Linearizability and fake Lax pair for a consistent around the cube nonlinear non-autonomous quad-graph equation

We discuss the linearization of a non-autonomous nonlinear partial difference equation belonging to the Boll classification of quad-graph equations consistent around the cube. We show that its Lax pair is fake. We present its generalized symmetries which turn out to be non-autonomous and depending on an arbitrary function of the dependent variables defined in two lattice points. These generalized symmetries are differential difference equations which, in some case, admit peculiar B\"acklund transformations.Comment: arXiv admin note: text overlap with arXiv:1311.2406 by other author

The Jacobi last multiplier for difference equations

We present a discretization of the Jacobi last multiplier, with some applications to the computation of solutions of difference equations.Comment: 9 page

Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method

The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely B\"acklund transformations and initial conservation laws, follow from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for generation of symmetries is developed and applied to discrete KdV. It can also be applied to all the other ABS equations

Freeze/thaw stress induces organelle remodeling and membrane recycling in cryopreserved human mature oocytes

Purpose: Our aim was to evaluate the ultrastructure of human metaphase II oocytes subjected to slow freezing and fixed after thawing at different intervals during post-thaw rehydration. Methods: Samples were studied by light and transmission electron microscopy. Results: We found that vacuolization was present in all cryopreserved oocytes, reaching a maximum in the intermediate stage of rehydration. Mitochondria-smooth endoplasmic reticulum (M-SER) aggregates decreased following thawing, particularly in the first and intermediate stages of rehydration, whereas mitochondria-vesicle (MV) complexes augmented in the same stages. At the end of rehydration, vacuoles and MV complexes both diminished and M-SER aggregates increased again. Cortical granules (CGs) were scarce in all cryopreserved oocytes, gradually diminishing as rehydration progressed. Conclusions: This study also shows that such a membrane remodeling is mainly represented by a dynamic process of transition between M-SER aggregates and MV complexes, both able of transforming into each other. Vacuoles and CG membranes may take part in the membrane recycling mechanism

The lattice Schwarzian KdV equation and its symmetries

In this paper we present a set of results on the symmetries of the lattice Schwarzian Korteweg-de Vries (lSKdV) equation. We construct the Lie point symmetries and, using its associated spectral problem, an infinite sequence of generalized symmetries and master symmetries. We finally show that we can use master symmetries of the lSKdV equation to construct non-autonomous non-integrable generalized symmetries.Comment: 11 pages, no figures. Submitted to Jour. Phys. A, Special Issue SIDE VI

Magnetostrictive Neel ordering of the spin-5/2 ladder compound BaMn2O3: distortion-induced lifting of geometrical frustration

The crystal structure and the magnetism of BaMn$_2$O$_3$ have been studied by thermodynamic and by diffraction techniques using large single crystals and powders. BaMn$_2$O$_3$ is a realization of a $S = 5/2$ spin ladder as the magnetic interaction is dominant along 180$^\circ$ Mn-O-Mn bonds forming the legs and the rungs of a ladder. The temperature dependence of the magnetic susceptibility exhibits well-defined maxima for all directions proving the low-dimensional magnetic character in BaMn$_2$O$_3$. The susceptibility and powder neutron diffraction data, however, show that BaMn$_2$O$_3$ exhibits a transition to antiferromagnetic order at 184 K, in spite of a full frustration of the nearest-neighbor inter-ladder coupling in the orthorhombic high-temperature phase. This frustration is lifted by a remarkably strong monoclinic distortion which accompanies the magnetic transition.Comment: 9 pages, 8 figures, 2 tables; in V1 fig. 2 was included twice and fig. 4 was missing; this has been corrected in V

Tunnel junctions of unconventional superconductors

The phenomenology of Josephson tunnel junctions between unconventional superconductors is developed further. In contrast to s-wave superconductors, for d-wave superconductors the direction dependence of the tunnel matrix elements that describe the barrier is relevant. We find the full I-V characteristics and comment on the thermodynamical properties of these junctions. They depend sensitively on the relative orientation of the superconductors. The I-V characteristics differ from the normal s-wave RSJ-like behavior.Comment: 4 pages, revtex, 4 (encapsulated postscript) figures (figures replaced

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

A Model Study of Displacement Instabilities during Cyclic Oxidation

The shape changes that occur at imperfections on the surface of an alumina-forming alloy, subject to thermal cycling, have been simulated and measured. Observations have been made by emplacing a surface groove into a FeCrAlY material. Upon thermal cycling, large shape distortions have been observed: whereas, for comparable isothermal oxidation, the shape changes are minimal. The simulations predict similar responses. Upon cycling, upward displacements (pile-up) occur around the perimeter, accompanied by downward displacements at the center. Yet, minimal displacements arise upon isothermal oxidation. To realize cyclic displacements comparable in magnitude to those found experimentally, large values of the in-plane growth strain are required and the bond coat must be relatively soft