Helium ion distributions in a 4 kJ plasma focus device by 1 mm-thick large-size polycarbonate detectors

Helium ion beam profile, angular and iso-ion beam distributions in 4 kJ Amirkabir plasma focus (APF) device were effectively observed by the unaided eyes and studied in single 1 mm-thick large-diameter (20 cm) polycarbonate track detectors (PCTD). The PCTDs were processed by 50 Hz–HV electrochemical etching using a large-size ECE chamber. The results show that helium ions produced in the APF device have a ring-shaped angular distribution peaked at an angle of ∼±60°$\sim \pm 60\mathrm{°}$ with respect to the top of the anode. Some information on the helium ion energy and distributions is also provided. The method is highly effective for ion beam studies.     

A facile route to diastereomeric phosphorus ylides. Chemoselective synthesis of dialkyl (E)-2-[1-(2-oxocyclopentylidene)ethyl]-2-butenedioates

2-Acetylcyclopentanone undergoes a smooth reaction with triphenylphosphine and dialkyl acetylenedicarboxylates to produce dialkyl 2-(1-acetyl-2-oxocyclopentyl)-3-(1,1,1-triphenyl-lambda(5)-phosphanylidene)succinates. These compounds undergo intramolecular Wittig reactions in boiling benzene to produce highly strained spirocyclobutene derivatives, which spontaneously undergo ring-opening reactions to produce dialkyl (E)-2-[1-(2-oxocyclopentyliden)ethyl]-2-butenedioates.     

Stability and Convergence Analyses of the FDM Based on Some L-Type Formulae for Solving the Subdiffusion Equation

Some well-known L-type formulae, i.e., L1, L1-2, and L1-2-3 formulae, are usually employed to approximate the Caputo fractional derivative of order α ∈ (0, 1). In this paper, we aim to elaborate on the stability and convergence analyses of some finite difference methods (FDMs) for solving the subdiffusion equation, i.e., a diffusion equation which exploits the Caputo time-fractional derivative of order $α$. In fact, the FDMs considered here are based on the usual central difference scheme for the spatial derivative, and the Caputo derivative is approximated by using methods such as the L1, L1-2, and L1-2-3 formulae. Thanks to a specific type of the discrete version of the Gronwall inequality, we show that the FDMs are unconditionally stable in the maximum norm and also discrete $H^1$ norm. Then, we prove that the finite difference method which uses the L1, L1-2, and L1-2-3 formulae has the global order of convergence $2−α$, $3−α$, and 3, respectively. Finally, some numerical tests confirm the theoretical results. A brief conclusion finishes the paper.     

Mean field modeling of isotropic random Cauchy elasticity versus microstretch elasticity

We show that the averaged response of random isotropic Cauchy elastic material can be described analytically. It leads to a higher gradient model with explicit expressions for the dependence on the second derivatives of the mean field. A subsequent penalty formulation coincides with a linear elastic micro-stretch model with specific choice of constitutive parameters, depending only on the average cut-off length (the internal characteristic length scale L_c > 0). Thus the microstretch displacement field can be interpreted as an approximated mean field response for these parameter ranges. The mean field free energy in this micro-stretch formulation is not uniformly pointwise positive, nevertheless, the model is well posed.      

Tuning of full band gap in anisotropic photonic crystal slabs using a liquid crystal

We analyze the tunability of full band gap in photonic crystal slabs created by square and triangular lattices of air holes in anisotropic tellurium background, considering that the regions above and below the slab are occupied by SiO₂ and the holes are infiltrated with liquid crystals. Using the supercell method based on plane wave expansion, we study the variation of full band gap by changing the optical axis orientation of liquid crystal. Our results demonstrate the existence and remarkable tunability of full band gap in both square and triangular lattices, largest band gap and tunability being obtained for the triangular lattice.