Dielectric relaxation phenomena of rigid polar liquid molecules under giga hertz electric field

The dielectric relaxation phenomena of rigid polar liquid molecules chloral and ethyltrichloroacetate (j) in benzene, n-hexane and n-heptane (i) under 4.2, 9.8 and 24.6 GHz electric fields at 30°C are studied to show the possible existence of double relaxation times τ ₂ and τ ₁ for rotations of the whole and the flexible parts of molecules. The probability of showing double relaxation is more in aliphatic solvents indicating their nonrigidity. The symmetric and asymmetric distribution parameters γ and δ are obtained from X _ij ^′ /X _0ij and X _ij ^″ /X _0ij and w _j →0 where X _ij ^′ and X _ij ^″ are real and imaginary parts of the complex orientational susceptibility X _i ^* and X _0ij is the low frequency susceptibility which is real. X _ij ’s are involved with the measured dielectric relative permittivities ε _ij ^′ , ε _in ^″ , ε _0ij and ε _∞ij of solutions. The theoretical weighted contributions c ₁ and c ₂ towards dielectric dispersions by Fröhlich’s method are compared with the experimental ones obtained from the graphical variation of X _ij ^′ /X _0ij and X _ij ^″ /X _0ij with weight fractions w _j ’s at w _j → 0. The measured dipole moments μ ₂ and μ ₁ of the whole and the flexible part of a polar molecule in terms of the linear coefficients β’s of X _ij ^′ ’s with w _j ’s and the estimated τ ₂ and τ ₁ reveal their associations with aliphatic solvents. The theoretical dipole moments μ _theo’s from the available bond angles and bond moments of the substituent polar groups of the molecules with the estimated μ’s suggest the mesomeric, inductive and electromeric effects in them under GHz electric field.     

On the second eigenvalue of the dirichlet laplacian

The multiplicity of the second eigenvalue of the Dirichlet Laplacian on smooth Riemannian surfaces with boundary that satisfy certain convexity condition is at most two. The proof is based on variational formulas for eigenvalues under the change of the domain.     

Microwave absorption studies of MgB2 superconductor

Microwave absorption studies have been carried out on MgB₂ superconductor using a standard X-band EPR spectrometer. The modulated low-field microwave absorption signals recorded for polycrystalline (grain size ∼ 10 μm) samples suggested the absence of weak-link character. The field dependent direct microwave absorption has been found to obey a ✓H dependence with two different slopes, which indicated a transition from strongly pinned lattice to flux flow regime.