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.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our system remains oscillatory. (C) 2009 Elsevier Inc. All rights reserved.

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Dirac equation in noncommutative space for hydrogen atom

We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S(1/2), 2P(1/2) and 2P(3/2) is lifted completely, such that new transition channels are allowed. (C) 2009 Elsevier B.V. All rights reserved.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

Cholesterol Mediates Chitosan Activity on Phospholipid Monolayers and Langmuir-Blodgett Films

The polysaccharide chitosan has been largely used in many biological applications as a fat and cholesterol reducer, bactericide agent, and wound healing material. While the efficacy for some of such uses is proven, little is known about the molecular-level interactions involved in these applications. In this study, we employ mixed Langmuir and Langmuir-Blodgett (LB) films of negatively charged dimyristoyl phosphatidic acid (DMPA) anti cholesterol as cell membrane models to investigate the role of cholesterol in the molecular-level action of chitosan. Chitosan does not remove cholesterol froth the monolayer. The interaction with chitosan tends to expand the DMPA monolayer due to its interpenetration within the film. On the other hand, cholesterol induces condensation of the DMPA monolayer. The competing effects cause the surface pressure isotherms of mixed DMPA-cholesterol films on a chitosan subphase to be unaffected by the cholesterol mole fraction, due to distinct degrees of chitosan penetration into the film in the presence of cholesterol. By combining polarization-modulated infrared reflection absorption spectroscopy (PM-IRRAS) and sum-frequency generation spectroscopy (SFG), we showed that chitosan induces order into negatively charged phospholipid layers, whereas the opposite occurs for cholesterol. In conclusion, chitosan has its penetration in the film modulated by cholesterol, and electrostatic interactions with negatively charged phospholipids, such as DMPA, are crucial for the action of chitosan.

Immobilization of Alcohol Dehydrogenase in Phospholipid Langmuir-Blodgett Films To Detect Ethanol

Enzyme immobilization in nanostructured films may be useful for a number of biomimetic systems, particularly if suitable matrixes are identified. Here we show that alcohol dehydrogenase (ADH) has high affinity toward a negatively charged phospholipid, dimyristoylphosphatidic acid (DMPA), which forms a Langmuir monolayer at an air-water interface. Incorporation of ADH into the DMPA monolayer was monitored with Surface pressure measurements; and polarization-modulation infrared reflection absorption spectroscopy, with the alpha-helices from ADH being mainly oriented parallel to the water surface. ADH remained at the interface even at high surface pressures, thus allowing deposition of Langmuir-Blodgett (LB) films from the DMPA-ADH film. Indeed, interaction with DMPA enhances the transfer of ADH, where the mass transferred onto a solid support increased from 134 ng for ADH on a Gibbs monolayer to 178 ng for an LB film with DMPA. With fluorescence spectroscopy it was possible to confirm that the ADH structure was preserved even after one month of the LB deposition. ADH-containing films deposited onto gold-interdigitated electrodes were employed in a sensor array capable of detecting ethanol at concentrations down to 10 ppb (in volume), using impedance spectroscopy as the method of detection.

Modeling Adsorption Processes of Poly-p-phenylenevinylene Precursor and Sodium Acid Dodecylbenzenesulfonate onto Layer-by-Layer Films Using a Langmuir-type Metastable Equilibrium Model

The adsorption kinetics curves of poly(xylylidene tetrahydrothiophenium chloride) (PTHT), a poly-p-phenylenevinylene (PPV) precursor, and the sodium salt of dodecylbenzene sulfonic acid (DBS), onto (PTHT/DBS)(n) layer-by-layer (LBL) films were characterized by means of UV-vis spectroscopy. The amount of PTHT/DBS and PTHT adsorbed on each layer was shown to be practically independent of adsorption time. A Langmuir-type metastable equilibrium model was used to adjust the adsorption isotherms data and to estimate adsorption/desorption coefficients ratios, k = k(ads)/k(des), values of 2 x 10(5) and 4 x 10(6) for PTHT and PTHT/DBS layers, respectively. The desorption coefficient has been estimated, using literature values for poly(o-methoxyaniline) desorption coefficient, as was found to be in the range of 10(-9) to 10(-6) s(-1), indicating that quasi equilibrium is rapidly attained.

Interaction of polysaccharide-protein complex from Agaricus blazei with Langmuir and Langmuir-Blodgett films of phospholipids

The use of natural substances in health applications may be hampered by the difficulties in establishing the mechanisms of action, especially at molecular-level. The protein-polysaccharide complex extracted from the mushroom Agaricus blazei Murill, referred to as CAb, has been considered for treating various diseases with probable interaction with cell membranes. In this study, we investigate the interaction between CAb and a cell membrane model represented by a Langmuir monolayer of dimyristoyl phosphatidic acid (DMPA). CAb affects the structural properties of DMPA monolayers causing expansion and increasing compressibility. In addition, interaction with DMPA polar heads led to neutralization of the electrical double layer, yielding a zero surface potential at large areas per molecule. CAb remained at the interface even at high surface pressures, which allowed transfer of Langmuir-Blodgett (LB) films onto solid supports with the CAb-DMPA mixture. The mass transferred, according to quartz crystal microbalance (QCM) measurements, increased linearly with the number of deposited layers. With UV-vis absorption, fluorescence and FTIR spectroscopies, we confirmed that the LB films contain polysaccharides, proteins and DMPA. Therefore, the CAb biological action must be attributed not only to polysaccharides but also to proteins in the complex. (C) 2008 Elsevier Inc. All rights reserved.

