Nonexistence of global solutions for a class of complex vector fields on two-torus

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon C(infinity) (S(1) ; R), defined on two-torus T(2) congruent to R(2)/2 pi Z(2). The kernel of transpose operator L is described and the solvability near the characteristic set is also studied. (c) 2008 Elsevier Inc. All rights reserved.

Global solutions for impulsive abstract partial differential equations

In this paper, we study the existence of global solutions for a class of impulsive abstract functional differential equation. An application involving a parabolic system With impulses is considered. (c) 2008 Elsevier Ltd. All rights reserved.

Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.

Iterative strong coupling of dimensionally heterogeneous models

In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.

A numerical method for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field

A finite difference technique, based on a projection method, is developed for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tome and McKee [32]; Tome et al. [34]). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution. (C) 2009 Elsevier B.V. All rights reserved.

Improvement in the Reduction Behavior of Novel ZrO(2)-CeO(2) Solid Solutions with a Tubular Nanostructure by Incorporation of Pd

In this work, 1 wt % Pd/ZrO(2)-CeO(2) mixed oxide nanotubes with 90 mol % CeO(2) were synthesized following a very simple, high-yield procedure and their properties were characterized by synchrotron radiation X-ray diffraction, X-ray absorption near-edge spectroscopy (XANES), and scanning and high-resolution transmission electron microscopy (SEM and HRTEM). In situ XANES experiments were carried out under reducing conditions to investigate the reduction behavior of these novel nanotube materials. The Pd/CeO(2)-based nanotubes exhibited the cubic phase (Fm3m space group). The nanotube walls were composed of nanoparticles with an average crystallite size of about 7 nm, and the nanotubes exhibited a large specific surface area (85 m(2).g(-1)). SEM and HRTEM studies showed that individual nanotubes were composed of a curved sheet of these nanoparticles. Elemental analysis showed that the Ce:Zr:Pd ratios appeared to be approximately constant across space, suggesting compositional homogeneity in the samples. XANES results indicated that the extent of reduction of these materials is low and that the Ce(4+) state is in the majority over the reduced Ce(3+) state. The results suggest that Pd cations-most likely Pd(2+)-form a Pd-Ce-Zr oxide solid solution and that the Pd(2+) is stabilized against reduction in this phase. However, incorporation of the Pd (1 wt %) into the crystal lattice of the nanotubes also appeared to destabilize Ce(4+) against reduction to Ce(3+) and caused a significant increase in its reducibility.

Metastable Phase Diagram of Nanocrystalline ZrO(2)-Sc(2)O(3) Solid Solutions

We have investigated the crystal structures and phase transitions of nanocrystalline ZrO(2)-1 to -13 mol % Sc(2)O(3) by synchrotron X-ray powder diffraction and Raman spectroscopy. ZrO(2)-Sc(2)O(3) nanopowders were synthesized by using a stoichiometric nitrate-lysine get-combustion route. Calcination processes at 650 and at 850 degrees C yielded nanocrystalline materials with average crystallite sizes of (10 +/- 1) and (25 +/- 2) nm, respectively. Only metastable tetragonal forms and the cubic phase were identified, whereas the stable monoclinic and rhombohedral phases were not detected in the compositional range analyzed in this work. Differently from the results of investigations reported in the literature for ZrO(2)-Sc(2)O(3) materials with large crystallite sizes, this study demonstrates that, if the crystallite sizes are small enough (in the nanometric range), the metastable t ``-form of the tetragonal phase is retained. We have also determined the t`-t `` and t ``-cubic compositional boundaries at room temperature and analyzed these transitions at high temperature. Finally, using these results, we built up a metastable phase diagram for nanocrystalline compositionally homogeneous ZrO(2)-Sc(2)O(3) solid solutions that strongly differs from that previously determined from compositionally homogeneous ZrO(2)-Sc(2)O(3), Solid solutions with much larger crystallite sizes.

Adsorption of Pb(2+), Cu(2+) and Cd(2+) in FDU-1 silica and FDU-1 silica modified with humic acid

Ordered mesoporous silica with cubic structure, type FDU-1, was synthesized under strong acid media using B-50-6600 poly(ethylene oxide)-poly(butilene oxide)-poly(ethylene oxide) triblock copolymer (EO(39)BO(47)EO(39)) and tetraethyl orthosilicate (TEOS). Humic acid (HA) was modified to the synthesis process at a concentration of 1.5 mmol per gram of SiO(2). Thermogravimetry, small angle X-ray diffraction, nitrogen adsorption and high resolution transmission electron microscopy were used to characterize the samples. The pristine FDU-1 and FDU-1 with incorporated 1.5 mmol of HA were tested for adsorption of Pb(2+), Cu(2+) and Cd(2+) in aqueous solution. Incorporation of humic acid into the FDU-1 silica afforded an adsorbent with strong affinity for Cd(2+), Cu(2+) and Pb(2+) from single ion solutions. Adsorption of Cu(2+) was significantly enhanced after incorporation of humic acid, a fact that can be explained by the formation of complexes with carboxylic and phenolic groups at low concentrations of the metal cation. The results demonstrated the potential applicability of FDU-1 with incorporated HA in the removal of low concentrations of heavy metal cations from aqueous solution, such as wastewaters, after usual precipitation of metal hydroxides in alkaline medium and proper pH conditioning in the range between 6 and 7. (C) 2007 Elsevier Inc. All rights reserved.

