General Relativity: A First Course for Physicists

Martin, Jerome; Shepley, L. C.

doi:10.1119/1.18456

Cited by 6 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our approach in defining a metric and obtaining a geodesic is similar to that of the procedure in general relativity theory [8,9] in that it considers both time and weight as equivalent variables. By solving the Euler-Lagrange equation of L N , we obtain the following geodesic equations in the affine parameter coordinate.…”

Section: Derivation Of An Adaptively Damped Oscillatormentioning

confidence: 99%

“…Solving the Euler-Lagrange equation using classical mechanics Lagrangian produces Newton's second law, which states that mass multiplied by acceleration is equal to the negative gradient of a potential [2]. However, this classical dynamics Lagrangian is not constant, as is that used for obtaining the geodesic of two points on a sphere [8]. Therefore, we are interested in defining a new Lagrangian whose value is a constant over time.…”

Section: Derivation Of An Adaptively Damped Oscillatormentioning

confidence: 99%

“…In this way, we obtained an adaptively damped second-order equation whose convergence to a global minimum is guaranteed by the singular crashing behavior of the heavy ball in an affine parameter coordinate. This affine parameter was introduced to define a new Lagrangian whose value is constant, as in ordinary differential geometry, to find the shortest curve connecting the two points on a sphere [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Global Minimization Algorithm Based on a Geodesic of a Lagrangian Formulation of Newtonian Dynamics

Kim

Jangmin

et al. 2007

Neural Process Lett

View full text Add to dashboard Cite

The global minimum search problem is important in neural networks because the error cost involved is formed as multiminima potential in weight parametric space. Therefore, parameters that produce a global minimum in a cost function are the best values for enhancing the performance of neural networks. Previously, a global minimum search based on a damped oscillator equation known as the heavy ball with friction (HBF) was studied. The kinetic energy overcomes a local minimum if the kinetic energy is sufficiently large or else the heavy ball will converge into a local minimum due to the action of friction. However, an appropriate damping coefficient has not been found in the HBF; therefore, the ball has to be shot again after it arrives at each local minimum until it finds a global minimum. In order to solve this problem, we determined an adaptive damping coefficient using the geodesic of Newtonian dynamics Lagrangian. This geometric method produces a second-order adaptively damped oscillator equation, the damping coefficient of which is the negative time derivative of the logarithmic function of the cost potential. Furthermore, we obtained a novel adaptive steepest descent by discretizing this second-order equation. To investigate the performance of this novel steepest descent, we applied our first-order update rule to the Rosenbrock-and Griewank-type potentials. The results show that our method determined the global minimum in most cases from various initial points. Our adaptive steepest descent may be applied in

show abstract

Section: Derivation Of An Adaptively Damped Oscillatormentioning

confidence: 99%

Section: Derivation Of An Adaptively Damped Oscillatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Global Minimization Algorithm Based on a Geodesic of a Lagrangian Formulation of Newtonian Dynamics

Kim

Jangmin

et al. 2007

Neural Process Lett

View full text Add to dashboard Cite

show abstract

“…In this chapter, we summarize the key theoretical aspects of gravitational waves; see, e.g., [1][2][3][4] for more details.…”

Section: Theoretical Aspectsmentioning

confidence: 99%

LIGO and Virgo Gravitational-wave Detectors and Their Science Reach

Buskulic¹,

Mandel²

2013

Acta Phys. Pol. B

View full text Add to dashboard Cite

Gravitational waves were predicted by Einstein in 1916 as wave solutions of the Einstein-Hilbert equations of General Relativity. Indirect experimental evidence of their existence was only obtained in the past 40 years, most famously through observations of the binary pulsar PSR 1913+16. Direct detection of gravitational waves is anticipated later this decade. It will be enabled by interferometric detectors Virgo and LIGO. We begin with a brief theoretical description and the historical background of the search for gravitational waves. We describe techniques used in interferometric detectors. We introduce the likely sources of gravitational waves and the foundations of data analysis. We briefly summarize key results to date and conclude with perspectives on future scientific payoffs.

show abstract

“…Then the electron is in an inertial frame and therefore does not radiate. This depends, however, on considering the electron as a point, so that there are no tidal forces, rather than an extended classical electromagnetic field in L. (12) Although we have an energy eigenstate in the first two equations of (3.1.D) and may operate with a suitable energy operator to obtain the energy eigenvalue for the Bohr interaction, We may apply de Broglie's relation (8) in M to the Bohr electron described…”

Section: Bohr's First Equationmentioning

confidence: 99%

QED Derived from the Two-Body Interaction

Bell

Cullerne

Diaz

2004

Foundations of Physics

View full text Add to dashboard Cite

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour. (2) We have also shown in part (1) (3) of this paper, that QED with the same transformational behaviour also holds in a second space which we called M-space. Here we use Mspace to show that QED can be reduced to two simple rules for a twobody interaction.

show abstract

General Relativity: A First Course for Physicists

Abstract: General relativity, black holes, and cosmology: A course for nonscientists Am.

Cited by 6 publications

References 0 publications

A Global Minimization Algorithm Based on a Geodesic of a Lagrangian Formulation of Newtonian Dynamics

A Global Minimization Algorithm Based on a Geodesic of a Lagrangian Formulation of Newtonian Dynamics

LIGO and Virgo Gravitational-wave Detectors and Their Science Reach

QED Derived from the Two-Body Interaction

Contact Info

Product

Resources

About