Langmuir-Blodgett films of diazobenzene molecules

Langmuir-Blodgett (LB) films from diazobenzene Sudan III have been investigated using surface potential measurements as a function of number of layers and deposition pressures, with the surface potential data being related to molecular dipole moments obtained from theoretical electronic structure calculations. The surface potential increased with the number of layers for SIII LB films, and then tended to saturate. Results from density functional theory (DIFT) and UV-vis spectroscopy indicated that the increase is due to addition of layers with oriented molecular dipoles, with the saturation tendency being attributed to a decrease in the amount of material deposited in each layer. The surface potential increased with the surface pressure used for deposition, probably owing to a higher contribution from the vertical component of the dipole moment as a closer molecular packing, which is associated with decreasing conformational entropy, was reached. (C) 2008 Elsevier Inc. All rights reserved.

Enhanced activity of horseradish peroxidase in Langmuir-Blodgett films of phospholipids

The immobilization of enzymes in nanostructured films has potential applications, e.g. in biosensing, for which the activity may not only be preserved, but also enhanced if optimized conditions are identified. Optimization is not straightforward because several requirements must be fulfilled, including a suitable matrix and film-forming technique. In this study, we show that horseradish peroxidase (HRP) has its activity enhanced when immobilized in Langmuir-Blodgett (LB) films, in conjunction with dipalmitoylphosphaticlylglycerol (DPPG). Incorporation of HRP into a DPPG monolayer at the air-water interface was demonstrated with compression isotherms, and Polarization-Modulation Infrared Reflection Absorption Spectroscopy (PM-IRRAS). From the PM-IRRAS data, we inferred that HRP was not denatured when adsorbed on a pre-formed, low pressure DPPG monolayer. A change in orientation was induced by the phospholipid matrix, with the amide C=O and NH groups from HRP being oriented perpendicular to the surface, parallel to the DPPG acyl chains, i.e. the alpha-helix was inserted into the monolayer. The mixed DPPG-HRP monolayer could be transferred onto solid supports, to which HRP activity was ca. 23% higher than in solution. The control of molecular architecture and choice of a suitable phospholipid matrix allowed HRP-containing LB films to be used in sensing peroxide. (c) 2008 Elsevier B.V. All rights reserved.

Langmuir and Langmuir-Blodgett (LB) films of tetrapyridyl metalloporphyrins

We report on the formation of Langmuir films of 5,10,15,20-tetra(4-pyridyl) 21H,23H-porphine,hereafter named tetrapyridyl porphyrins with distinct central ions (2H(+), Zn(2+), Cu(2+), Ni(2+)). The films were characterized with surface pressure and surface potential isotherms and in situ UV-vis absorbance. The measurements indicated strong aggregation of porphyrin monomers at the air-water interface, with a red shift of the Soret band in comparison with the spectrum obtained from CHCl(3) solutions. The shift was larger for the non-substituted H(2)TPyP, and depended on the metal ion. Significantly, aggregation occurred right after spreading of the Langmuir film, with on further shifts in the UV-vis spectra upon compression of the film, or even after transferring them onto solid substrates in the form of Langmuir-Blodgett (LB) films. The buildup of LB films from H(2)TPyP and ZnTPyP was monitored with UV-vis spectroscopy, indicating an equal amount of material deposited in each deposition step. Using FTIR in the transmission and reflection modes, we inferred that the H(2)TPyP molecules exhibit no preferential orientation in the LB films, while for ZnTPyP there is preferential orientation, with the porphyrin molecules anchored to the substrate by the lateral pyridyl groups. (C) 2008 Elsevier B.V. All rights reserved.

Interaction of horseradish peroxidase with Langmuir monolayers of phospholipids

The method employed to incorporate guest molecules onto phospholipid Langmuir monolayers plays an important role in the interaction between the monolayer and the guest molecules. In this paper, we show that for the interaction between horseradish peroxidase (HRP) and a monolayer of dipalmitoylphosphatidylglycerol (DPPG) does depend on the method of HRP incorporation. The surface pressure isotherms of the mixed DPPG/HRP monolayers, for instance, were less expanded when the two materials were co-spread than in the case where HRP was injected into the subphase. Therefore, the method for incorporation affected not only the penetration of HRP but also the changes in molecular packing caused to the DPPG monolayer. With experiments with the monolayer on a pendant drop, we observed that the incorporation of HRP affects the dynamic elasticity of the DPPG monolayer, on a way that varies with the surface pressure. At low pressures, HRP causes the monolayer to be more rigid, while the converse is true for surface pressures above 8 mN/m. Taken all the results together, we conclude that HRP is more efficiently incorporated if injected into the subphase on which a DPPG monolayer had been spread and that the interaction between HRP and DPPG is maintained even at high surface pressures. This is promising for the possible transfer of mixed films onto solid substrates and for applications in biosensors and drug delivery systems. (c) 2008 Elsevier B.V. All rights reserved.