Investigating Route to Chaos in Nonlinear Plasmonic Dimer

The route to chaos of a plasmonic dimer formed of two identical nanoparticles with Kerr-type nonlinear response and illuminated by an external electric field is reported. It is shown that this system has a complex dynamical behavior with chaotic nature. This complexity is analyzed using Lyapunov exponents, the Kaplan–Yorke dimension, and correlation dimensions. The existence of familiar period-doubling sequences route to chaos is pointed out, and domains corresponding to the onset of period doubling and chaos in the plane of parameters are evidenced.     

Moving immersed boundary method

A novel implicit immersed boundary method of high accuracy and efficiency is presented for the simulation of incompressible viscous flow over complex stationary or moving solid boundaries. A boundary force is often introduced in many immersed boundary methods to mimic the presence of solid boundary, such that the overall simulation can be performed on a simple Cartesian grid. The current method inherits this idea and considers the boundary force as a Lagrange multiplier to enforce the no‐slip constraint at the solid boundary, instead of applying constitutional relations for rigid bodies. Hence excessive constraint on the time step is circumvented, and the time step only depends on the discretization of fluid Navier‐Stokes equations, like the CFL condition in present work. To determine the boundary force, an additional moving force equation is derived. The dimension of this derived system is proportional to the number of Lagrangian points describing the solid boundaries, which makes the method very suitable for moving boundary problems since the time for matrix update and system solving is not significant. The force coefficient matrix is made symmetric and positive definite so that the conjugate gradient method can solve the system quickly. The proposed immersed boundary method is incorporated into the fluid solver with a second‐order accurate projection method as a plug‐in. The overall scheme is handled under an efficient fractional step framework, namely, prediction, forcing, and projection. Various simulations are performed to validate current method, and the results compare well with previous experimental and numerical studies.     

2‐Arylhydrazono‐3‐oxopropanals in heterocyclic synthesis: Synthesis of arylazopyrazole,arylazoisoxazole and dialkylpyridazine‐5,6‐dicarboxylate derivatives. New one‐step synthesis of arylazopyrimidines

A novel synthesis of arylpyrazole, isoxazole, dialkyl 1,6‐dihydropyridazine 5,6‐dicarboxylate derivatives and a new one‐step synthesis of azolopyrimidines under microwave‐assisted conditions are reported.     

New efficient route to dissymmetric 2,4-di(het)aryl-pyrido[3,2-d]pyrimidines via regioselective cross-coupling reactions

The first access to dissymmetric 2,4-di(het)aryl-pyrido[3,2-d]pyrimidines III is reported. Two mild alternative routes led to the rarely targeted compounds from 2,4-dichloro- and 2-chloro-4-isopropylsulfanyl-pyrido[3,2-d]pyrimidine by two successive palladium-catalyzed reactions involving an original regioselective chlorine discrimination. Alternatively, type III compounds were elaborated from 2 by C-2 chlorine further displacement of the C-4 isopropylsulfanyl group, which acted as a temporary C-4 protecting group. These results open the way to innovative synthesis strategies of various bis-functionalized pyrimidine series.     

Conversion of a porous material based on a Mn(II)-TCNQF(4) honeycomb net to a molecular magnet upon desolvation

Removal of methanol molecules from the interstices of a metal-organic framework based on a 2-D hexagonal Mn(II)-TCNQF(4) net results in stronger magnetic interactions and leads to a glassy magnetically ordered state; the magnetic behavior can be reversibly cycled upon solvation-desolvation of the material.     

Additive Maps Preserving Local Spectrum

Let X be a complex Banach space, and let be the space of bounded operators on X. Given and x ∈ X, denote by σ_T (x) the local spectrum of T at x. We prove that if is an additive map such that

Augmented hybrid finite element method for domain decomposition

We present an Augmented Hybrid Finite Element Method for Domain Decompositon. In this method, finite element approximations are defined independently on each subdomain and do not match at interface. This dows the user to mda local change of design, of meshes on one aubdomain without modifying other subdomains. Optimal reaults are obtained for a second-order model problem.     

Proximal methods for a class of bilevel monotone equilibrium problems

We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a simple proximal method. Under mild conditions, the weak convergence of the sequences generated by the algorithm is obtained. Using this result we obtain corollaries which improve several corresponding results in this field.