Attractor Solution Research Articles

Stopping rule of multi-start local search for structural optimization

Stopping rule for multi-start local search is investigated for application to structural optimization problems with moderately large number of local optima. The size of attractor of an unknown local optimal solution is estimated using the information of already obtained solutions. A stopping rule is defined using the likelihood of obtaining the specific set of local optimal solutions. This way, characteristics of the specific optimization problem is successfully incorporated. The proposed rule is first verified using the mathematical problems in comparison with the existing rule utilizing the estimated ratio of the total size of attractors to the size of feasible domain. The rule is next applied to an optimization problem of a plane frame under constraints on inter-story drift angle and stress against static loads. Characteristics of the distribution of attractors of optimal solutions are also investigated.

Inflation with a smooth constant-roll to constant-roll era transition

In this paper we study canonical scalar field models with a varying second slow-roll parameter, that allow transitions between constant-roll eras. In the models with two constant-roll eras it is possible to avoid fine-tunings in the initial conditions of the scalar field. We mainly focus on the stability of the resulting solutions and we also investigate if these solutions are attractors of the cosmological system. We shall calculate the resulting scalar potential and by using a numerical approach, we examine the stability and attractor properties of the solutions. As we show, the first constant-roll era is dynamically unstable towards linear perturbations and the cosmological system is driven by the attractor solution to the final constant-roll era. As we demonstrate, it is possible to have a nearly-scale invariant power spectrum of primordial curvature perturbations in some cases, however this is strongly model dependent and depends on the rate of the final constant-roll era. Finally, we present in brief the essential features of a model that allows oscillations between constant-roll eras.

A Riemann-Hilbert approach to rotating attractors

We construct rotating extremal black hole and attractor solutions in gravity theories by solving a Riemann-Hilbert problem associated with the Breitenlohner-Maison linear system. By employing a vectorial Riemann-Hilbert factorization method we explicitly factorize the corresponding monodromy matrices, which have second order poles in the spectral parameter. In the underrotating case we identify elements of the Geroch group which implement Harrison-type transformations which map the attractor geometries to interpolating rotating black hole solutions. The factorization method we use yields an explicit solution to the linear system, from which we do not only obtain the spacetime solution, but also an explicit expression for the master potential encoding the potentials of the infinitely many conserved currents which make this sector of gravity integrable.

Growth and dissolution of spherical density enhancements in SCDEW cosmologies

Strongly Coupled Dark Energy plus Warm dark matter (SCDEW) cosmologies are based on the finding of a conformally invariant (CI) attractor solution during the early radiative expansion, requiring then the stationary presence of ∼ 1 % of coupled-DM and DE, since inflationary reheating. In these models, coupled-DM fluctuations, even in the early radiative expansion, grow up to non-linearity, as shown in a previous associated paper. Such early non-linear stages are modelized here through the evolution of a top-hat density enhancement. As expected, its radius R increases up to a maximum and then starts to decrease. Virial balance is reached when the coupled-DM density contrast is just 25–26 and DM density enhancement is \U0001d4aa(10 %) of total density. Moreover, we find that this is not an equilibrium configuration as, afterwards, coupling causes DM particle velocities to increase, so that the fluctuation gradually dissolves. We estimate the duration of the whole process, from horizon crossing to dissolution, and find zhorizon/zerasing ∼ 3 × 104. Therefore, only fluctuations entering the horizon at z ≲ 109–1010 are able to accrete WDM with mass ∼ 100 eV—as soon as it becomes non-relativistic—so avoiding full disruption. Accordingly, SCDEW cosmologies, whose WDM has mass ∼ 100 eV, can preserve primeval fluctuations down to stellar mass scale.

Inflationary α -attractor cosmology: A global dynamical systems perspective

We study flat FLRW $\alpha$-attractor $\mathrm{E}$- and $\mathrm{T}$-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both illustrative figures and a complete description of the entire solution spaces of these models, including asymptotics. In particular, it is shown that observational viability, which requires a sufficient number of $e$-folds, is associated with a solution given by a one-dimensional center manifold of a past asymptotic de Sitter state, where the center manifold structure also explains why nearby solutions are attracted to this `inflationary attractor solution.' A center manifold expansion yields a description of the inflationary regime with arbitrary analytic accuracy, where the slow-roll approximation asymptotically describes the tangency condition of the center manifold at the asymptotic de Sitter state.

Plasma Wave Seed for Raman Amplifiers.

