Multidimensional simple waves in fully relativistic fluids

A special version of multi--dimensional simple waves given in [G. Boillat, {\it J. Math. Phys.} {\bf 11}, 1482-3 (1970)] and [G.M. Webb, R. Ratkiewicz, M. Brio and G.P. Zank, {\it J. Plasma Phys.} {\bf 59}, 417-460 (1998)] is employed for fully relativistic fluid and plasma flows. Three essential modes: vortex, entropy and sound modes are derived where each of them is different from its nonrelativistic analogue. Vortex and entropy modes are formally solved in both the laboratory frame and the wave frame (co-moving with the wave front) while the sound mode is formally solved only in the wave frame at ultra-relativistic temperatures. In addition, the surface which is the boundary between the permitted and forbidden regions of the solution is introduced and determined. Finally a symmetry analysis is performed for the vortex mode equation up to both point and contact transformations. Fundamental invariants and a form of general solutions of point transformations along with some specific examples are also derived.Comment: 21 page

Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions

Hamiltonian systems of hydrodynamic type occur in a wide range of applications including fluid dynamics, the Whitham averaging procedure and the theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the integrability of such systems by the generalised hodograph transform implies that integrable Hamiltonians depend on a certain number of arbitrary functions of two variables. On the contrary, in 2+1 dimensions the requirement of the integrability by the method of hydrodynamic reductions, which is a natural analogue of the generalised hodograph transform in higher dimensions, leads to finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we classify integrable two-component Hamiltonian systems of hydrodynamic type for all existing classes of differential-geometric Poisson brackets in 2D, establishing a parametrisation of integrable Hamiltonians via elliptic/hypergeometric functions. Our approach is based on the Godunov-type representation of Hamiltonian systems, and utilises a novel construction of Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page

The Influence of Chemical Surface Treatment on the Corrosion Resistance of Titanium Castings Used in Dental Prosthetics

Abstract Air abrasion process is used for cleaning casting surface of prosthetic components, and to prepare the surface of these elements for the application of veneering items. Its side effect, however, is that abrasive particles are embedded in the treated surface, which can be up to 30% of the surface and it constitutes the side effect of this procedure. Such a significant participation of foreign material can not be indifferent to the properties of the surface. Embedded particles can be the place of stress concentration causing cracking of ceramics, and may deteriorate corrosion resistance by forming corrosive microlinks. In the latter cases, it would be advisable to remove elements embedded into the surface. The simplest method is chemical etching or electrochemical one. Nevertheless, these procedures should not significantly change the parameters of the surface. Among many possible reagents only a few fulfills all the above conditions. In addition, processing should not impair corrosion resistance of titanium, which is one of the most important factors determining its use as a prosthetic restoration in the mouth. The study presented results of corrosion resistance of titanium used to make prosthetic components by means of casting method, which were subjected to chemical processing designed to remove the embedded abrasive particles. The aim of the study was to investigate whether etching with selected reagents affects the corrosion resistance of titanium castings. For etching the following reagents were used: 30% HNO 3 + 3% HF + H 2 O, HNO 3 + HF+ glycerol (1:2:3), 4% HF in H 2 O 2 , 4% HF in H 2 O, with a control sandblasted sample, not subjected to etching. Tests demonstrated that the etching affected corrosion properties of test samples, in each case the reduction of the corrosion potential occurred -possibly due to the removal of particles of Al 2 O 3 from the surface and activation of the surface. None of the samples underwent pitting corrosion as a result of polarization to 9 V. Values of the polarization resistance, and potentiodynamic characteristics indicated that the best corrosion resistance exhibited the samples after etching in a mixture of 4% solution of HF in H 2 O 2 . They showed very good passivation of the surface

Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

We investigate multi-dimensional Hamiltonian systems associated with constant Poisson brackets of hydrodynamic type. A complete list of two- and three-component integrable Hamiltonians is obtained. All our examples possess dispersionless Lax pairs and an infinity of hydrodynamic reductions.Comment: 34 page

The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type

We obtain the necessary and sufficient conditions for a two-component (2+1)-dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions. These conditions are in involution, implying that the systems in question are locally parametrized by 15 arbitrary constants. It is proved that all such systems possess three conservation laws of hydrodynamic type and, therefore, are symmetrizable in Godunov's sense. Moreover, all such systems are proved to possess a scalar pseudopotential which plays the role of the `dispersionless Lax pair'. We demonstrate that the class of two-component systems possessing a scalar pseudopotential is in fact identical with the class of systems possessing infinitely many hydrodynamic reductions, thus establishing the equivalence of the two possible definitions of the integrability. Explicit linearly degenerate examples are constructed.Comment: 15 page

Riemann Invariants and Rank-k Solutions of Hyperbolic Systems

In this paper we employ a "direct method" in order to obtain rank-k solutions of any hyperbolic system of first order quasilinear differential equations in many dimensions. We discuss in detail the necessary and sufficient conditions for existence of these type of solutions written in terms of Riemann invariants. The most important characteristic of this approach is the introduction of specific first order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method of solving multi-dimensional systems of PDEs. We have demonstrated the usefulness of our approach through several examples of hydrodynamic type systems; new classes of solutions have been obtained in a closed form.Comment: 30 page

The Peptidoglycan-Binding Protein SjcF1 Influences Septal Junction Function and Channel Formation in the Filamentous Cyanobacterium Anabaena

