Order parameter studies from effective order geometry in 4O.Om and 7O.Om liquid crystalline compounds

The effective geometry parameter, α_g = n _o /n _e, is used to evaluate the orientational order parameter, S, in the case of N-(p-n-butyloxybenzylidene)-p-n-alkoxy anilines, 4O.Om and N-(p-n-heptyloxybenzylidene)-p-n-alkoxy anilines, 7O.Om compounds with m?=?3–7 and 9 in the former case and m?=?3, 5–7 and 9 in the later materials. The results obtained are compared with those calculated using the standard techniques of molecular polarisability and birefringence. The effective geometry parameter's influence on the deflection of light by the liquid crystal compounds is also studied. The variation of temperature gradient of the ordinary refractive index, dn _o /dT, and extraordinary refractive index, dn _e /dT, of the liquid crystals is also studied.     

The heavy-ion spin-orbit interaction

An expression for the induced spin-orbit potential in a heavy-ion collision is derived by making and adiabatic approximation to the effective interaction in second-order perturbation theory. An explicit form for the induced spin-orbit interaction for the case of a projectile of arbitrary ground state spin S is given and is shown to be equivalent to the result obtained using the methods of geometrical magnetism.     

An Optimal Algorithm to Solve the All-Pairs Shortest Paths Problem on Permutation Graphs

In this paper we present an optimal algorithm to solve the all-pairs shortest path problem on permutation graphs with n vertices and m edges which runs in O(n ²) time. Using this algorithm, the average distance of a permutation graph can also be computed in O(n ²) time.     

Minimum 2-tuple dominating set of permutation graphs

For a fixed positive integer k, a k-tuple dominating set of a graph G=(V,E) is a subset D?V such that every vertex in V is dominated by at least k vertex in D. The k-tuple domination number γ _×k (G) is the minimum size of a k-tuple dominating set of G. The special case when k=1 is the usual domination. The case when k=2 was called double domination or 2-tuple domination. A 2-tuple dominating set D ₂ is said to be minimal if there does not exist any D′?D ₂ such that D′ is a 2-tuple dominating set of G. A 2-tuple dominating set D ₂, denoted by γ _×2(G), is said to be minimum, if it is minimal as well as it gives 2-tuple domination number. In this paper, we present an efficient algorithm to find a minimum 2-tuple dominating set on permutation graphs with n vertices which runs in O(n ²) time.     

A theoretical insight into the reducing properties of bicyclic dithia hydrocarbons and hetero-bicyclic dithiolopyrrolone compounds with rotation-restricted planar disulfide linkage

Structural Chemistry - The current study primarily involves the investigation of reducing properties of dithia-substituted bicyclic hydrocarbons. Adiabatic electron affinities (AEA) of the selected...     

A Computational Approach to Determine Average Reservoir Pressure in a Coalbed Methane (CBM) Well Flowing Under Dominant Matrix Shrinkage Effect

Desorption of gas from coal matrix alters the pore volume of fracture network. Consequently, cleat porosity and permeability of reservoir changes as pressure depletes. The method of standard pressure analysis calculations produces incorrect results in the case of coalbed methane reservoirs producing under dominant matrix shrinkage effect. The change in cleat porosity and permeability due to shrinkage of coal matrix following gas desorption with pressure depletion invalidates the underlying assumptions made in the derivation of diffusivity equation. Consequently, equations of pseudo-steady state commonly used in conventional reservoirs no longer remain valid as the porosity and permeability values change with pressure depletion. In this paper, effort has been made to describe pseudo-steady-state flow in coalbed methane reservoirs in the form of a new equation that accounts for pressure dependency of cleat porosity and permeability due to shrinkage of coal matrix. The concept of Al-Hussainy et al. (1966) has been extended to define a new pseudo-pressure function which assimilates within itself the pressure dependence of porosity and permeability Palmer and Mansoori (1998). Equation has been used to relate the cleat porosity with pressure. The equation-based computational method suggested in this paper finds its usefulness in estimating average reservoir pressure for any known flowing bottom hole pressure and thus reducing the frequency of future pressure buildup tests. The new equation is also useful in predicting reservoir pressure under the situation when coal matrix shrinks below desorption pressure. The equation used in the computational method has been validated with the help of numerical simulator CMG-GEM.     