It is proposed to replace the traditional counterpropagating laser seed in backward Raman amplifiers with a plasma wave seed. In the linear regime, namely, for a constant pump amplitude, a plasma wave seed may be found by construction that strictly produces the same output pulse as does a counterpropagating laser seed. In the nonlinear regime, or pump-depletion regime, the plasma-wave-initiated output pulse can be shown numerically to approach the same self-similar attractor solution for the corresponding laser seed. In addition, chirping the plasma wave wavelength can produce the same beneficial effects as chirping the seed wave frequency. This methodology is attractive because it avoids issues in preparing and synchronizing a frequency-shifted laser seed.

Scalar-tensor linear inflation

We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f(φ)R/2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.

Explosive attractor solutions to a universal cubic delay equation

New explosive attractor solutions have been found in a universal cubic delay equation that has been studied in both the plasma and the fluid mechanics literature. Through computational simulations and analytic approximations, it is found that the oscillatory component of the explosive mode amplitude solutions are described through multi-frequency Fourier expansions with respect to a pseudo-time variable. The spectral dependence of these solutions as a function of a system parameter, ϕ, is studied. The mode amplitude that is described in the explosive regime has two main features: a well-known envelope (t0−t)−5/2, with t0 the blow-up time of the amplitude, and a spectrum of discrete oscillations with ever-increasing frequencies, which may give experimental information about the properties of a system's equilibrium.

Cosmology ofq-deformed dark matter and dark energy

Abstract In this study, we propose a novel dark cosmology consisting an interacting q -deformed spinor field dark matter and scalar field dark energy. We investigate the proposed deformed dark cosmology in metric-affine Einstein– Cartan–Sciama–Kibble theory. Firstly, we construct the action integral of the model, in order to obtain the energy–momentum tensor of the deformed dark matter and dark energy, from which the energy density and pressure of the deformed dark matter and dark energy can be obtained, respectively. After obtaining the deformed energy densities and pressures, we set up the Friedmann equations, continuity equations and equation of motions for this dark model. Then, we obtain the attractor solutions and stability analysis of the model for the accelerated expansion phase of the universe. We also investigate the effect of deformation parameter on the stable accelerated expansion behavior. Consequently, by mapping the interaction term and the field potentials we present the relationship between them and obtain the constraint on the interaction term in order to obtain a stable attractor solution.

Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless SU(2) gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.

Global attractors for nonclassical diffusion equations with hereditary memory and a new class of nonlinearities

We study the existence and long-time behavior in terms of existence of global attractors of weak solutions to a class of nonclassical diffusion equations with hereditary memory and a new class of nonlinearities, which contains all nonlinearities of polyno

Velocity Integration in a Multilayer Neural Field Model of Spatial Working Memory

We analyze a multilayer neural field model of spatial working memory, focusing on the impact of interlaminar connectivity, spatial heterogeneity, and velocity inputs. Models of spatial working memory typically employ networks that generate persistent activity via a combination of local excitation and lateral inhibition. Our model comprises a multilayer set of equations that describes connectivity between neurons in the same and different layers using an integral term. The kernel of this integral term then captures the impact of different interlaminar connection strengths, spatial heterogeneity, and velocity input. We begin our analysis by focusing on how interlaminar connectivity shapes the form and stability of (persistent) bump attractor solutions to the model. Subsequently, we derive a low-dimensional approximation that describes how spatial heterogeneity, velocity input, and noise combine to determine the position of bump solutions. The main impact of spatial heterogeneity is to break the translation ...

Stealth magnetic field in de Sitter spacetime

In the context of a U(1) gauge theory non-minimally coupled to scalar-tensor gravity, we find a cosmological attractor solution that represents a de Sitter universe with a homogeneous magnetic field. The solution fully takes into account backreaction of the magnetic field to the geometry and the scalar field. Such a solution is made possible by scaling-type global symmetry and fine-tuning of two parameters of the theory. If the fine-tuning is relaxed then the solution is deformed to an axisymmetric Bianchi type-I universe with constant curvature invariants, a homogeneous magnetic field and a homogeneous electric field. Implications to inflationary magnetogenesis are briefly discussed.

Cosmology in doubly coupled massive gravity: Constraints from SNIa, BAO and CMB

Massive gravity in the presence of doubly coupled matter field via en effective composite metric yields an accelerated expansion of the universe. It has been recently shown that the model admits stable de Sitter attractor solutions and could be used as a dark energy model. In this work, we perform a first analysis of the constraints imposed by the SNIa, BAO and CMB data on the massive gravity model with the effective composite metric and show that all the background observations are mutually compatible at the one sigma level with the model.

Extending the ΛCDM model through shear-free anisotropies

If the spacetime metric has anisotropic spatial curvature, one can still expand the universe as if it were isotropic, provided that the energy–momentum tensor satisfies a certain constraint. This leads to the so-called shear-free (SF) metrics, which have the interesting property of violating the cosmological principle while still preserving the isotropy of the cosmic microwave background (CMB) radiation. In this work, we show that SF cosmologies correspond to an attractor solution in the space of models with anisotropic spatial curvature. Through a rigorous definition of linear perturbation theory in these spacetimes, we show that SF models represent a viable alternative to explain the large-scale evolution of the universe, leading, in particular to a kinematically equivalent Sachs–Wolfe (SW) effect. Alternatively, we discuss some specific signatures that SF models would imprint on the temperature spectrum of CMB.

Buckling and nonlinear dynamics of elastically coupled double-beam systems

This paper deals with damped transverse vibrations of elastically coupled double-beam system under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends. The related stationary problem is proved to admit both unimodal (only one eigenfunction is involved) and bimodal (two eigenfunctions are involved) buckled solutions, and their number depends on structural parameters and applied axial loads. The occurrence of a so complex structure of the steady states motivates a global analysis of the longtime dynamics. In this regard, we are able to prove the existence of a global regular attractor of solutions. When a finite set of stationary solutions occurs, it consists of the unstable manifolds connecting them.

Dynamical evolution of primordial dark matter haloes through mergers

Primordial dark matter (DM) haloes are the smallest gravitationally bound DM structures from which the first stars, black holes, and galaxies form and grow in the early universe. However, their structures are sensitive to the free streaming scale of DM, which in turn depends on the nature of DM particles. In this work, we test the hypothesis that the slope of the central cusps in primordial DM haloes near the free streaming scale depends on the nature of merging process. By combining and analysing data from a cosmological simulation with the cutoff in the small-scale matter power spectrum as well as a suite of controlled, high-resolution simulations of binary mergers, we find that (1) the primordial DM haloes form preferentially through major mergers in radial orbits; (2) their central DM density profile is more susceptible to a merging process compared to that of galaxy and cluster-size DM haloes; (3) consecutive major mergers drive the central density slope to approach the {\it universal} form characterized by the NFW profile, which is shown to be robust to the impacts of mergers and serves an attractor solution for the density structure of DM haloes. Our work highlights the importance of dynamical processes on the structure formation during the Dark Ages.

Self-similar equilibration of strongly interacting systems from holography

We study the equilibration of a class of far-from-equilibrium strongly interacting systems using gauge-gravity duality. The systems we analyze are $2+1$ dimensional and have a four-dimensional gravitational dual. A prototype example of a system we analyze is the equilibration of a two-dimensional fluid which is translational invariant in one direction and is attached to two different heat baths with different temperatures at infinity in the other direction. We realize such setup in gauge-gravity duality by joining two semi-infinite asymptotically anti-de Sitter (AdS) black branes of different temperatures, which subsequently evolve towards equilibrium by emitting gravitational radiation towards the boundary of AdS. At sufficiently late times the solution converges to a similarity solution, which is only sensitive to the left and right equilibrium states and not to the details of the initial conditions. This attractor solution not only incorporates the growing region of equilibrated plasma but also the outwardly propagating transition regions, and can be constructed by solving a single ordinary differential equation.

Dynamical analysis of modified gravity with nonminimal gravitational coupling to matter

We perform a phase space analysis of a generalized modified gravity theory with nonminimally coupling between geometry and matter. We apply the dynamical system approach to this generalized model and find that in the cosmological context, different choices of Lagrangian density will apparently result in different phases of the Universe. By carefully choosing the variables, we prove that there is an attractor solution to describe the late time accelerating universe when the modified gravity is chosen in a simple power-law form of the curvature scalar. We further examine the temperature evolution based on the thermodynamic understanding of the model. Confronting the model with supernova type Ia data sets, we find that the nonminimally coupled theory of gravity is a viable model to describe the late time Universe acceleration.

An interacting dark energy model with nonminimal derivative coupling

Abstract We study cosmological dynamics of an extended gravitational theory that gravity is coupled non-minimally with derivatives of a dark energy component and there is also a phenomenological interaction between the dark energy and dark matter. Depending on the direction of energy flow between the dark sectors, the phenomenological interaction gets two different signs. We show that this feature affects the existence of attractor solution, the rate of growth of perturbations and stability of the solutions. By considering an exponential potential as a self-interaction potential of the scalar field, we obtain accelerated scaling solutions that are attractors and have the potential to alleviate the coincidence problem. While in the absence of the nonminimal derivative coupling there is no attractor solution for phantom field when energy transfers from dark matter to dark energy, we show an attractor solution exists if one considers an explicit nonminimal derivative coupling for phantom field in this case of energy transfer. We treat the cosmological perturbations in this setup with details to show that with phenomenological interaction, perturbations can grow faster than the minimal case.