A martingale approach to state estimation in delay-differential systems

A rigorous derivation of filtering arid smoothing equations for linear stochastic systems with time delay is presented. The estimation equations are obtained in term of the innovation process of the problem under consideration. The method used is based on a representation theorem on Gaussian martingales.     

Strong isospin violation andη−π mixing in |ΔS|=1 weak transition

We consider the effects ofη−π mixing on the violation of the |ΔI|=1/2 rule in |ΔS|=1 weak transitions. The processes considered are theK→2π,K→3π, Λ, Ξ and Λ hyperon decays.     

Covariance of spontaneous symmetry breaking in non-inertial frames

It is pointed out that contrary to a recent claim the process of symmetry breaking is covariant in a non-inertial frame.     

Local-field effect near the surface of dipolar lattices

The local-field correction near the surface of a dipolar crystal has been studied by explicitly computing the non-retarded electric field produced by a finite array of classical point dipoles induced by a time-varying electric field. Crystals of simple cubic, f.c.c. and b.c.c. structures are considered, and results presented for the self-consitent dipole moment and the local electric field at a lattice point. The utility of the method and its possible applications are discussed.     

\mathcal{P}\mathcal{T}-symmetric quartic anharmonic oscillator and position-dependent mass in a perturbative approach

To lowest order of perturbation theory we show that an equivalence can be established between a -symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian h. An important feature of h is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also determine the associated physical quantities.     

Exploration of the secondary structure specific differential solvation dynamics between the native and molten globule states of the protein HP-36

Recent experiments have shown that the time dependence of fluorescence Stokes shift of a chromophore is substantially different when the chromophore is located in a molten globule (MG) state and in the native state of the same protein. To understand the origin of this difference, particularly the role of water in the differential solvation of the protein in the native and the MG states, we have carried out fully atomistic molecular dynamics simulations with explicit water of a partially unfolded MG state of the protein HP-36 and compared the results with the solvation dynamics of the protein in the folded native state. It is observed that the polar solvation dynamics of the three helical segments of the protein is influenced in a nonuniform heterogeneous manner in the MG state. While the equilibrium solvation time correlation function for helix-3 has been found to relax faster in the MG state as compared to that in the native state, the decay of the corresponding function for the other two helices slows down in the MG state. A careful analysis shows that the origin of such heterogeneous relative solvation behavior lies in the differential location of the polar probe residues and their exposure to bulk solvent. We find a significant negative cross-correlation between the contribution (to the solvation energy of a tagged amino acid residue) of water and the other groups of the protein, indicating a competing role in solvation. The sensitivity of solvation dynamics to the secondary structure and the immediate environment can be used to discriminate the partially unfolded and folded states. These results therefore should be useful in explaining recent solvation dynamics experiments on native and MG states of proteins.     

Structural and magnetic study of swift heavy ion irradiated W/Fe multilayer structure

The present study reports the effect of swift heavy ion irradiation on structural and magnetic properties of sputtered W/Fe multilayer structure (MLS) having bilayer compositions of [W(10 Å)/Fe(20 Å)]_10BL. The MLS is irradiated by 120 MeV Au⁹⁺ ions of fluences 1×10¹³ and 4×10¹³ ions/cm². Techniques like X-ray reflectivity (XRR), cross-sectional transmission electron microscopy (X-TEM) and DC magnetization with a vibrating sample magnetometer (VSM) are used for structural and magnetic characterization of pristine and irradiated MLS. Analysis of XRR data using Parratt’s formalism shows a significant increase in W/Fe layer roughness. X-TEM studies reveal that intra-layer microstructure of Fe layers in MLS becomes nano-crystalline on irradiation. DC magnetization study shows that with spacer layer thickness interlayer coupling changes between ferromagnetic to antiferromagnetic.     

Franck-Condon factors and r-centroids of B-X, C-X and C-A band systems of AlO molecule

Using the high resolution Fourier transform spectrometer the B²Σ⁺-X²Σ⁺ band system of AlO molecule has been recorded. The rotational structure of eighteen bands belonging to B²Σ⁺-X²Σ⁺ transition of AlO have been analyzed which led to accurate rotational and vibrational constants of ground and excited states. A few bands, viz. (2, 1), (3, 2), (4, 3), (2, 3), (3, 4), (4, 5), and (5, 6) were analyzed for the first time. Using these constants, the Franck-Condon factors and r-centroids were computed for the bands of B-X, C-X and C-A band systems for the v′ = 0-8; v″ = 0-8 matrix using the method developed by Jarmain and Nicholls. The F-C factors and r-centroids obey the established relationships.