scholarly journals Высокодисперсионные электростатические зеркала вращательной симметрии с времяпролетной фокусировкой по энергии третьего порядка

2020 ◽  
Vol 90 (7) ◽  
pp. 1195
Author(s):  
С.Б. Бимурзаев ◽  
Н.У. Алдияров ◽  
З.С. Саутбекова
Keyword(s):  
Rotational Symmetry ◽  
Time Of Flight ◽  
Fundamental Solutions ◽  
Space Time ◽  
Particle Energy ◽  
Third Order ◽  
Coaxial Cylinders ◽  
Gaussian Plane ◽  
Chromatic Aberrations ◽  
Axis Of Symmetry

Expressions describing the time of flight of charged particles taking into account time-of-flight chromatic aberrations in electrostatic mirrors of rotational symmetry are presented. The conditions of time-of-flight focusing by particle energy up to the third order inclusively in the three-electrode mirrors, the electrodes of which are coaxial cylinders of equal diameter, were determined by numerical calculations. Various modes of operation of such mirrors are considered: 1) space-time-of-flight focusing in the Gaussian plane of the mirror; 2) space-time-of-flight focusing in the focal plane of the mirror; 3) time-of-flight focusing in telescopic mode; 4) time-of-flight focusing in collimator mode. The results of calculations are presented for two fundamental solutions of the equation of paraxial trajectories. One of these solutions describes trajectories whose direct and reverse branches coincide, and the second solution describes trajectories whose direct and reverse branches are symmetrical with respect to the axis of symmetry of the field. It is shown that the time-of-flight dispersion of the mirror by mass, determined on the basis of the second solution, is several times higher than that obtained on the basis of the first solution for all modes of its operation.

High Dispersive Electrostatic Mirrors of Rotational Symmetry with the Third Order Time-of-Flight Focusing by Energy

2020 ◽  
Vol 65 (7) ◽  
pp. 1150-1155
Author(s):  
S. B. Bimurzaev ◽  
N. U. Aldiyarov ◽  
Z. S. Sautbekova
Keyword(s):  
Rotational Symmetry ◽  
Time Of Flight ◽  
Third Order ◽  
The Third

NUMERICAL SIMULATIONS FOR SPACE–TIME FRACTIONAL DIFFUSION EQUATIONS

2013 ◽  
Vol 10 (02) ◽  
pp. 1341001 ◽  
Author(s):  
LEEVAN LING ◽  
MASAHIRO YAMAMOTO
Keyword(s):  
Diffusion Equation ◽  
Fractional Derivative ◽  
Time Derivative ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Long Time ◽  
Liouville Fractional Derivative ◽  
Time Fractional Diffusion Equation

We consider the solutions of a space–time fractional diffusion equation on the interval [-1, 1]. The equation is obtained from the standard diffusion equation by replacing the second-order space derivative by a Riemann–Liouville fractional derivative of order between one and two, and the first-order time derivative by a Caputo fractional derivative of order between zero and one. As the fundamental solution of this fractional equation is unknown (if exists), an eigenfunction approach is applied to obtain approximate fundamental solutions which are then used to solve the space–time fractional diffusion equation with initial and boundary values. Numerical results are presented to demonstrate the effectiveness of the proposed method in long time simulations.

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

scholarly journals Enabling unification of the general theory of relativity and quantum electro-dynamics by visualizing a particle energy configuration

2016 ◽  
Vol 2 (11) ◽  
pp. 288
Author(s):  
William S. Oakley
Keyword(s):  
General Theory ◽  
Radial Strain ◽  
Space Time ◽  
Particle Energy ◽  
Two Dimensions ◽  
Emergent Properties ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Curved Space ◽  
Strong Force

<p class="abstract">The long standing major issue in physics has been the inability to unify the two main theories of quantum electro-dynamics (QED) and the general theory of relativity (GTR), both of which are well proven and cannot accommodate significant change. The problem is resolved by combining the precepts of GTR and QED in a conceptual model describing the electron as electromagnetic (EM) energy localized in relativistic quantum loops near an event horizon. EM energy is localized by propagating in highly curved space-time of closed geometry, the local metric index increases, and the energy is thus relativistic to the observer at velocity v &lt; c, with the curved space-time thereby evidencing gravity. The presence of gravity leads to the observer notion of mass. Particle energy is in dynamic equilibrium with relativistic loop circumferential metric strain at the strong force scale opposed by radial metric strain. The resulting particle is a quantum black hole with the circumferential strong force in the curved metric orthogonal in two dimensions to all particle radials. The presence of energy E is thus evident in observer space reduced by c<sup>2</sup> to E/c<sup>2</sup> = mass. The circumferential strain diminishes as it extends into the surrounding metric as the particle’s gravitational field. The radial strain projects outward into observer space and is therein evident as electric field. Gravity, unit charge, and their associated fields are emergent properties and Strong and electric forces are equal within the particle, quantizing gravity and satisfying the Planck scale criteria of force equality. A derived scaling factor produces the gravity effect experienced by the observer and the GRT-QED unification issue is thereby largely resolved.</p>

scholarly journals Adequate Soliton Solutions to the Space-Time Fractional Telegraph Equation and Modified Third-Order KdV Equation through A Reliable Technique

2021 ◽  
Author(s):  
Ummay Sadia ◽  
Mohammad Asif Arefin ◽  
Mustafa Inc ◽  
M. Hafiz Uddin
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Traveling Wave ◽  
Telegraph Equation ◽  
Space Time ◽  
Nonlinear Evolution Equations ◽  
Communication Line ◽  
Third Order ◽  
Wave Solutions ◽  
Fractional Telegraph Equation

Abstract The space-time fractional telegraph equation and the space-time fractional modified third-order Kdv equations are significant molding equations in theoretic physics, mathematical physics, plasma physics also other fields of nonlinear sciences. The space time-fractional telegraph equation, which appears in the investigation of an electrical communication line and includes voltage in addition to current which is dependent on distance and time, is also applied to communication lines of wholly frequencies, together with direct current, as well as high-frequency conductors, audio frequency (such as telephone lines), and low frequency (for example cable television) used in the extension of pressure waves into the lessons of pulsatory blood movement among arteries also the one-dimensional haphazard movement of bugs towards an obstacle. The presence of chain rule and the derivative of composite functions allows the nonlinear fractional differential equations (NLFDEs) to translate into the ordinary differential equation employing wave alteration. To explore such categories of resolutions, the extended tanh-method is accomplished via Conformable fractional derivatives. A power sequence in tanh was originally used as an ansatz to provide analytical solutions of the traveling wave type of certain nonlinear evolution equations. To convert this problem to a standard differential equation, a partial complex transformation that has been summarized succinctly is utilized correctly thus, with all of the free parameters, numerous exact logical arrangements are required. The results are found as hyperbolic and rational functions involving parameters, when specific values are supplied to the parameters solitary wave solutions are formed from traveling wave solutions. The outcomes achieved in this study are king type, single soliton, double soliton, multiple solitons, bell shape, and other sorts of forms and we demonstrated that these solutions were validated through the Maple software. The proposed approach for solving nonlinear fractional partial differential equations has been developed to be operative, unpretentious, quick, and reliable to usage.

Sign in / Sign up

Export Citation Format

Share Document