Dephasing and inhibition of spin interference from semi-classical self-gravitation

We present a detailed derivation of a model to study effects of self-gravitation from semi-classical gravity, described by the Schrödinger-Newton equation, employing spin superposition states in inhomogeneous magnetic fields, as proposed recently for experiments searching for gravity induced entanglement. Approximations for the experimentally relevant limits are discussed. Results suggest that spin interferometry could provide a more accessible route towards an experimental test of quantum aspects of gravity than both previous proposals to test semi-classical gravity and the observation of gravitational spin entanglement.

Development of a virtual biomechanical manikin used in vibrations studies in occupied spaces

In this paper is developed and applied a virtual biomechanical manikin used in occupied spaces. This multi-nodal numerical model is applied in the vibrations of the different sections of the human body, under transient conditions. The integration of second order equations systems, based in Newton equation, after being converted in a first order equation system, is solved through the Runge-Kutta-Fehlberg method with error control. This multi-nodal numerical model will be used, in this work, in the study of the vibrations that a standing person is subjected when stimuli are applied to the feet. The influence of various types of stimuli is analyzed, with periodic irregularities, in the dynamic response of the vibrations in different sections of the human body. The signals of the stimuli, the displacement of some sections of the body and the power spectrum of the same signals will be presented. In the study the influence of the floor vibration in the human body sections is analyzed and presented.

A new three-term spectral conjugate gradient algorithm with higher numerical performance for solving large scale optimization problems based on Quasi-Newton equation

A new spectral three-term conjugate gradient algorithm in virtue of the Quasi-Newton equation is developed for solving large-scale unconstrained optimization problems. It is proved that the search directions in this algorithm always satisfy a sufficiently descent condition independent of any line search. Global convergence is established for general objective functions if the strong Wolfe line search is used. Numerical experiments are employed to show its high numerical performance in solving large-scale optimization problems. Particularly, the developed algorithm is implemented to solve the 100 benchmark test problems from CUTE with different sizes from 1000 to 10,000, in comparison with some similar ones in the literature. The numerical results demonstrate that our algorithm outperforms the state-of-the-art ones in terms of less CPU time, less number of iteration or less number of function evaluation.

An improved quasi-Newton equation on the quasi-Newton methods for unconstrained optimizations

<span><span>Quasi-Newton methods are a class of numerical methods for </span>solving the problem of unconstrained optimization. To improve the overall efficiency of resulting algorithms, we use the quasi-Newton methods which is interesting for quasi-Newton equation. In this manuscript, we present a modified BFGS update formula based on the new quasi-Newton equation, which give a new search direction for solving unconstrained optimizations proplems. We analyse the convergence rate of quasi-Newton method under some mild condition. Numerical experiments are conducted to demonstrate the efficiency of new methods using some test problems. The results indicates that the proposed method is competitive compared to the BFGS methods as it yielded fewer iteration and fewer function evaluations.</span>

Fractional Schrödinger equation in gravitational optics

This paper addresses issues surrounding the concept of fractional quantum mechanics, related to lights propagation in inhomogeneous nonlinear media, specifically restricted to a so-called gravitational optics. Besides Schrödinger–Newton equation, we have also concerned with linear and nonlinear Airy beam accelerations in flat and curved spaces and fractal photonics, related to nonlinear Schrödinger equation, where impact of the fractional Laplacian is discussed. Another important feature of the gravitational optics’ implementation is its geometry with the paraxial approximation, when quantum mechanics, in particular, fractional quantum mechanics, is an effective description of optical effects. In this case, fractional-time differentiation reflexes this geometry effect as well.

Classical Mechanics According to Newton and Hamilton

This chapter introduces classical mechanics, starting with the familiar definitions of position, momentum, velocity, acceleration force, kinetic, potential, and total energy. It is shown how the Newton equation of motion is solved for the one-dimensional harmonic oscillator, which is a point mass oscillating around the position x = 0 driven by a force that is proportional to x (Hooke’s law). Next, the minimal action principle, the Lagrange equation of motion, and the classical Hamilton function (Hamiltonian) and conjugated variables are introduced. The chapter also discusses angular momentum and rotational motion.

A Modified Dai–Liao Conjugate Gradient Method with a New Parameter for Solving Image Restoration Problems

One adaptive choice for the parameter of the Dai–Liao conjugate gradient method is suggested in this paper, which is obtained with modified quasi–Newton equation. So we get a modified Dai–Liao conjugate gradient method. Some interesting features of the proposed method are introduced: (i) The value of parameter t of the modified Dai–Liao conjugate gradient method takes both the gradient and function value information. (ii) We establish the global convergence property of the modified Dai–Liao conjugate gradient method under some suitable assumptions. (iii) Numerical results show that the modified DL method is effective in practical computation and the image restoration problems.

A new variants of quasi-newton equation based on the quadratic function for unconstrained optimization

<p>The focus for quasi-Newton methods is the quasi-Newton equation. A new quasi-Newton equation is derived for quadratic function. Then, based on this new quasi-Newton equation, a new quasi-Newton updating formulas are presented. Under appropriate conditions, it is shown that the proposed method is globally convergent. Finally, some numerical experiments are reported which verifies the effectiveness of the new method.</p>