The multicomponent 2D Toda hierarchy: dispersionless limit

The factorization problem of the multi-component 2D Toda hierarchy is used to analyze the dispersionless limit of this hierarchy. A dispersive version of the Whitham hierarchy defined in terms of scalar Lax and Orlov--Schulman operators is introduced and the corresponding additional symmetries and string equations are discussed. Then, it is shown how KP and Toda pictures of the dispersionless Whitham hierarchy emerge in the dispersionless limit. Moreover, the additional symmetries and string equations for the dispersive Whitham hierarchy are studied in this limit.Comment: Revised version with an overall improved presentatio

Crum transformation and Wronskian type solutions for supersymmetric KdV equation

©1997 Elsevier Science B.V. We should like to thank Allan Fordy and Kimio Ueno for making the reference [ 15] available to us.Darboux transformation is reconsidered for the supersymmetric KdV system. By iterating the Darboux transformation, a supersymmetric extension of the Crum transformation is obtained for the Manin-Radul SKdV equation, in doing so one gets Wronskian superdeterminant representations for the solutions. Particular examples provide us explicit supersymmetric extensions, super solitons, of the standard soliton of the KdV equation. The KdV soliton appears as the body of the super soliton.Depto. de Física TeóricaFac. de Ciencias FísicasTRUEpu

Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy

We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type determinants. We also study the n-th Gel'fand-Dickey hierarchy introducing spectral operators and obtaining similar results. We reduce the above-mentioned results to the Kadomtsev-Petviashvili I and II real forms, obtaining corresponding vectorial Darboux transformations. In particular for the Kadomtsev-Petviashvili I hierarchy, we get the line soliton, the lump solution, and the Johnson-Thompson lump, and the corresponding determinant formulae for the nonlinear superposition of several of them. For Kadomtsev-Petviashvili II apart from the line solitons, we get singular rational solutions with its singularity set describing the motion of strings in the plane. We also consider the I and II real forms for the Gel'fand-Dickey hierarchies obtaining the vectorial Darboux transformation in both cases

String equations in Whitham hierarchies: tau-functions and Virasoro constraints

A scheme for solving Whitham hierarchies satisfying a special class of string equations is presented. The tau-function of the corresponding solutions is obtained and the differential expressions of the underlying Virasoro constraints are characterized. Illustrative examples of exact solutions of Whitham hierarchies are derived and applications to conformal maps dynamics are indicated.Comment: 26 pages, 2 figure

S-functions, reductions and hodograph solutions of the r-th dispersionless modified KP and Dym hierarchies

We introduce an S-function formulation for the recently found r-th dispersionless modified KP and r-th dispersionless Dym hierarchies, giving also a connection of these $S$-functions with the Orlov functions of the hierarchies. Then, we discuss a reduction scheme for the hierarchies that together with the $S$-function formulation leads to hodograph systems for the associated solutions. We consider also the connection of these reductions with those of the dispersionless KP hierarchy and with hydrodynamic type systems. In particular, for the 1-component and 2-component reduction we derive, for both hierarchies, ample sets of examples of explicit solutions.Comment: 35 pages, uses AMS-Latex, Hyperref, Geometry, Array and Babel package

Mechanism of the synergistic inactivation of Escherichia coli by UV-C light at mild temperatures

UV light only penetrates liquid food surfaces to a very short depth, thereby limiting its industrial application in food pasteurization. One promising alternative is the combination of UV light with mild heat (UV-H), which has been demonstrated to produce a synergistic bactericidal effect. The aim of this article is to elucidate the mechanism of synergistic cellular inactivation resulting from the simultaneous application of UV light and heat. The lethality of UV-H treatments remained constant below ~45ºC, while lethality increased exponentially as the temperature increased. The percentage of synergism reached a maximum (40.3%) at 55ºC. Neither the flow regimen nor changes in the dose delivered by UV lamps contributed to the observed synergism. UV-H inactivation curves of the parental Escherichia coli strain obtained in a caffeic acid selective recovery medium followed a similar profile to those obtained with uvrA mutant cells in a nonselective medium. Thermal fluidification of membranes and synergistic lethal effects started around 40 to 45ºC. Chemical membrane fluidification with benzyl alcohol decreased the UV resistance of the parental strain but not that of the uvrA mutant. These results suggest that the synergistic lethal effect of UV-H treatments is due to the inhibition of DNA excision repair resulting from the membrane fluidification caused by simultaneous heating

