We address the problem of local and global well-posedness of Gross-Neveu (GN) equations for low regularity initial data. Combined with the standard machinery of X R , Y R and X s,b spaces, we obtain local-wellposedness of (GN) for initial data u, v ∈ H s with s ≥ 0. To prove the existence of global solution for the critical space L 2 , we show non concentration of L 2 norm.
Submicrosized chevrel Mo 6 S 8 powder is synthesized using mechanical milling of the starting materials and the powder yield is increased by using modified synthesis method. The effect of particle size is investigated using various electrochemical techniques. The submicrosized chevrel shows enhanced discharge capacity compared with that of microsized chevrel, and voltage profile indicates that the low capacity arising from Mg trapping at the Mg-1 site is improved for submicrosized chevrel. Mg trapping is also verified by ex situ X-ray diffraction measurement and the results are in good agreement with the electrochemical profile. Open-circuit voltage measurements and AC-impedance spectroscopy are used to identify the kinetics of Mg 2+ insertion. The improved electrochemical properties obtained with the submicrosized chevrel are attributed to the smaller particles that provide shorter diffusion lengths for Mg 2+ ions.
We study the emergence of asymptotic patterns in Winfree ensemble such as the partial/complete phase-locking and bump states under the effect of heterogeneous frustrations. Although the Winfree model is the first model for the synchronization of limit-cycle oscillators, there is little literature on the mathematical validity of asymptotic patterns compared to the vast literature of the well-studied Kuramoto model. Recently, it has received a renewed attention in nonlinear dynamics and statistical physics communities due to its diverse asymptotic patterns that it can generate. In particular, we provide a rigorous result on the existence of bump states in a homogeneous ensemble with the same natural frequency. Our provided results exhibit the robustness of emerging asymptotic patterns with respect to frustrations. We derive several sufficient frameworks for the unique existence of an equilibrium state, bump states and uniform stability with respect to initial data.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.