Nonlinear Self-interaction Term Research Articles

Vainshtein screening in Horndeski theories nonminimally and kinetically coupled to ordinary matter

We study the Vainshtein screening mechanism in Horndeski theories in the presence of a scalar field $\phi$ nonminimally and kinetically coupled to ordinary matter field. A general interacting Lagrangian describing this coupling is characterized by energy transfer $f_1$ and momentum exchange $f_2$. For a spherically symmetric configurations on top of the cosmological background, we investigate the static perturbations in linear and nonlinear regimes with respect to the scalar field perturbation. In the former regime, the parametrized post-Newtonian parameter generally deviates from unity as long as the matter coupling or $G_{4,\phi}$ exists. On the other hand, in the latter regime, we show that the nonlinear self-interaction term of scalar field successfully activates the Vainshtein mechanism even in the presence of the couplings $f_1$ and $f_2$. The gravitational potentials recover the Newtonian behavior deep inside the Vainshtein radius. The bounds on coupling terms not to substantially change the Vainshtein radius are also given.

SELCIE: a tool for investigating the chameleon field of arbitrary sources

The chameleon model is a modified gravity theory that introduces an additional scalar field that couples to matter through a conformal coupling. This `chameleon field' possesses a screening mechanism through a nonlinear self-interaction term which allows the field to affect cosmological observables in diffuse environments whilst still being consistent with current local experimental constraints. Due to the self-interaction term the equations of motion of the field are nonlinear and therefore difficult to solve analytically. The analytic solutions that do exist in the literature are either approximate solutions and or only apply to highly symmetric systems. In this work we introduce the software package SELCIE (https://github.com/C-Briddon/SELCIE.git). This package equips the user with tools to construct an arbitrary system of mass distributions and then to calculate the corresponding solution to the chameleon field equation. It accomplishes this by using the finite element method and either the Picard or Newton nonlinear solving methods. We compared the results produced by SELCIE with analytic results from the literature including discrete and continuous density distributions. We found strong (sub-percentage) agreement between the solutions calculated by SELCIE and the analytic solutions.

Modified Asano-Ohya-Khrennikov quantum-like model for decision-making process in a two-player game with nonlinear self- and cross-interaction terms of brain's amygdala and prefrontal-cortex.

In this report, we propose a modification on the Asano-Ohya-Khrennikov quantum-like decision-making process model of a two-player game by adding additional nonlinear terms to the related comparison step dynamical equation. The additions are in the form of a self-interaction and cross-interaction of the brain’s amygdala and prefrontal cortex. We show that the cross-interaction significantly determines the final decision of a player, whether it becomes a rational or an irrational choice. In contrast, the nonlinear self-interaction term provides a feedback mechanism that speeds up the corresponding decision-making process. We also suggest the form of expectation values of the overall reaction rate coefficients of those nonlinear terms by making an analogy with the original model formulation.

Attached eddy model revisited using a minimal quasi-linear approximation

Townsend’s model of attached eddies for boundary layers is revisited within a quasi-linear approximation. The velocity field is decomposed into a mean profile and fluctuations. While the mean is obtained from the nonlinear equations, the fluctuations are modelled by replacing the nonlinear self-interaction terms with an eddy-viscosity-based turbulent diffusion and stochastic forcing. Under this particular approximation, the resulting fluctuation equations remain linear, enabling solutions to be superposed, the same theoretical idea used in the original attached eddy model. By leveraging this feature, the stochastic forcing is determined self-consistently by solving an optimisation problem which minimises the difference between the Reynolds shear stresses from the mean and fluctuation equations, subject to a constraint that the averaged Reynolds shear-stress spectrum is sufficiently smooth in the spatial wavenumber space. The proposed quasi-linear approximation is subsequently applied to channel flow for Reynolds number ranging from 500 to 20 000. The best result is obtained when the Reynolds stress is calculated by retaining only the two leading proper orthogonal decomposition modes, which further filters out the modelling artefact caused by the unphysical stochastic forcing. In this case, the resulting turbulence intensity profile and energy spectra exhibit the same qualitative behaviour as direct numerical simulation (DNS) data throughout the entire wall-normal domain, while reproducing the early theoretical predictions of the original attached eddy model within a controlled approximation to the Navier–Stokes equations. Finally, the proposed quasi-linear approximation reveals that the peak streamwise and spanwise turbulence intensities may deviate slightly from the logarithmic scaling with the Reynolds number for , and the supporting evidence is presented using the existing DNS data.

Nonlinear interactions of the radion field

We study the Randall-Sundrum model with two branes. The Standard Model fields are localized on the brane with a negative tension, the gravitational field and scalar Goldberg-Wise field propagate in the multidimensional bulk. For this model we construct the Lagrangian for the scalar fluctuations of the gravitational and scalar fields above a background solution. We obtain an effective four-dimensional Lagrangian, which contains nonlinear self-interaction terms of the radion field up to the fourth order and nonlinear interactions of the radion and the Standard Model fields.

Understanding Anomalous Synoptic Eddy Vorticity Forcing in Pacific–North American Teleconnection Pattern Events

Abstract Utilizing a decomposition of anomalous eddy vorticity forcing (EVF) proposed by Song in 2016 and a modified Geophysical Fluid Dynamics Laboratory (GFDL) dynamical core atmospheric model, this study provides a different understanding of physical mechanisms that are responsible for the formation of the anomalous synoptic EVF (SEVF) associated with Pacific–North American teleconnection pattern (PNA) events. A series of short-term control experiments (CEs) and initial-value modified experiments (IVMEs) is conducted. In each case of CEs, there are no obvious PNA-like circulation anomalies. IVMEs are exactly the same as CEs except that appropriate small perturbations are introduced into the initial-value fields of CEs. The modified initial-value fields led to a gradual development of the PNA-like flow anomalies in IVMEs. Based on these numerical results, deformations of the synoptic eddy due to the emergence of the PNA pattern can be easily acquired by subtracting the synoptic eddy in CEs from the synoptic eddy in IVMEs . The anomalous SEVF associated with the PNA events in the model can be decomposed into ensembles of two linear and interaction terms (EVF1 and EVF2) and a nonlinear self-interaction term (EVF3). It is demonstrated that the physical essence of the anomalous SEVF associated with the PNA events is a competition result between EVF1 plus EVF2 and EVF3. Results also indicate that the different signs of SEVF associated with the positive and negative PNA events are not necessarily related to the different tilts of the synoptic eddy.

