Directional approach to spatial structure of solutions to the Navier-Stokes equations in the plane

We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of $u_\infty$. Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as \emph{time} direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations

Improved modelling of helium and tritium production for spallation targets

Reliable predictions of light charged particle production in spallation reactions are important to correctly assess gas production in spallation targets. In particular, the helium production yield is important for assessing damage in the window separating the accelerator vacuum from a spallation target, and tritium is a major contributor to the target radioactivity. Up to now, the models available in the MCNPX transport code, including the widely used default option Bertini-Dresner and the INCL4.2-ABLA combination of models, were not able to correctly predict light charged particle yields. The work done recently on both the intranuclear cascade model INCL4, in which cluster emission through a coalescence process has been introduced, and on the de-excitation model ABLA allows correcting these deficiencies. This paper shows that the coalescence emission plays an important role in the tritium and $^3He$ production and that the combination of the newly developed versions of the codes, INCL4.5-ABLA07, now lead to good predictions of both helium and tritium cross sections over a wide incident energy range. Comparisons with other available models are also presented.Comment: 6 pages, 9 figure

INCL Intra-Nuclear Cascade and ABLA De-excitation Models in GEANT4

peer reviewe

New potentialities of the Liège intranuclear cascade (INCL) model for reactions induced by nucleons and light charged particles

The new version (INCL4.6) of the Li`ege intranuclear cascade (INC) model for the description of spallation reactions is presented in detail. Compared to the standard version (INCL4.2), it incorporates several new features, the most important of which are: (i) the inclusion of cluster production through a dynamical phase space coalescence model, (ii) the Coulomb deflection for entering and outgoing charged particles, (iii) the improvement of the treatment of Pauli blocking and of soft collisions, (iv) the introduction of experimental threshold values for the emission of particles, (v) the improvement of pion dynamics, (vi) a detailed procedure for the treatment of light-cluster induced reactions taking care of the effects of binding energy of the nucleons inside the incident cluster and of the possible fusion reaction at low energy. Performances of the new model concerning nucleon-induced reactions are illustrated. Whenever necessary, the INCL4.6 model is coupled to the ABLA07 deexcitation model and the respective merits of the two models are then tentatively disentangled. Good agreement is generally obtained in the 200 MeV-2 GeV range. Below 200 MeV and down to a few tens of MeV, the total reaction cross section is well reproduced and differential cross sections are reasonably well described. The model is also tested for light-ion induced reactions at low energy, below 100 MeV incident energy per nucleon. Beyond presenting the update of the INCL4.2 model, attention has been paid to applications of the new model to three topics for which some particular aspects are discussed for the first time: production of clusters heavier than alpha particles, longitudinal residue recoil velocity and its fluctuations, total reaction cross section and the residue production cross sections for low energy incident light ions.Comment: 29 pages, 26 figure

Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall

Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction

Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model. The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to translation, global minimizer of the associated free energy. Furthermore, we prove that this global minimizer is a radially decreasing compactly supported continuous density function which is smooth inside its support, and it is characterized as the unique compactly supported stationary state of the evolution model. This unique profile is the clear candidate to describe the long time asymptotics of the diffusion dominated classical Keller-Segel model for general initial data.Comment: 30 pages, 2 figure

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of compact support for the vorticit

Proton NMR visible mobile lipid signals in sensitive and multidrug-resistant K562 cells are modulated by rafts

BACKGROUND: Most cancer cells are characterized by mobile lipids visible on proton NMR ((1)H-NMR), these being comprised mainly of methyl and methylene signals from lipid acyl chains. Erythroleukemia K562 cells show narrow signals at 1.3 and 0.9 ppm, corresponding to mobile lipids (methylene and methyl, respectively), which are reduced when K562 cells are multidrug resistant (MDR). While the significance of the mobile lipids is unknown, their subcellular localization is still a matter of debate and may lie in the membrane or the cytoplasm. In this study, we investigate the role of cholesterol in the generation of mobile lipid signals. RESULTS: The proportion of esterified cholesterol was found to be higher in K562-sensitive cells than in resistant cells, while the total cholesterol content was identical in both cell lines. Cholesterol extraction in the K562 wild type (K562wt) cell line and its MDR counterpart (K562adr), using methyl-β-cyclodextrin, was accompanied by a rise of mobile lipids in K562wt cells only. The absence of caveolae was checked by searching for the caveolin-1 protein in K562wt and K562adr cells. However, cholesterol was enriched in another membrane microdomain designated as "detergent-insoluble glycosphingomyelin complexes" or rafts. These microdomains were studied after extraction with triton X-100, a mild non-ionic detergent, revealing mobile lipid signals preserved only in the K562wt spectra. Moreover, following perturbation/disruption of these microdomains using sphingomyelinase, mobile lipids increased only in K562wt cells. CONCLUSION: These results suggest that cholesterol and sphingomyelin are involved in mobile lipid generation via microdomains of detergent-insoluble glycosphingomyelin complexes such as rafts. Increasing our knowledge of membrane microdomains in sensitive and resistant cell lines may open up new possibilities in resistance reversion