Filamentous, heterocyst-forming cyanobacteria exchange nutrients and regulators between cells for diazotrophic growth. Two alternative modes of exchange have been discussed involving transport either through the periplasm or through septal junctions linking adjacent cells. Septal junctions and channels in the septal peptidoglycan are likely filled with septal junction complexes. While possible proteinaceous factors involved in septal junction formation, SepJ (FraG), FraC, and FraD, have been identified, little is known about peptidoglycan channel formation and septal junction complex anchoring to the peptidoglycan. We describe a factor, SjcF1, involved in regulation of septal junction channel formation in the heterocyst-forming cyanobacterium Anabaena sp. strain PCC 7120. SjcF1 interacts with the peptidoglycan layer through two peptidoglycan-binding domains and is localized throughout the cell periphery but at higher levels in the intercellular septa. A strain with an insertion in sjcF1 was not affected in peptidoglycan synthesis but showed an altered morphology of the septal peptidoglycan channels, which were significantly wider in the mutant than in the wild type. The mutant was impaired in intercellular exchange of a fluorescent probe to a similar extent as a sepJ deletion mutant. SjcF1 additionally bears an SH3 domain for protein-protein interactions. SH3 binding domains were identified in SepJ and FraC, and evidence for interaction of SjcF1 with both SepJ and FraC was obtained. SjcF1 represents a novel protein involved in structuring the peptidoglycan layer, which links peptidoglycan channel formation to septal junction complex function in multicellular cyanobacteria. Nonetheless, based on its subcellular distribution, this might not be the only function of SjcF1.Peer reviewe

Multimode solutions of first-order elliptic quasilinear systems obtained from Riemann invariants

Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links between two techniques, that of the symmetry reduction method and of the generalized method of characteristics. A variant of the conditional symmetry method for constructing this type of solution is proposed. A specific feature of that approach is an algebraic-geometric point of view, which allows the introduction of specific first-order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method for solving elliptic homogeneous systems of PDEs. A further generalization of the Riemann invariants method to the case of inhomogeneous systems, based on the introduction of specific rotation matrices, enables us to weaken the integrability condition. It allows us to establish a connection between the structure of the set of integral elements and the possibility of constructing specific classes of simple mode solutions. These theoretical considerations are illustrated by the examples of an ideal plastic flow in its elliptic region and a system describing a nonlinear interaction of waves and particles. Several new classes of solutions are obtained in explicit form, including the general integral for the latter system of equations

Structural analysis and corrosion studies on an ISO 5832-9 biomedical alloy with TiO2 sol–gel layers

The aim of this study was to demonstrate the relationship between the structural and corrosion properties of an ISO 5832-9 biomedical alloy modified with titanium dioxide (TiO2) layers. These layers were obtained via the sol–gel method by acid-catalyzed hydrolysis of titanium isopropoxide in isopropanol solution. To obtain TiO2 layers with different structural properties, the coated samples were annealed at temperatures of 200, 300, 400, 450, 500, 600 and 800 C for 2 h. For all the prepared samples, accelerated corrosion measurements were performed in Tyrode’s physiological solution using electrochemical methods. The most important corrosion parameters were determined: corrosion potential, polarization resistance, corrosion rate, breakdown and repassivation potentials. Corrosion damage was analyzed using scanning electron microscopy. Structural analysis was carried out for selected TiO2 coatings annealed at 200, 400, 600 and 800 C. In addition, the morphology, chemical composition, crystallinity, thickness and density of the deposited TiO2 layers were determined using suitable electron and X-ray measurement methods. It was shown that the structure and character of interactions between substrate and deposited TiO2 layers depended on annealing temperature. All the obtained TiO2 coatings exhibit anticorrosion properties, but these properties are related to the crystalline structure and character of substrate–layer interaction. From the point of view of corrosion, the best TiO2 sol–gel coatings for stainless steel intended for biomedical applications seem to be those obtained at 400 C.This study was supported by Grant No. N N507 501339 of the National Science Centre. The authors wish to express their thanks to J. Borowski (MEDGAL, Poland) for the Rex 734 alloy

Design and synthesis of new quinazolin-4-one derivatives with negative mGlu7mGlu_7 receptor modulation activity and antipsychotic-like properties

Following the glutamatergic theory of schizophrenia and based on our previous study regarding the antipsychotic-like activity of mGlu7 NAMs, we synthesized a new compound library containing 103 members, which were examined for NAM mGlu7 activity in the T-REx 293 cell line expressing a recombinant human mGlu7 receptor. Out of the twenty-two scaffolds examined, active compounds were found only within the quinazolinone chemotype. 2-(2-Chlorophenyl)-6-(2,3-dimethoxyphenyl)-3-methylquinazolin-4(3H)-one (A9-7, ALX-171, mGlu7 IC50 = 6.14 µM) was selective over other group III mGlu receptors (mGlu4 and mGlu8), exhibited satisfactory drug-like properties in preliminary DMPK profiling, and was further tested in animal models of antipsychotic-like activity, assessing the positive, negative, and cognitive symptoms. ALX-171 reversed DOI-induced head twitches and MK-801-induced disruptions of social interactions or cognition in the novel object recognition test and spatial delayed alternation test. On the other hand, the efficacy of the compound was not observed in the MK-801-induced hyperactivity test or prepulse inhibition. In summary, the observed antipsychotic activity profile of ALX-171 justifies the further development of the group of quinazolin-4-one derivatives in the search for a new drug candidate for schizophrenia treatment