Application of HPM to Solve Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates

In this article, Homotopy Perturbation Method (HPM) is used to provide two approximate solutions to the nonlinear differential equation that describes the behaviour for the unsteady squeezing flow of a second grade fluid between circular plates. Comparing results between approximate and numerical solutions shows that our results are capable to provide an accurate solution and are extremely efficient

A High Accurate Approximation for a Galactic Newtonian Nonlinear Model Validated by Employing Observational Data

This article proposes Perturbation Method (PM) to solve nonlinear problems. As case study PM is employed to provide a detailed study of a nonlinear galactic model. Our approach is rather elementary and seeks to explain as much detail as possible the material of this work.In particular our solution gives rise qualitatively, to the known flat rotation curves. In fact, we compare the numerical solution and the obtained approximation by employing observational data proving the validity and high accuracy of the model under study

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM

Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM

Classical Perturbation Method for the Solution of a Model of Diffusion and Reaction

In this paper, we employ perturbation method (PM) to solve nonlinear problems. As case study PM is employed to obtain approximate solutions for the nonlinear differential equation that models the diffusion and reaction in porous catalysts. We find that the square residual error (S.R.E) of our solutions is in the range and this requires only the third order approximation of PM, which shows the effectiveness of the method

The scattering of SH waves by a finite crack with a superposition based diffraction technique

The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencie

Fungal Virulence and Development Is Regulated by Alternative Pre-mRNA 3′End Processing in Magnaporthe oryzae

RNA-binding proteins play a central role in post-transcriptional mechanisms that control gene expression. Identification of novel RNA-binding proteins in fungi is essential to unravel post-transcriptional networks and cellular processes that confer identity to the fungal kingdom. Here, we carried out the functional characterisation of the filamentous fungus-specific RNA-binding protein RBP35 required for full virulence and development in the rice blast fungus. RBP35 contains an N-terminal RNA recognition motif (RRM) and six Arg-Gly-Gly tripeptide repeats. Immunoblots identified two RBP35 protein isoforms that show a steady-state nuclear localisation and bind RNA in vitro. RBP35 coimmunoprecipitates in vivo with Cleavage Factor I (CFI) 25 kDa, a highly conserved protein involved in polyA site recognition and cleavage of pre-mRNAs. Several targets of RBP35 have been identified using transcriptomics including 14-3-3 pre-mRNA, an important integrator of environmental signals. In Magnaporthe oryzae, RBP35 is not essential for viability but regulates the length of 3′UTRs of transcripts with developmental and virulence-associated functions. The Δrbp35 mutant is affected in the TOR (target of rapamycin) signaling pathway showing significant changes in nitrogen metabolism and protein secretion. The lack of clear RBP35 orthologues in yeast, plants and animals indicates that RBP35 is a novel auxiliary protein of the polyadenylation machinery of filamentous fungi. Our data demonstrate that RBP35 is the fungal equivalent of metazoan CFI 68 kDa and suggest the existence of 3′end processing mechanisms exclusive to the fungal kingdom

Purinergic signalling and immune cells

This review article provides a historical perspective on the role of purinergic signalling in the regulation of various subsets of immune cells from early discoveries to current understanding. It is now recognised that adenosine 5'-triphosphate (ATP) and other nucleotides are released from cells following stress or injury. They can act on virtually all subsets of immune cells through a spectrum of P2X ligand-gated ion channels and G protein-coupled P2Y receptors. Furthermore, ATP is rapidly degraded into adenosine by ectonucleotidases such as CD39 and CD73, and adenosine exerts additional regulatory effects through its own receptors. The resulting effect ranges from stimulation to tolerance depending on the amount and time courses of nucleotides released, and the balance between ATP and adenosine. This review identifies the various receptors involved in the different subsets of immune cells and their effects on the function of these cells

Diffuse fields in dynamic elasticity

International audiencen this article the problem of Green function retrieval from correlations is approached from a theoretical point of view and for this purpose an integral identity is considered: a representation theorem of the correlation type for an inhomogeneous region embedded in a homogeneous space. The full homogeneous case is studied with the theorem and it is concluded that, in the resulting field, the energy is equipartitioned. In infinite space this means that the ratio of P and S energy densities stabilizes to a constant value. That equipartition is reached in the classical sense is also demonstrated. Thus, in infinite space the energy densities associated with the possible degrees of freedom tend to share in equal parts the available energy. The representation theorem permits the verification of the well known result that by averaging correlations of motions from diffuse, equipartitioned fields within an inhomogeneous, anisotropic, elastic medium it is possible to retrieve its Green function. As a result of this it is shown that the average autocorrelation of the diffuse displacement field at a point is proportional to the imaginary part of the Green function at the source precisely at this point. As a consequence, the energy density of the diffuse field is proportional to the trace of the imaginary part of the Green tensor at the source. Thus, the analytical form of the Green function permits the establishment, in and around an inhomogeneous region, of the theoretical energy density of a diffuse field. In both homogeneous and inhomogeneous cases (i.e. localized elastic inclusions or cavities) the equipartition of the background illumination (the so called incident field in scattering theory) is a necessary and sufficient condition to retrieve the exact Green function from correlations. Local effects lead to energy ratios that fluctuate in space and frequency. The boundary of a half-space produces in its interior fluctuations of energy densities that are local effects of the diffuse field. These results may be useful to assess the diffuse nature of seismic ground motion from a limited set of observation points and to detect the presence of a target by its signature in the distribution of diffuse energy