Blow-Up Rate Estimates and Liouville Type Theorems for a Semilinear Heat Equation with Weighted Source

We study the Liouville-type theorem for the semilinear parabolic equation \(u_t-\Delta u =|x|^a u^p\) with \(p>1\) and \(a\in {\mathbb R}\). Relying on the recent result of Quittner (Math Ann, doi: 10.1007/s00208-015-1219-7, 2015), we establish the optimal Liouville-type theorem in dimension \(N=2\), in the class of nonnegative bounded solutions. We also provide a partial result in dimension \(N\ge 3\). As applications of Liouville-type theorems, we derive the blow-up rate estimates for the corresponding Cauchy problem.     

Mössbauer Studies of Core-Shell FeO/Fe3O4 Nanoparticles

Physics of the Solid State - FeO/Fe3O4 nanoparticles were synthesized by thermal decomposition. Electron microscopy revealed that these nanoparticles were of the core-shell type and had a spherical...     

Anomalous flow deflection at earth's low-Alfvén-Mach-Number bow shock

Earth's magnetosphere is an obstacle to the supersonic solar wind and the bow shock is formed in the front side of it. In ordinary hydrodynamics, the flow decelerated at the shock is diverted around the obstacle symmetrically about the Earth-Sun line, which is indeed observed in the magnetosheath most of the time. Here we show a case under a very low-density solar wind in which duskward flow was observed in the dawnside magnetosheath. A Rankine-Hugoniot test shows that the magnetic effect is crucial for this "wrong flow" to appear. A full three-dimensional magnetohydrodynamics (MHD) simulation of the situation confirming this interpretation and earlier simulations is also performed. It is illustrated that in addition to the "wrong flow" feature, various peculiar characteristics appear in the global picture of the MHD flow interaction with the obstacle.     

Insights into the cooperativity between multiple interactions of dimethyl sulfoxide with carbon dioxide and water

Interactions of dimethyl sulfoxide with carbon dioxide and water molecules which induce 18 significantly stable complexes are thoroughly investigated. An addition of CO₂ or H₂O molecules into the DMSO⋯1CO₂ and DMSO⋯1H₂O systems leads to an increase in the stability of the resulting complexes, in which it is larger for a H₂O addition than a CO₂. The overall stabilization energy of the DMSO⋯1,2CO₂ is mainly contributed by the S=O⋯C Lewis acid–base interaction, whereas the O − H⋯O hydrogen bond plays a significant role in stabilizing complexes of DMSO⋯1,2H₂O and DMSO⋯1CO₂⋯1H₂O. Remarkably, the complexes of DMSO⋯2H₂O are found to be more stable than DMSO⋯1CO₂⋯1H₂O and DMSO⋯2CO₂. The level of the cooperativity of multiple interactions in ternary complexes tends to decrease in going from DMSO⋯2H₂O to DMSO⋯1CO₂⋯1H₂O and finally to DMSO⋯2CO₂. It is generally found that the red shift of the O − H bond involved in an O − H⋯O hydrogen bond increases while the blue shift of a C − H bond in a C − H⋯O hydrogen bond decreases when a cooperative effect occurs in ternary complexes as compared to those of the corresponding binary complexes. © 2018 Wiley Periodicals, Inc.     

Perylene π‐Bridges Equally Delocalize Anions and Cations: Proportioned Quinoidal and Aromatic Content

A complete experimental and theoretical study has been carried out for aromatic and quinoidal perylene‐based bridges substituted with bis(diarylamine) and bis(arylimine) groups respectively. The through‐bridge inter‐redox site electronic couplings (V_AB) have been calculated for their respective mixed‐valence radical cation and radical anion species. The unusual similitudes of the resulting V_AB values for the given structures reveal the intervention of molecular shapes with balanced semi‐quinoidal/semi‐aromatic structures in the charge delocalization. An identical molecular object equally responding to the injection of either positive or negative charges is rare in the field of organic π‐conjugated molecules. However, once probed herein for perylene‐based systems, it can be extrapolated to other π‐conjugated bridges. As a result, this work opens the door to the rational design of true ambipolar bulk and molecular conductors.     

Evidence for electron acceleration up to approximately 300 keV in the magnetic reconnection diffusion region of earth's magnetotail

We report direct measurements of high-energy particles in a rare crossing of the diffusion region in Earth's magnetotail by the Wind spacecraft. The fluxes of energetic electrons up to approximately 300 keV peak near the center of the diffusion region and decrease monotonically away from this region. The diffusion region electron flux spectrum obeys a power law with an index of -3.8 above approximately 2 keV, and the electron angular distribution displays strong field-aligned bidirectional anisotropy at energies below approximately 2 keV, becoming isotropic above approximately 6 keV. These observations indicate significant electron acceleration inside the diffusion region. Ions show no such energization.     

A decomposition method using a pricing mechanism for min concave cost flow problems with a hierarchical structure

In this paper we develop a decomposition method using a pricing mechanism which has been widely applied to linear and convex programs for a class of nonconvex optimization problems that are min concave cost flow problems under directed, uncapacitated networks with a hierarchical structure.This paper was completed during the author's stay supported by a Sophia lecturing-research Grant at Sophia University, Tokyo, Japan.     

Observations of electron diffusion regions at the subsolar magnetopause

Electric and magnetic field observations on the Polar satellite at the subsolar magnetopause show that the magnetopause current is often striated. The largest of the resulting current channels are interpreted as electron diffusion regions because their widths are several electron skin depths and the electron flow U(e) within them does not satisfy E-->+U-->(e)xB-->=0. The data suggest that the magnetopause contains many such electron diffusion regions and that they are required because E-->xB-->/B(2) drifting electrons cannot carry the large filamentary currents imposed on the local plasma. The most probable interpretation of E-->+U-->(e)xB--> not equal 0 is that the pressure term on the right side of the generalized Ohm's law balances this inequality.     

Self- and mutual-diffusion coefficients measurements by 31P NMR 1D profiling and PFG-SE in dextran gels

31P NMR 1D profiling was successfully introduced to measure macroscale mutual-diffusion coefficients (D(m)) of phosphate ions in dextran gels. Series of 1D profiles describing the phosphate concentration along cylindrical dextran gels were acquired at different times. These profiles that included over 600 points could be fitted using equations derived from Fick's law, with D(m) as the single fitting parameter. Release and penetration profiles were recorded providing two alternative approaches for allowing the determination of D(m). The D(m) values were compared with microscale self-diffusion coefficients (D(s)) measured by pulsed field gradient spin echo (PFG-SE) technique. D(m) values, measured between 25 and 45 degrees C, were systematically lower than D(s). The experimental diffusion time and the associated diffusion length of D(s) (60 ms, 10 microm) are short compared to those of D(m) (up to 18 h, 50 mm). These scale differences are considered to be the origin of different D(s) and D(m) and provide information relative to the network in these gels.