A new length scale, and modified Einstein–Cartan–Dirac equations for a point mass

We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale [Formula: see text], dubbed the Compton–Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here, we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume the wave function collapse and localization for large masses. The small mass limit yields the Dirac equation. We explain why the Kerr–Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value. The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck’s constant [Formula: see text] (but not [Formula: see text]) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton’s gravitational constant [Formula: see text] (but not [Formula: see text]), and is important in the macroscopic limit. We construct the Einstein–Cartan–Dirac equations which include the length [Formula: see text]. We find a potentially significant change in the coupling constant of the torsion driven cubic nonlinear self-interaction term in the Dirac–Hehl–Datta equation. We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck’s constant and the parameters of dynamical collapse models.

The evolution towards the rod-like axisymmetric structure for turbulent stress tensor

Modelling the turbulent stress tensor is a main task for both large eddy simulations and methods based on Reynolds averaged Navier-Stokes equations. The turbulent stress is known as the subgrid-scale stress in the former and the Reynolds stress in the latter. In this paper, we examine the observation that the stress tensor tends to evolve towards a rod-like axisymmetric configuration. This observation has been well documented for the subgrid-scale stress. However, for the Reynolds stress, the available data are still too limited to draw a definite conclusion. In the first part of the paper, we show that the tendency is also universal for the Reynolds stress by direct numerical simulations of decaying anisotropic turbulence. To show the universality, it is crucial to examine the decaying process from initial turbulent fields with a wide range of levels of anisotropy. Such initial fields are generated by a novel synthetic turbulence model based on the so-called constrained multi-turnover Lagrangian map. In the second part, we use the direct numerical simulation data to study the dynamical mechanisms of the evolution towards the rod-like structures. Among others, the analyses show that the nonlinear self-interaction term is the driving force of the process, and that the pressure tends to enhance the disk-like axisymmetric structure but overall tends to reduce the anisotropy of the stress tensor. The results shed light on the subtle difference between the pressure and the nonlinear self-interaction terms.

Cosmological Perturbations in General Modified Gravity Theories

We derive the equations of linear cosmological perturbations for the general Lagrangian density f (R, φ, X)/ 2+ Lc ,w hereR is a Ricci scalar, φ is a scalar field, and X = �∂ µ φ∂µφ/2 is a field kinetic energy. We take into account a nonlinear self-interaction term Lc = ξ(φ)˜φ(∂ µ φ∂µφ), which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds.

Density perturbations in general modified gravitational theories

We derive the equations of linear cosmological perturbations for the general Lagrangian density $f (R,\phi, X)/2+L_c$, where $R$ is a Ricci scalar, $\phi$ is a scalar field, and $X=-(\nabla \phi)^2/2$ is a field kinetic energy. We take into account a nonlinear self-interaction term $L_c$ recently studied in the context of "Galileon" cosmology, which keeps the field equations at second order. Taking into account a scalar-field mass explicitly, the equations of matter density perturbations and gravitational potentials are obtained under a quasi-static approximation on sub-horizon scales. We also derive conditions for the avoidance of ghosts and Laplacian instabilities associated with propagation speeds. Our analysis includes most of modified gravity models of dark energy proposed in literature and thus it is convenient to test the viability of such models from both theoretical and observational points of view.

Wave-Corpuscle Mechanics for Electric Charges

It is well known that the concept of a point charge interacting with the electromagnetic (EM) field has a problem. To address that problem we introduce the concept of wave-corpuscle to describe spinless elementary charges interacting with the classical EM field. Every charge interacts only with the EM field and is described by a complex valued wave function over the 4-dimensional space time continuum. A system of many charges interacting with the EM field is defined by a local, gauge and Lorentz invariant Lagrangian with a key ingredient—a nonlinear self-interaction term providing for a cohesive force assigned to every charge. An ideal wave-corpuscle is an exact solution to the Euler-Lagrange equations describing both free and accelerated motions. It carries explicitly features of a point charge and the de Broglie wave. Our analysis shows that a system of well separated charges moving with nonrelativistic velocities are represented accurately as wave-corpuscles governed by the Newton equations of motion for point charges interacting with the Lorentz forces. In this regime the nonlinearities are “stealthy” and don’t show explicitly anywhere, but they provide for the binding forces that keep localized every individual charge. The theory can also be applied to closely interacting charges as in hydrogen atom where it produces discrete energy spectrum.

Generational mass generation and symmetry breaking.

A BCS theory of quark and lepton mass generation leads to a nonlinear self-interaction term in the Lagrangian whose natural representation is the democratic basis. We show, within the BCS framework, how the original ${\mathrm{U}(3)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{U}(3)}_{R}$ symmetry of the massless ur quarks and ur leptons is systematically broken so as to lead to the observed quark and lepton spectra, consistent with their mass hierarchies, and the additional hierarchy of weak mixing angles manifested in the Kobayashi-Maskawa matrix. Experiment cannot currently distinguish between such symmetry breaking as proposed by Fritzsch and Plankl, by us, or by others.