Multiple positive bound state solutions for a critical Choquard equation

In this paper we consider the problem(P lambda()) {-Delta u + V-lambda(x)u = (I-mu * vertical bar u vertical bar(2 mu*))vertical bar u vertical bar(2 mu*-2)u in R-N,u > 0 in R-N,where V-lambda = lambda + V-0 with lambda >= 0, V-0 is an element of L-N/2(R-N), I-mu = 1/vertical bar x vertical bar(mu) is the Riesz potential with 0 < mu < min{N, 4} and 2(mu)* = 2N-mu/N-2 with N >= 3. Under some smallness assumption on V-0 and lambda we prove the existence of two positive solutions of (P-lambda). In order to prove the main results, we used variational methods combined with degree theory

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

Simple bimolecular reactions $A_1+A_2\rightleftharpoons A_3+A_4$ are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction $H_2+Cl\rightleftharpoons HCl+H$, and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.Comment: 11 pages, 5 figures, to appear in vol.42 of the Brazilian Journal of Physic

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels

Modelling and analysis of time dependent processes in a chemically reactive mixture

In this paper, we study the propagation of sound waves and the dynamics of local wave disturbances induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in themodel in a proper way. For both time-dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen–Chlorine system as reference. Several numerical computations are included illustrating the behavior of the phase velocity and attenuation coefficient in a low-frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.The paper is partially supported by the Research Centre of Mathematics of the University of Minho, with the Portuguese Funds from the Foundation for Science and Technology (FCT) through the Project UID/MAT/00013/2013. We wish to thank the anonymous Referees for their valuable comments and suggestions that helped us to improve the paper.info:eu-repo/semantics/publishedVersio

International Glossina Genome Initiative 2004-2014: a driver for post-genomic era research on the African continent

Human African trypanosomiasis (HAT), also known as sleeping sickness, is a neglected disease that impacts 70 million people distributed over 1.55 million km2 in sub- Saharan Africa and includes at least 50% of the population of theDemocratic Republic of the Congo [1]. Trypanosoma brucei gambiense accounts for more than 98% of the infections in central and West Africa, the remaining infections being from Trypanosoma brucei rhodesiense in East Africa [2]. The parasites are transmitted to the hosts through the bite of an infected tsetse fly. Disease control is challenging as there are no vaccines, and effective, easily delivered drugs are still lacking. Treatment invariably involves lengthy hospitalization, with both medical and socioeconomic consequences.Web of Scienc

Microfluidic systems for the analysis of the viscoelastic fluid flow phenomena in porous media

In this study, two microfluidic devices are proposed as simplified 1-D microfluidic analogues of a porous medium. The objectives are twofold: firstly to assess the usefulness of the microchannels to mimic the porous medium in a controlled and simplified manner, and secondly to obtain a better insight about the flow characteristics of viscoelastic fluids flowing through a packed bed. For these purposes, flow visualizations and pressure drop measurements are conducted with Newtonian and viscoelastic fluids. The 1-D microfluidic analogues of porous medium consisted of microchannels with a sequence of contractions/ expansions disposed in symmetric and asymmetric arrangements. The real porous medium is in reality, a complex combination of the two arrangements of particles simulated with the microchannels, which can be considered as limiting ideal configurations. The results show that both configurations are able to mimic well the pressure drop variation with flow rate for Newtonian fluids. However, due to the intrinsic differences in the deformation rate profiles associated with each microgeometry, the symmetric configuration is more suitable for studying the flow of viscoelastic fluids at low De values, while the asymmetric configuration provides better results at high De values. In this way, both microgeometries seem to be complementary and could be interesting tools to obtain a better insight about the flow of viscoelastic fluids through a porous medium. Such model systems could be very interesting to use in polymer-flood processes for enhanced oil recovery, for instance, as a tool for selecting the most suitable viscoelastic fluid to be used in a specific formation. The selection of the fluid properties of a detergent for cleaning oil contaminated soil, sand, and in general, any porous material, is another possible application

Multiplicity of Positive Solutions for an Obstacle Problem in R

In this paper we establish the existence of two positive solutions for the obstacle problem \displaystyle \int_{\Re}\left[u'(v-u)'+(1+\lambda V(x))u(v-u)\right] \geq \displaystyle \int_{\Re} f(u)(v-u), \forall v\in \Ka where $f$ is a continuous function verifying some technical conditions and \Ka is the convex set given by \Ka =\left\{v\in H^{1}(\Re); v \geq \varphi \right\}, with $\varphi \in H^{1}(\Re)$ having nontrivial positive part with compact support in $\Re$. \vspace{0.2cm} \noindent \emph{2000 Mathematics Subject Classification} : 34B18, 35A15, 46E39. \noindent \emph{Key words}: Obstacle problem, Variational methods, Positive solutions.Comment: To appear in Progress in Nonlinear Differential Equations and their Application

Chromatin differentiation between Theobroma cacao L. and T. grandiflorum Schum

A comparative analysis of mitotic chromosomes of Theobroma cacao (cacao) and T. grandiflorum (cupuaçu) was performed aiming to identify cytological differences between the two most important species of this genus. Both species have symmetric karyotypes, with 2n = 20 metacentric chromosomes ranging in size from 2.00 to 1.19 μm (cacao) and from 2.21 to 1.15 μm (cupuaçu). The interphase nuclei of both species were of the arreticulate type, displaying up to 20 chromocentres, which were more regularly shaped in cacao than in cupuaçu. Prophase chromosomes of both species were more condensed in the proximal region, sometimes including the whole short arm. Both species exhibited only one pair of terminal heterochromatic bands, positively stained with chromomycin A 3 , which co-localized with the single 45S rDNA site. Each karyotype displayed a single 5S rDNA site in the proximal region of another chromosome pair. Heterochromatic bands were also observed on the centromeric/pericentromeric regions of all 20 chromosomes of cacao after C-banding followed by Giemsa or DAPI staining, whereas in cupuaçu they were never detected. These data suggest that the chromosomes of both species have been largely conserved and their pericentromeric chromatin is the only citologically differentiated region

Microdevices for extensional rheometry of low viscosity elastic liquids : a review

Extensional flows and the underlying stability/instability mechanisms are of extreme relevance to the efficient operation of inkjet printing, coating processes and drug delivery systems, as well as for the generation of micro droplets. The development of an extensional rheometer to characterize the extensional properties of low viscosity fluids has therefore stimulated great interest of researchers, particularly in the last decade. Microfluidics has proven to be an extraordinary working platform and different configurations of potential extensional microrheometers have been proposed. In this review, we present an overview of several successful designs, together with a critical assessment of their capabilities and limitations