Vectorial Ribaucour Transformations for the Lame Equations

The vectorial extension of the Ribaucour transformation for the Lame equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an example we apply the vectorial Ribaucour transformation to the Cartesian background.Comment: 12 pages. LaTeX2e with AMSLaTeX package

Non-degenerate solutions of universal Whitham hierarchy

The notion of non-degenerate solutions for the dispersionless Toda hierarchy is generalized to the universal Whitham hierarchy of genus zero with $M+1$ marked points. These solutions are characterized by a Riemann-Hilbert problem (generalized string equations) with respect to two-dimensional canonical transformations, and may be thought of as a kind of general solutions of the hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions $H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of two-dimensional canonical transformations. The solution of the Riemann-Hilbert problem is described by period maps on the space of $(M+1)$-tuples $(z_\alpha(p) : \alpha = 0,1,...,M)$ of conformal maps from $M$ disks of the Riemann sphere and their complements to the Riemann sphere. The period maps are defined by an infinite number of contour integrals that generalize the notion of harmonic moments. The $F$-function (free energy) of these solutions is also shown to have a contour integral representation.Comment: latex2e, using amsmath, amssym and amsthm packages, 32 pages, no figur

Genotypic and phenotypic characterization of a Salmonella Typhimurium strain resistant to pulsed electric fields

Pulsed Electric Fields (PEF) technology is regarded as one of the most interesting alternatives to current food preservation methods, due to its capability to inactivate vegetative microorganisms while leaving the product's organoleptic and nutritional properties mostly unchanged. However, many aspects regarding the mechanisms of bacterial inactivation by PEF are still not fully understood. The aim of this study was to obtain further insight into the mechanisms responsible for the increased resistance to PEF of a Salmonella Typhimurium SL1344 variant (SL1344-RS, Sagarzazu et al., 2013), and to quantify the impact that the acquisition of PEF resistance has on other aspects of S. enterica physiology, such as growth fitness, biofilm formation ability, virulence and antibiotic resistance. WGS, RNAseq and qRT-PCR assays indicated that the increased PEF resistance of the SL1344-RS variant is due to a higher RpoS activity caused by a mutation in the hnr gene. This increased RpoS activity also results in higher resistance to multiple stresses (acidic, osmotic, oxidative, ethanol and UV-C, but not to heat and HHP), decreased growth rate in M9-Gluconate (but not in TSB-YE or LB-DPY), increased ability to adhere to Caco-2 cells (but no significant change in invasiveness) and enhanced antibiotic resistance (to six out of eight agents). This study significantly contributes to the understanding of the mechanisms of the development of stress resistance in Salmonellae and underscores the crucial role played by RpoS in this process. Further studies are needed to determine whether this PEF-resistant variant would represent a higher, equal or lower associated hazard than the parental strain

Component release after exposure of Staphylococcus aureus cells to pulsed electric fields

The objective of this work was to get further insights on the mechanism of inactivation of bacterial cells by pulsed electric fields (PEF) through the study of the release of intracellular components after exposing Staphylococcus aureus cells in McIvlaine buffer (pH 7.0, 2 mS/cm) to PEF treatments of different intensity (18 and 25 kV/cm) and treatment times (from 20 to 400 mu s). Release of most compounds, except proteins, was almost immediate after the treatment, but the relative amount released depended on the molecule studied. A good correlation between the release of the smallest components studied (particularly ions) and membrane permeabilization (as measured by NaCl sensitization and PI entry) was observed. On the other hand, results obtained suggested that S. aureus inactivation by PEF would be related to the exit of cytoplasmic proteins of a molecular weight higher than 6 kDa. Results obtained in this work indicated that increasing PEF treatment time would reduce the capability of S. aureus cells to repair the electropores formed and suggested that this might be due to the formation of pores of a larger size, which S. aureus cells would be unable to reseal in a situation of homeostasis loss. Industrial relevance: Results reported here can help to design more effective treatments for microbial inactivation using PEF on food, and therefore facilitate its industrial implementation