Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Group B Streptococcus GAPDH Is Released upon Cell Lysis, Associates with Bacterial Surface, and Induces Apoptosis in Murine Macrophages

Glyceraldehyde 3-phosphate dehydrogenases (GAPDH) are cytoplasmic glycolytic enzymes that, despite lacking identifiable secretion signals, have been detected at the surface of several prokaryotic and eukaryotic organisms where they exhibit non-glycolytic functions including adhesion to host components. Group B Streptococcus (GBS) is a human commensal bacterium that has the capacity to cause life-threatening meningitis and septicemia in newborns. Electron microscopy and fluorescence-activated cell sorter (FACS) analysis demonstrated the surface localization of GAPDH in GBS. By addressing the question of GAPDH export to the cell surface of GBS strain NEM316 and isogenic mutant derivatives of our collection, we found that impaired GAPDH presence in the surface and supernatant of GBS was associated with a lower level of bacterial lysis. We also found that following GBS lysis, GAPDH can associate to the surface of many living bacteria. Finally, we provide evidence for a novel function of the secreted GAPDH as an inducer of apoptosis of murine macrophages

Thermal behavior of ceramic particles in a gaseous medium at high temperature

Numerical simulation of the interaction between the spherical particle and plasma gas is carried out. The aim of this study is to investigatethermal transfer between the plasma gas and solid particle during the plasma spray process and to validate the well-known empirical correlation of the Ranz and Marshall. In the conditions of molten or semi-molten states of prepared substrate, the medium (plasma jet) can affect the high velocities of particles. On the basis of direct numerical simulation, the computational analysis has been carried out by using computational fluid dynamics (CFD) of heat transfer in atmospheric pressure and mid-temperature range (3000k–12000k) of a plasma flow over a spherical particle. Our proposed model improves correlation with experiments compared to the existing approaches in the literature

Electrified viscous thin film flow over topography

The gravity-driven flow of a liquid film down an inclined wall with periodic indentations in the presence of a normal electric field is investigated. The film is assumed to be a perfect conductor, and the bounding region of air above the film is taken to be a perfect dielectric. In particular, the interaction between the electric field and the topography is examined by predicting the shape of the film surface under steady conditions. A nonlinear, non-local evolution equation for the thickness of the liquid film is derived using a long-wave asymptotic analysis. Steady solutions are computed for flow into a rectangular trench and over a rectangular mound, whose shapes are approximated with smooth functions. The limiting behaviour of the film profile as the steepness of the wall geometry is increased is discussed. Using substantial numerical evidence, it is established that as the topography steepness increases towards rectangular steps, trenches, or mounds, the interfacial slope remains bounded, and the film does not touch the wall. In the absence of an electric field, the film develops a capillary ridge above a downward step and a slight depression in front of an upward step. It is demonstrated how an electric field may be used to completely eliminate the capillary ridge at a downward step. In contrast, imposing an electric field leads to the creation of a free-surface ridge at an upward step. The effect of the electric field on film flow into relatively narrow trenches, over relatively narrow mounds, and down slightly inclined substrates is also considered

Thermal behavior of ceramic particles in a gaseous medium at high temperature

Numerical simulation of the interaction between the spherical particle and plasma gas is carried out. The aim of this study is to investigatethermal transfer between the plasma gas and solid particle during the plasma spray process and to validate the well-known empirical correlation of the Ranz and Marshall. In the conditions of molten or semi-molten states of prepared substrate, the medium (plasma jet) can affect the high velocities of particles. On the basis of direct numerical simulation, the computational analysis has been carried out by using computational fluid dynamics (CFD) of heat transfer in atmospheric pressure and mid-temperature range (3000k–12000k) of a plasma flow over a spherical particle. Our proposed model improves correlation with experiments compared to the existing approaches in the literature

Investigation of the milling route for the development of colloidal suspensions to be used as binder in refractory castables

Refractories castables bonded with CAC (calcium aluminate cement) have a limitation when they are used at high temperature in micro-silica containing system and/or in acidic corrosive environments. The CAC binder reacts with the micro-silica and/or acidic components to form liquid/viscous compounds deteriorating the refractory material.Refractory castables bonded with HA (hydratable alumina) perform better in these environments. However, the drying step of such materials needs time and energy for the water evacuation to avoid the lining cracking.The use of CS (colloidal silica) as binder seems to hinder the drawback of CAC and HA binders. However, the presence of free amorphous silica in the castable composition limits their uses in basic environments by forming liquid/viscous phases at high temperature with a reduction of castable refractoriness.In this context, new colloidal bonding systems that could improve the high performances of refractory castables such as boehmite and spinel colloidal suspensions, were developed

Interpolation and partial differential equations

One of the main motivations for developing the theory of interpolation was to apply it to the theory of partial differential equations (PDEs). Nowadays interpolation theory has been developed in an almost unbelievable way {see the bibliography of Maligranda [Interpolation of Operators and Applications (1926-1990), 2nd ed. (Luleå University, Luleå, 1993), p. 154]}. In this article some model examples are presented which display how powerful this theory is when dealing with PDEs. One main aim is to point out when it suffices to use classical interpolation theory and also to give concrete examples of situations when nonlinear interpolation theory has to be applied. Some historical remarks are also included and the relations to similar results are pointed outGodkänd; 1994; 20070208 (kani)</p