scholarly journals Opening the reheating box in multifield inflation

2021 ◽  
Vol 2021 (12) ◽  
pp. 022
Author(s):  
Jérôme Martin ◽  
Lucas Pinol
Keyword(s):  
Fine Structure ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Scalar Fields ◽  
Numerical Calculations ◽  
Numerical Code ◽  
Good Precision ◽  
Perfect Fluids ◽  
Decay Products ◽  
Reheating Process

Abstract The robustness of multi-field inflation to the physics of reheating is investigated. In order to carry out this study, reheating is described in detail by means of a formalism which tracks the evolution of scalar fields and perfect fluids in interaction (the inflatons and their decay products). This framework is then used to establish the general equations of motion of the background and perturbative quantities controlling the evolution of the system during reheating. Next, these equations are solved exactly by means of a new numerical code. Moreover, new analytical techniques, allowing us to interpret and approximate these solutions, are developed. As an illustration of a physical prediction that could be affected by the micro-physics of reheating, the amplitude of non-adiabatic perturbations in double inflation is considered. It is found that ignoring the fine-structure of reheating, as usually done in the standard approach, can lead to differences as big as ∼ 50%, while our semi-analytic estimates can reduce this error to ∼ 10%. We conclude that, in multi-field inflation, tracking the perturbations through the details of the reheating process is important and, to achieve good precision, requires the use of numerical calculations.

The stress-energy tensor

2019 ◽  
pp. 59-65
Author(s):  
Steven Carlip
Keyword(s):  
Equations Of Motion ◽  
Scalar Fields ◽  
Gravitational Energy ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Field Equations ◽  
Perfect Fluids ◽  
Stress Energy ◽  
Relationship Of ◽  
The Relationship

The “source” of gravity in the Einstein field equations is the stress-energy tensor. After a discussion of why gravitational mass should be part of a rank two tensor, this chapter derives the stress-energy tensor for a variety of types of matter: point particles, perfect fluids, scalar fields, and electromagnetism. The chapter discusses the relationship of differential and integral conservation laws, and introduces the problem of gravitational energy. It concludes with a discussion of one of the most remarkable results of general relativity, the fact that equations of motion for matter do not need to be introduced separately, but follow from the field equations.

scholarly journals Long-Term Predictions for Highly Eccentric Orbits

1993 ◽  
Vol 132 ◽  
pp. 353-363
Author(s):  
José M. Ferrándiz ◽  
M. Eugenia Sansaturio ◽  
Jesús Vigo
Keyword(s):  
Equations Of Motion ◽  
Analytical Techniques ◽  
Artificial Satellites ◽  
Numerical Techniques ◽  
Dynamical Models ◽  
Eccentric Orbits

AbstractPredictability in orbital behaviour of artificial satellites depends on several factors: the accuracy required, the particular dynamical models formulated, the sets of variables chosen to describe them, the numerical or analytical techniques used and, specially, the specific trajectories to be established. In this paper we address the problem of predictability for highly eccentric satellites with (J2 + J22)-perturbation, by using numerical techniques to integrate the equations of motion when expressed in different sets of regular variables.

scholarly journals A General Method for Transforming Nonphysical Configurations in BPS States

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
J. R. L. Santos ◽  
A. de Souza Dutra ◽  
O. C. Winter ◽  
R. A. C. Correa
Keyword(s):  
Scalar Field ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Cosmological Parameters ◽  
Topological Defects ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Complex Scalar Field ◽  
Bps States ◽  
General Method

In this work, we apply the so-called BPS method in order to obtain topological defects for a complex scalar field Lagrangian introduced by Trullinger and Subbaswamy. The BPS approach led us to compute new analytical solutions for this model. In our investigation, we found analytical configurations which satisfy the BPS first-order differential equations but do not obey the equations of motion of the model. Such defects were named nonphysical ones. In order to recover the physical meaning of these defects, we proposed a procedure which can transform them into BPS states of new scalar field models. The new models here founded were applied in the context of hybrid cosmological scenarios, where we derived cosmological parameters compatible with the observed Universe. Such a methodology opens a new window to connect different two scalar fields systems and can be implemented in several distinct applications such as Bloch Branes, Lorentz and Symmetry Breaking Scenarios, Q-Balls, Oscillons, Cosmological Contexts, and Condensed Matter Systems.

Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture

2000 ◽  
Vol 68 (1) ◽  
pp. 42-48 ◽  
Author(s):  
A. F. Vakakis ◽  
O. Gendelman
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Resonance Capture ◽  
Damped System ◽  
Energy Pumping ◽  
Analytical Approximations ◽  
Nonlinear Mechanical ◽  
Nonlinear Transient ◽  
Mechanical Oscillators

We study energy pumping in an impulsively excited, two-degrees-of-freedom damped system with essential (nonlinearizable) nonlinearities by means of two analytical techniques. First, we transform the equations of motion using the action-angle variables of the underlying Hamiltonian system and bring them into the form where two-frequency averaging can be applied. We then show that energy pumping is due to resonance capture in the 1:1 resonance manifold of the system, and perform a perturbation analysis in an Oε neighborhood of this manifold in order to study the attracting region responsible for the resonance capture. The second method is based on the assumption of 1:1 internal resonance in the fast dynamics of the system, and utilizes complexification and averaging to develop analytical approximations to the nonlinear transient responses of the system in the energy pumping regime. The results compare favorably to numerical simulations. The practical implications of the energy pumping phenomenon are discussed.

TOPOLOGICAL DEFECTS AND THE TRIAL ORBIT METHOD

2002 ◽  
Vol 17 (29) ◽  
pp. 1945-1953 ◽  
Author(s):  
D. BAZEIA ◽  
W. FREIRE ◽  
L. LOSANO ◽  
R. F. RIBEIRO
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Topological Defects ◽  
Scalar Fields ◽  
Explicit Solutions ◽  
Orbit Method ◽  
First Order ◽  
Real Scalar ◽  
Second Order Equations ◽  
First Order Differential Equations

We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects and search for explicit defect solutions using the trial orbit method. As we know, under certain circumstances the second-order equations of motion can be solved by solutions of first-order differential equations. In this case we show that the trial orbit method can be used very efficiently to obtain explicit solutions.

Geometric Insight Into the Dynamics of a Rigid Body Using the Spatial Triangle of Screws

2001 ◽  
Author(s):  
Gordon R. Pennock ◽  
Patrick J. Meehan
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Rate Of Change ◽  
Time Rate ◽  
Open Chain ◽  
Spatial Mechanisms ◽  
Kinetics Of ◽  
Insight Into

Abstract Geometric relationships between the velocity screw and momentum screw are presented, and the dual angle between these two screws is shown to provide important insight into the kinetics of a rigid body. Then the centripetal screw is defined, and the significance of this screw in a study of the dynamics of a rigid body is explained. The dual-Euler equation, which is the dual form of the Newton-Euler equations of motion, is shown to be a spatial triangle. The vertices of the triangle are the centripetal screw, the time rate of change of momentum screw, and the force screw. The sides of the triangle are three dual angles between the three vertices. The spatial triangle provides valuable geometrical insight into the dynamics of a rigid body and is believed to be a meaningful alternative to existing analytical techniques. The authors believe that the work presented in this paper will prove useful in a dynamic analysis of closed-loop spatial mechanisms and multi-rigid body open-chain systems.

Stationary States of the Classically Radiating Electron in an Attractive Potential

1977 ◽  
Vol 32 (6) ◽  
pp. 659-660 ◽  
Author(s):  
M. Sorg
Keyword(s):  
Equations Of Motion ◽  
Numerical Calculations ◽  
Attractive Potential ◽  
Stationary States ◽  
Non Local ◽  
Non Local Equations

Abstract It is shown by explicit numerical calculations, that the recently proposed non-local equations of motion, which can be supplied by a modified form of the well-known Caldirola equation, all admit the possibility of stationary radiationless motions in an attractive potential.

Vibrations and instability of double-nanowire-systems as electric current carriers

2015 ◽  
Vol 29 (25) ◽  
pp. 1550144 ◽  
Author(s):  
Keivan Kiani
Keyword(s):  
Electric Current ◽  
Dynamic Instability ◽  
Tensile Force ◽  
Equations Of Motion ◽  
Analytical Techniques ◽  
Building Blocks ◽  
Transverse Displacement ◽  
Vibration Modes ◽  
Dynamic Interactions ◽  
Energy Equations

Current-carrying nanowires are expected to be building blocks of the upcoming micro-nano-electromechanical devices, however, little is known on their dynamic interactions in a bundle. As a pivotal step towards realizing such a crucial mechanism, this work is devoted to vibrations and instability of a double-nanowire-system as an electric current carrier. Using Biot–Savart law, the Lorentz interactional forces between doubly parallel current-carrying nanowires are evaluated. Accounting for the surface elastic energy, equations of motion pertinent to the in-plane and out-of-plane vibrations are established. Using analytical techniques, the explicit expressions of both static and purely dynamic parts of the nanowires’ displacements are obtained. For each component of the transverse displacement field, two major vibration modes are observed: in-phase and out-of-phase modes. The frequencies associated with these vibration modes are analytically calculated. Further, the condition corresponds to the dynamic instability of the system is discovered, and the roles of initial tensile force, electric current, and interwire distance on frequencies and stability of the system are addressed.

Sign in / Sign up

Export Citation Format

Share Document