Search results for "Weak"

An Adaptive Alternating Direction Method of Multipliers

2021

AbstractThe alternating direction method of multipliers (ADMM) is a powerful splitting algorithm for linearly constrained convex optimization problems. In view of its popularity and applicability, a growing attention is drawn toward the ADMM in nonconvex settings. Recent studies of minimization problems for nonconvex functions include various combinations of assumptions on the objective function including, in particular, a Lipschitz gradient assumption. We consider the case where the objective is the sum of a strongly convex function and a weakly convex function. To this end, we present and study an adaptive version of the ADMM which incorporates generalized notions of convexity and penalty…

Variable exponent p(x)-Kirchhoff type problem with convection

2022

Abstract We study a nonlinear p ( x ) -Kirchhoff type problem with Dirichlet boundary condition, in the case of a reaction term depending also on the gradient (convection). Using a topological approach based on the Galerkin method, we discuss the existence of two notions of solutions: strong generalized solution and weak solution. Strengthening the bound on the Kirchhoff type term (positivity condition), we establish existence of weak solution, this time using the theory of operators of monotone type.

Free-surface flows solved by means of SPH schemes with numerical diffusive terms

2010

A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …

Weak convergence theorems for asymptotically nonexpansive mappings and semigroups

2001

Euclid Preparation. XIV. The Complete Calibration of the Color–Redshift Relation (C3R2) Survey: Data Release 3

2021

Stanford, S. A., et al.

Do metric fluctuations affect the Higgs dynamics during inflation?

2017

We show that the dynamics of the Higgs field during inflation is not affected by metric fluctuations if the Higgs is an energetically subdominant light spectator. For Standard Model parameters we find that couplings between Higgs and metric fluctuations are suppressed by $\mathcal{O}(10^{-7})$. They are negligible compared to both pure Higgs terms in the effective potential and the unavoidable non-minimal Higgs coupling to background scalar curvature. The question of the electroweak vacuum instability during high energy scale inflation can therefore be studied consistently using the Jordan frame action in a Friedmann--Lema\^itre--Robertson--Walker metric, where the Higgs-curvature coupling …

Can we measure the neutrino mass hierarchy in the sky?

2010

Cosmological probes are steadily reducing the total neutrino mass window, resulting in constraints on the neutrino-mass degeneracy as the most significant outcome. In this work we explore the discovery potential of cosmological probes to constrain the neutrino hierarchy, and point out some subtleties that could yield spurious claims of detection. This has an important implication for next generation of double beta decay experiments, that will be able to achieve a positive signal in the case of degenerate or inverted hierarchy of Majorana neutrinos. We find that cosmological experiments that nearly cover the whole sky could in principle distinguish the neutrino hierarchy by yielding 'substan…

Magnetic fields and chiral asymmetry in the early hot universe

2016

In this paper, we study analytically the process of external generation and subsequent free evolution of the lepton chiral asymmetry and helical magnetic fields in the early hot universe. This process is known to be affected by the Abelian anomaly of the electroweak gauge interactions. As a consequence, chiral asymmetry in the fermion distribution generates magnetic fields of non-zero helicity, and vice versa. We take into account the presence of thermal bath, which serves as a seed for the development of instability in magnetic field in the presence of externally generated lepton chiral asymmetry. The developed helical magnetic field and lepton chiral asymmetry support each other, consider…

Mesonic enhancement of the weak axial charge and its effect on the half-lives and spectral shapes of first-forbidden J+↔J− decays

2018

The effects of the enhancement of the axial-charge matrix element γ5 were studied in medium heavy and heavy nuclei for first-forbidden J+↔J− decay transitions using the nuclear shell model. Noticeable dependence on the enhancement ϵMEC of the axial-charge matrix element, as well as on the value of the axial-vector coupling constant gA was found in the spectral shapes of $^{93}$Y, $^{95}$Sr, and $^{97}$Y. The importance of the spectrum of $^{138}$Cs in the determination of gA is discussed. Half-life analyses in the A≈95 and A≈135 regions were done, and consistent results gA≈0.90, 0.75, and 0.65, corresponding to the three enhancement scenarios ϵMEC=1.4, 1.7, and 2.0, were obtained. Connectio…

Dark matter from unification

2013

We consider a minimal extension of the Standard Model (SM), which leads to unification of the SM coupling constants, breaks electroweak symmetry dynamically by a new strongly coupled sector and leads to novel dark matter candidates. In this model, the coupling constant unification requires the existence of electroweak triplet and doublet fermions singlet under QCD and new strong dynamics underlying the Higgs sector. Among these new matter fields and a new right handed neutrino, we consider the mass and mixing patterns of the neutral states. We argue for a symmetry stabilizing the lightest mass eigenstates of this sector and determine the resulting relic density. The results are constrained …