Haar wavelet method for solving some nonlinear Parabolic equations

Wavelet transform or wavelet analysis is a recently developed mathematical tool in applied mathematics. In this paper, we develop an accurate and efficient Haar transform or Haar wavelet method for some of the well-known nonlinear parabolic partial differential equations. The equations include the Nowell-whitehead equation, Cahn-Allen equation, FitzHugh-Nagumo equation, Fisher’s equation, Burger’s equation and the Burgers-Fisher equation. The proposed scheme can be used to a wide class of nonlinear equations. The power of this manageable method is confirmed. Moreover the use of Haar wavelets is found to be accurate, simple, fast, flexible, convenient, small computation costs and computationally attractive.     

Ab-Initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H₃C? NO₂ bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H₃C? NO₂ bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H₃C? NO₂ bond dissociation energies.     

Industrial cutting waste granite dust reinforced cardanol benzoxazine/epoxy resin hybrid composites for high-voltage electrical insulation applications

An attempt has been made to develop hybrid composites from benzoxazine monomer (C-ddm) hybridized with DGEBA epoxy resin (EP) and reinforced with varying weight percentages (20 wt%, 40 wt%, 60 wt%, 80 wt% and 100 wt%) of glycidoxypropyltrimethoxy- silane (GPTMS) functionalized granite dust (GD) obtained from industrial granite cutting and polishing process in order to utilize them for electrical insulation applications. The thermal stability of granite dust reinforced poly(EP-co-C-ddm) composites was studied by TGA analysis. Among the composites samples studied, 100 wt% GD reinforced poly(EP-co-C-ddm) composites possess better thermal stability than that of other neat matrices and composites. Among the composites prepared using varying weight percentages of functionalized GD reinforcement, it was observed that 80 wt% GD reinforced poly(EP-co-C-ddm) composites possesses better hydrophobic character than that of other neat matrices and composites. The value of LOI calculated for neat matrix (poly[EP-co-C-ddm]) and 20 wt%, 40 wt%, 60 wt%, 80 wt% and 100 wt% GD reinforced composites was found to be 22, 28, 34, 40, 43 and 45 respectively. The 80 wt% GD reinforced poly(EP-co-C-ddm) composites possess the higher values of tensile strength and flexural strength of 47 MPa and 140 MPa, respectively than those of their samples. The values of electrical surface resistivity and electrical volume resistivity of all the neat matrices and GD reinforced polybenzoxazine composites were found to be in the order of 10¹² and 10¹³ respectively. The values of dielectric strength obtained from break down voltage (BDV) for neat matrix [poly(EP-co-C-ddm)] and 20 wt%, 40 wt%, 60 wt%, 80 wt% and 100 wt% of GD reinforced poly(EP-co-C-ddm) composites are 15.0, 15.5, 16.5, 17.0, 17.0 and 17.0 kV/mm, respectively. Data obtained from thermal stability, hydrophobic behavior and dielectric studies it was inferred that the hybrid polymer composites developed in the present work can be conveniently used in the form insulators, sealants, adhesives and matrices where application demands at high-performance industrial and engineering applications.     

Synthesis of a novel cyclic donor-acceptor conjugate for selective recognition of ATP

[reaction and structures: see text] Novel cyclophane 1 was synthesized, and its interactions with phosphate, adenosine, AMP, ADP, and ATP have been investigated. With addition of ATP, significant decrease in absorbance of 1 was observed, whereas other guest molecules showed negligible effect. The complex between 1 and ATP was confirmed through cyclic voltammetry and 1H NMR. The uniqueness of the system is that it complexes selectively with ATP in a cavity and involves synergistic effects of both electrostatic and pi-pi stacking interactions.     

Synthesis,polymerization, and thermal properties of a new acetylene-terminated schiff base

A new acetylene-terminated Schiff base monomer, N,N′-(1,4-phenylenedimethylidyne)-bis-(4-ethynylaniline) (PPP), was synthesized and was characterized by nuclear magnetic resonance and infrared spectroscopy. This monomer was then polymerized to yield a new polymer (PPPP) with alternating units of aromatic imine and diacetylene via an oxidative coupling polymerization of the acetylenic terminal groups. The monomer was also polymerized by thermal curing at elevated temperatures up to 400°C to afford a crosslinked polymer network without significant structural decomposition. Thermal properties and thermal reactions of the monomer and the polymers were studied by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). The polymers exhibit excellent thermal stabilities in an inert atmosphere. Electronic properties of the polymers are also discussed.     

Electron spin resonance in X-irradiated sodium sulphate

Reliable results are reported for the various triple-dipole dispersion energy coefficients needed to evaluate the (exact) triple-dipole dispersion energy for all three-body interactions involving He, Ne, Ar, Kr, Xe, H₂, N₂, CO, O₂ and NO, and at least one molecule. A total of 645 unique coefficients, corresponding to 185 unique interactions, are considered.     

Investigation of glassy behavior in lead barium ytterbium tantalate relaxors

The glassy behavior of lead barium ytterbium tantalate relaxors has been investigated. The frequency dependence of the temperature, T′_m (the temperature corresponding to the maximum value dielectric constant) is analyzed using Vogel-Fulcher relation and power law. The fitting parameters reveal that the power law explains the relaxation mechanism much better than the Vogel-Fulcher relation. The temperature dependence of dielectric constant at temperatures much higher and lower than T′_m is analyzed by two exponential functions, which gives an idea about the production of polar clusters at high temperature and the distribution of freezing temperatures at lower temperature.     

Ab-initio electrostatic molecular potential contour maps for initiation step and Ab-Initio MRD-CI calculations for propagation step of cationic polymerization of oxetanes

The initiation step in the cationic polymerization of cyclic ethers is influenced by basicity and ring strain. We carried out ab-initio MODPOT/VRDDO/MERGE calculations on a variety of substituted oxetanes and generated electrostatic molecular potential contour (EMPC) maps in three-dimensions around the molecules. The size of the negative EMPC map region around the oxygen enabled us to predict the propensity to polymerize prior to the syntheses of the actual monomers themselves. We carried out ab-initio MODPOT/VRDDO/MERGE MRD-CI calculations for the propagation step of oxetane reacting with protonated oxetanes to cause ring opening of protonated oxetane. Similar MRD-CI calculations on variously substituted oxetanes will shed insight into relative copolymerization preferences.     

A Symmetry-Broken Charge-Separated State in the Marcus Inverted Region

We report a long-lived charge-separated state in a chromophoric pair ( DC-PDI₂ ) that uniquely integrates the advantages of fundamental processes of photosynthetic reaction centers: i) Symmetry-breaking charge-separation (SB-CS) and ii) Marcus-inverted-region dependence. The near-orthogonal bichromophoric DC-PDI₂ manifests an ultrafast evolution of the SB-CS state with a time constant of =0.35±0.02 ps and a slow charge recombination (CR) kinetics with =4.09±0.01 ns in ACN. The rate constant of CR of DC-PDI₂ is 11 686 times slower than SB-CS in ACN, as the CR of the PDI radical ion-pair occurs in the deep inverted region of the Marcus parabola ( >λ). In contrast, an analogous benzyloxy (BnO)-substituted DC-BPDI₂ showcases a ≈10-fold accelerated CR kinetics with lowering to ≈1536 in ACN, by virtue of a decreased CR driving force. The present investigation demonstrates a control of molecular engineering to tune the energetics and kinetics of the SB-CS material, which is essential for next-generation optoelectronic devices.