Tetragonal-cubic phase boundary in nanocrystalline ZrO(2)-Y(2)O(3) solid solutions synthesized by gel-combustion

By means of synchrotron X-ray powder diffraction (SXPD) and Raman spectroscopy, we have detected, in a series of nanocrystalline and compositionally homogeneous ZrO(2)-Y(2)O(3) solid solutions, the presence at room temperature of three different phases depending on Y(2)O(3) content, namely two tetragonal forms and the cubic phase. The studied materials, with average crystallite sizes within the range 7-10 nm, were synthesized by a nitrate-citrate gel-combustion process. The crystal structure of these phases was also investigated by SXPD. The results presented here indicate that the studied nanocrystalline ZrO(2)-Y(2)O(3) solid solutions exhibit the same phases reported in the literature for compositionally homogeneous materials containing larger (micro)crystals. The compositional boundaries between both tetragonal forms and between tetragonal and cubic phases were also determined. (C) 2011 Elsevier B.V. All rights reserved.

Crystallization of nordstrandite in ethylene glycol water solutions: electron microscopic studies

The present work shows the growth of nordstrandile microcrystals observed by transmission and scanning electron microscopy. Nordstrandite was synthesised from non-crystalline aluminium hydroxide reacted in 20% ethylene glycol/water solution, at room temperature. This material was characterized by TEM, SEM, SAED, XRD and EDS/TEM, during six month and revealed the formation and growth of nordstrandite. Fibrillar pseudoboehmite is the only aluminium hydroxide which could be identified during the first two weeks. The nuclei grow, from complete dissolution/recrystallization of pseudoboehmite fibrils, into platy rectangular microscrystals of nordstrandite. Some tabular microcrystals recrystallise, forming after six months only the mufti-point nordstrandite stars. This electron-optical study suggest that the star shape results from the overlapping of rectangular plates, and pseudoboehmite fibrils act as the precursor of nordstrandite crystallisation in ethylene glycol/water solution.

Sound waves and solitons in hot and dense nuclear matter

Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density. The equation of state is derived from a relativistic mean field model, which is a variant of the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations leads to differential equations for the density perturbation. We solve them numerically for linear and spherical perturbations and follow the propagation of the initial pulses. For linear perturbations we find single soliton solutions and solutions with one or more solitons followed by ""radiation"". Depending on the equation of state a strong damping may occur. We consider also the evolution of perturbations in a medium without dispersive effects. In this case we observe the formation and breaking of shock waves. We study all these equations also for matter at finite temperature. Our results may be relevant for the analysis of RHIC data. They suggest that the shock waves formed in the quark gluon plasma phase may survive and propagate in the hadronic phase. (C) 2009 Elseiver. B.V. All rights reserved.

MRI study of radiation effect on Fricke gel solutions

The quality control optimization of medical processes that use ionizing radiation in the treatment of diseases like cancer is a key element for patient safety and success of treatment. The major medical application of radiation is radiotherapy, i.e. the delivery of dose levels to well-defined target tissues of a patient with the purpose of eliminating a disease. The need of an accurate tumour-edge definition with the purpose of preserving healthy surrounding tissue demands rigorous radiation treatment planning. Dosimetric methods are used for dose distribution mapping region of interest to assure that the prescribed dose and the irradiated region are correct. The Fricke gel (FXG) is the main dosimeter that supplies visualization of the three-dimensional (3D) dose distribution. In this work the dosimetric characteristics of the modified Fricke dosimeter produced at the Radiation Metrology Centre of the Institute of Energetic and Nuclear Research (IPEN) such as gel concentration dose response dependence, xylenol orange addition influence, dose response between 5 and 50Gy and signal stability were evaluated by magnetic resonance imaging (MRI). Using the same gel solution, breast simulators (phantoms) were shaped and absorbed dose distributions were imaged by MRI at the Nuclear Resonance Laboratory of the Physics Institute of Sao Paulo University. (C) 2007 Elsevier Ltd. All rights reserved.

Energy-momentum tensor in thermal strong-field QED with unstable vacuum

Themean value of the one-loop energy-momentum tensor in thermal QED with an electric-like background that creates particles from vacuum is calculated. The problem is essentially different from calculations of effective actions ( similar to the action of Heisenberg-Euler) in backgrounds that respect the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and the duration over which one can neglect the back-reaction of created particles are established.

Comments on regularization of identity based solutions in string field theory

We analyze the consistency of the recently proposed regularization of an identity based solution in open bosonic string field theory. We show that the equation of motion is satisfied when it is contracted with the regularized solution itself. Additionally, we propose a similar regularization of an identity based solution in the modified cubic superstring field theory.