The concept of quasi-integrability: a concrete example

We use the deformed sine-Gordon models recently presented by Bazeia et al [1] to take the first steps towards defining the concept of quasi-integrability. We consider one such definition and use it to calculate an infinite number of quasi-conserved quantities through a modification of the usual techniques of integrable field theories. Performing an expansion around the sine-Gordon theory we are able to evaluate the charges and the anomalies of their conservation laws in a perturbative power series in a small parameter which describes the ""closeness"" to the integrable sine-Gordon model. We show that in the case of the two-soliton scattering the charges, up to first order of perturbation, are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We indicate that this property may hold or not to higher orders depending on the behavior of the two-soliton solution under a special parity transformation. For closely bound systems, such as breather-like field configurations, the situation however is more complex and perhaps the anomalies have a different structure implying that the concept of quasi-integrability does not apply in the same way as in the scattering of solitons. We back up our results with the data of many numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.

SOME COMMENTS ON QUASI-INTEGRABILITY

In this paper we present our preliminary results which suggest that some field theory models are `almost` integrable; i.e. they possess a large number of `almost` conserved quantities. First we demonstrate this, in some detail, on a class of models which generalise sine-Gordon model in (1+1) dimensions. Then, we point out that many field configurations of these models look like those of the integrable systems and others are very close to being integrable. Finally we attempt to quantify these claims looking in particular, both analytically and numerically, at some long lived field configurations which resemble breathers.

Quasi-perfect state transfer in a bosonic dissipative network

In this paper we propose a scheme for quasi-perfect state transfer in a network of dissipative harmonic oscillators. We consider ideal sender and receiver oscillators connected by a chain of nonideal transmitter oscillators coupled by nearest-neighbour resonances. From the algebraic properties of the dynamical quantities describing the evolution of the network state, we derive a criterion, fixing the coupling strengths between all the oscillators, apart from their natural frequencies, enabling perfect state transfer in the particular case of ideal transmitter oscillators. Our criterion provides an easily manipulated formula enabling perfect state transfer in the special case where the network nonidealities are disregarded. We also extend such a criterion to dissipative networks where the fidelity of the transferred state decreases due to the loss mechanisms. To circumvent almost completely the adverse effect of decoherence, we propose a protocol to achieve quasi-perfect state transfer in nonideal networks. By adjusting the common frequency of the sender and the receiver oscillators to be out of resonance with that of the transmitters, we demonstrate that the sender`s state tunnels to the receiver oscillator by virtually exciting the nonideal transmitter chain. This virtual process makes negligible the decay rate associated with the transmitter line at the expense of delaying the time interval for the state transfer process. Apart from our analytical results, numerical computations are presented to illustrate our protocol.

Quartz recrystallization regimes, c-axis texture transitions and fluid inclusion reequilibration in a prograde greenschist to amphibolite facies mylonite zone (Ribeira Shear Zone, SE Brazil)

The crystal-plastic behavior of quartz mylonites from the Ribeira Shear Zone (SE Brazil), a major strike-slip structure that was active during a prograde metamorphic phase related to the Neoproterozoic Brasiliano-Pan African Orogeny, was investigated using a multi-method approach. Geothermobarometry results indicate deformational conditions ranging from similar to 300 to similar to 630 degrees C and 500-700 MPa. A strong correlation between mapped metamorphic zones and a dominance of different dynamic recrystallization mechanisms of quartz occurs within the mylonite zone. Bulging recrystallization (BLG) dominates within the chlorite zone between 300 and 410 degrees C, subgrain rotation recrystallization (SGR) operates within the biotite zone from 410 to 520 degrees C, and grain boundary migration recrystallization (GBM) dominates in the garnet zone above 520 degrees C. The development of quartz c-axis textures is mainly governed by temperature and dynamic recrystallization mechanisms. Textures from BLG zone mylonites are characterized by maxima around Z; SGR zone mylonites display single girdles or asymmetric type I crossed girdles; and GBM zone mylonites comprise maxima around Y and intermediate between X and Z. The scarcity or absence of water-bearing fluid inclusions in quartz mylonites from the SGR and GBM zones, which are dominated by carbonic inclusions, suggests water-deficient conditions, whereas BLG zone mylonites are dominated by water-bearing inclusions. This evidence indicates that water was available in the protoliths but has been eliminated with increasing deformation and deformation temperature. No effect of the water content variation on the quartz microstructural and recrystallized grain size evolution was detected, and little influence on c-axis texture development was observed. Most of the fluid inclusion densities were reequilibrated during the shear zone exhumation history, recording a decompression in the range of 300-500 MPa, while microstructural reequilibration effects related to the prograde metamorphism are largely preserved. Fluid inclusion microstructures and densities from two SGR zone samples preserved evidence for a near isothermal compression within the interior of the Ribeira Shear Zone during the prograde metamorphism. (C) 2009 Elsevier B.V. All rights reserved.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

FROM TRISECTIONS IN MODULE CATEGORIES TO QUASI-DIRECTED COMPONENTS

In this paper, we define and study a special type of trisections in a module category, namely the compact trisections which characterize quasi-directed components. We apply this notion to the study of laura algebras and we use it to define a class of algebras with predictable Auslander-Reiten components.