are in motion on the screen. New algorithms based on studies of the human visual system\u27s sensitivity to motion are being developed to compensate for these artifacts. This paper describes a series of experiments that incorporate eyetracking in the psychophysical determination of spatio-velocity contrast sensitivity in order to build on the 2D spatiovelocity contrast sensitivity function (CSF) model first described by Kelly and later refined by Daly. We explore whether the velocity of the eye has an additional effect on sensitivity and whether the model can be used to predict sensitivity to more complex stimuli. There were a total of five experiments performed in this research. The first four experiments utilized Gabor patterns with three different spatial and temporal frequencies and were used to investigate and/or populate the 2D spatio-velocity CSF. The fifth experiment utilized a disembodied edge and was used to validate the model. All experiments used a two interval forced choice (2IFC) method of constant stimuli guided by a QUEST routine to determine thresholds. The results showed that sensitivity to motion was determined by the retinal velocity produced by the Gabor patterns regardless of the type of motion of the eye. Based on the results of these experiments the parameters for the spatio-velocity CSF model were optimized to our experimental conditions

Improved decision support for engine-in-the-loop experimental design optimization

Experimental optimization with hardware in the loop is a common procedure in engineering and has been the subject of intense development, particularly when it is applied to relatively complex combinatorial systems that are not completely understood, or where accurate modelling is not possible owing to the dimensions of the search space. A common source of difficulty arises because of the level of noise associated with experimental measurements, a combination of limited instrument precision, and extraneous factors. When a series of experiments is conducted to search for a combination of input parameters that results in a minimum or maximum response, under the imposition of noise, the underlying shape of the function being optimized can become very difficult to discern or even lost. A common methodology to support experimental search for optimal or suboptimal values is to use one of the many gradient descent methods. However, even sophisticated and proven methodologies, such as simulated annealing, can be significantly challenged in the presence of noise, since approximating the gradient at any point becomes highly unreliable. Often, experiments are accepted as a result of random noise which should be rejected, and vice versa. This is also true for other sampling techniques, including tabu and evolutionary algorithms. After the general introduction, this paper is divided into two main sections (sections 2 and 3), which are followed by the conclusion. Section 2 introduces a decision support methodology based upon response surfaces, which supplements experimental management based on a variable neighbourhood search and is shown to be highly effective in directing experiments in the presence of a significant signal-to-noise ratio and complex combinatorial functions. The methodology is developed on a three-dimensional surface with multiple local minima, a large basin of attraction, and a high signal-to-noise ratio. In section 2, the methodology is applied to an automotive combinatorial search in the laboratory, on a real-time engine-in-the-loop application. In this application, it is desired to find the maximum power output of an experimental single-cylinder spark ignition engine operating under a quasi-constant-volume operating regime. Under this regime, the piston is slowed at top dead centre to achieve combustion in close to constant volume conditions. As part of the further development of the engine to incorporate a linear generator to investigate free-piston operation, it is necessary to perform a series of experiments with combinatorial parameters. The objective is to identify the maximum power point in the least number of experiments in order to minimize costs. This test programme provides peak power data in order to achieve optimal electrical machine design. The decision support methodology is combined with standard optimization and search methods – namely gradient descent and simulated annealing – in order to study the reductions possible in experimental iterations. It is shown that the decision support methodology significantly reduces the number of experiments necessary to find the maximum power solution and thus offers a potentially significant cost saving to hardware-in-the-loop experi- mentation

The Role of the Superior Order GLCM in the Characterization and Recognition of the Liver Tumors from Ultrasound Images

The hepatocellular carcinoma (HCC) is the most frequent malignant liver tumor. It often has a similar visual aspect with the cirrhotic parenchyma on which it evolves and with the benign liver tumors. The golden standard for HCC diagnosis is the needle biopsy, but this is an invasive, dangerous method. We aim to develop computerized,noninvasive techniques for the automatic diagnosis of HCC, based on information obtained from ultrasound images. The texture is an important property of the internal organs tissue, able to provide subtle information about the pathology. We previously defined the textural model of HCC, consisting in the exhaustive set of the relevant textural features, appropriate for HCC characterization and in the specific values of these features. In this work, we analyze the role that the superior order Grey Level Cooccurrence Matrices (GLCM) and the associated parameters have in the improvement of HCC characterization and automatic diagnosis. We also determine the best spatial relations between the pixels that lead to the highest performances, for the third, fifth and seventh order GLCM. The following classes will be considered: HCC, cirrhotic liver parenchyma on which it evolves and benign liver tumors

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically