Grand unification and proton stability near the Peccei-Quinn scale

We show that in an SU(2)circle timesU(1) model with a Dine-Fischler-Srednicki-like invisible axion it is possible to obtain (i) the convergence of the three gauge coupling constants at an energy scale near the Peccei-Quinn scale; (ii) the correct value for sin(2)theta<^>(W)(M-Z); (iii) the stabilization of the proton by the cyclic Z(13)circle timesZ(3) symmetries which also stabilize the axion as a solution to the strong CP problem. Concerning the convergence of the three coupling constants and the prediction of the weak mixing angle at the Z peak, this model is as good as the minimal supersymmetric standard model with mu(SUSY)=M-Z. We also consider the standard model with six and seven Higgs doublets. The main calculations were done in the 1-loop approximation but we briefly consider the 2-loop contributions.

Superfluid Fermi-Fermi mixture: Phase diagram, stability, and soliton formation

We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluid Fermi-Fermi mixture (of distinct mass) at zero temperature using energy densities for the superfluid fermions in one (1D), two (2D), and three (3D) dimensions. We also derive the dynamical time-dependent nonlinear Euler-Lagrange equation satisfied by the mixture in one dimension using this energy density. We obtain the linear stability conditions for the mixture in terms of fermion densities of the components and the interspecies Fermi-Fermi interaction. In equilibrium there are two possibilities. The first is that of a uniform mixture of the two components, the second is that of two pure phases of two components without any overlap between them. In addition, a mixed and a pure phase, impossible in 1D and 2D, can be created in 3D. We also obtain the conditions under which the uniform mixture is stable from an energetic consideration. The same conditions are obtained from a modulational instability analysis of the dynamical equations in 1D. Finally, the 1D dynamical equations for the system are solved numerically and by variational approximation (VA) to study the bright solitons of the system for attractive interspecies Fermi-Fermi interaction in 1D. The VA is found to yield good agreement to the numerical result for the density profile and chemical potential of the bright solitons. The bright solitons are demonstrated to be dynamically stable. The experimental realization of these Fermi-Fermi bright solitons seems possible with present setups.

Synchronization: Stability and duration time

We consider the problem of stability and duration of the synchronization process between self-excited oscillators, both in their regular and chaotic states. Making use of the properties of Hill equation describing the deviation between the slave and the master, we derive the stability conditions and expressions of the synchronization time. A fairly good agreement is obtained between the analytical and numerical results.

Binding three-particles at the edge of stability

The stability threshold for an Efimov state is determined as a function of the physical scales of the system. Light exotic nuclei and triatomic molecules are investigated. Scaling, universality, and renormalization-group invariance properties are discussed in this context.

Stability of atomic condensed systems with attractive two-body interactions

In the present report, we review recent investigations that we have conducted on the stability of atomic condensed systems, when the two-body interaction is attractive. In particular, the dynamics that occurs in the condensate due to nonconservative terms is considered in the context of an extension of the mean-field Gross-Pitaevskii approximation. Considering the relative intensity of the nonconservative parameters, chaotic and solitonic solutions are verified. Also discussed is the possibility of a liquid-gas phase transition in the presence of positive three-body elastic collisions.

Stability and collapse of a coupled Bose-Einstein condensate

The dynamics of a coupled Bose-Einstein condensate involving trapped atoms in two quantum states is studied using the time-dependent Gross-Pitaevskii equation including an interaction which can transform atoms from one state to the other. We find interesting oscillation of the number of atoms in each of the states. For all repulsive interactions, stable condensates are formed. When some of the atomic interactions are attractive, the possibility of collapse is studied by including an absorptive contact interaction and a quartic three-body recombination term. One or both components of the condensate may undergo collapse when one or more of the nonlinear terms are attractive in nature. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean-field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions, where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Stability and collapse of a hybrid Bose-Einstein condensate of atoms and molecules

The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can transform two atoms into a molecule and vice versa. We find an interesting oscillation of the number of atoms and molecules for a BEC of fixed mass. This oscillation is a consequence of continuous transformation in the condensate of two atoms into a molecule and vice versa. For the study of collapse an absorptive contact interaction and an imaginary quartic three-body recombination term are included in the GP equation. It is possible to have a collapse of one or both components when one or more of the nonlinear terms in the GP equation are attractive in nature, respectively.

Identification of the Mass and Stability Interval of Strong Potential in Heavy Mesons

In this paper, we have calculated the masses of mesons containing t-quark and their spins' coupling coefficients. This was achieved by solving Lippmann-Schwinger equation for the quark-antiquark bound state of heavy mesons in configuration space. Heavy meson masses submitted criteria for the strong nuclear interactive potential between two quarks. We investigated the stability of a few suitable potentials and offered the best of these potentials for heavy mesons.

Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.

Stability of differential equations with piecewise constant argument via discrete equations

Lyapunov stability for a class of differential equation with piecewise constant argument (EPCA) is considered by means of the stability of a discrete equation. Applications to some nonlinear autonomous equations are given improving some linear known cases.

Stability results for impulsive functional differential equations with infinite delay

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermal stability of the martensitic transformation of Cu-Al-Ni-Mn-Ti

The development of new shape memory alloys with high martensitic transformation temperature increases the potential for applications. The development and use of these new alloys depends on the stability of the structure during cycling at high temperatures. If it is possible to guarantee that on alloys keeps the structure during cycling, then the alloy can be used because of the shape memory properties. The aim of this work is to obtain a kinetic model of the forward and backward martensitic transformation of two Cu-Al-Ni-Mn-Ti alloys. Differential scanning calorimetry has been performed in order to establish the kinetic stability of the martensite and the beta transformation. (c) 2006 Elsevier B.V. All rights reserved.