Layer-by-layer electrostatic-assembly: magnetic-field assisted ordering of organic molecules

During the layer-by-layer (LbL) electrostatic assembly process, we orient organic molecules (nickel phthalocyanine) by an external magnetic field. Orientation of the magnetic moment of the molecules in a monolayer is immobilized by depositing a monolayer of a suitable polycation. Due to the orientation of magnetic moments, the electrostatic adsorption process becomes enhanced in subsequent layers. By cycling the deposition sequence layer after layer, we have achieved highly ordered and closely packed LbL films of the molecules with their magnetic moments oriented perpendicular to the substrate. Nonmagnetic copper phthalocyanine expectedly showed neither a magnetic-field assisted alignment nor an enhanced adsorption in LbL film deposition process.     

An analytic representation of quantum field theory

The connection between a space of quadratically integrable functions of real variablesq and a Hilbert space of analytic functions of complex variablesz established byBargmann is used to introduce quantised field operators for which the -functions of the commutation relations inq-space are replaced by analytic kernel functions inz-space, and a reference to distributions can be avoided.Bargmann's representation is first somewhat modified, so that the derivative terms in the field equations retain their form in the new representation. Local interaction terms inq-space obtain a non-local appearance inz-space. The transition to a 4-dimensional formulation inz-space has to resort to a Euclidean metric. The equations can be derived directly by starting from an action integral inz-space, and applying a variational calculus in which variations are restricted to analytic functions. Explicit analytic expressions are given for free field propagators.     

Redox-initiated vinyl polymerization with thiourea as the reductant

A few redox systems containing thiourea as reductant have been found to be quite effective in initiating vinyl polymerization in aqueous media and polymers obtained in the process have all been found to contain amino endgroups to various extents by the application of dye techniques. Quite a few oxidants have so far been utilized for this purpose; among them are ferric chloride (Fe³⁺), ethylene dibiguanide complex salts of tripositive silver (Ag³⁺), hydrogen peroxide (H₂O₂), persulfate (S₂O₈^2?), bromate (BrO₃^?) + hydrochloric acid (HCl). In case of oxidants Fe³⁺ and Ag³⁺, amino endgroups are mainly incorporated in polymers; but in case of oxidants H₂O₂ and S₂O₈^2?, fragments of oxidants are also incorporated as hydroxyl and sulfate endgroups. BrO₃^?, however, forms a very efficient redox-initiating system with thiourea, as is evidenced by its capability of polymerizing even hydroquinone-stabilized water-soluble vinyl monomers at very low temperature (～0°C.) and at a quite rapid rate. Besides amino endgroups, sulfonate endgroups have also been detected in polymers in this case, and the relative extents of these two types of endgroups depend generally on the acid concentration of the system. Evidences so far collected indicate the generation of S? C(?NH)NH₂ radicals in the system by oxidation of isothiourea, HS? C(?NH)NH₂, and these are incorporated in polymers as endgroups. Sulfonate endgroups may be generated by oxidation of these amino-bearing endgroups. Suitable initiation mechanisms have been suggested in each case.     

An unprecedented polyborate ester anion: X-ray diffraction studies on [1,8-C10H6(NMe2)2H][B5O6(OMe)4

The slow hydrolysis of B(OMe)3 in a CH2Cl2 solution in the presence of 1,8-C10H6(NMe2)2 (5:1 ratio) led to the formation of the novel isolated pentaborate ester anion [B5O6(OMe)4]-, which was characterized by a single-crystal X-ray diffraction study as the salt [1,8-C10H6(NMe2)2H][B5O6(OMe)4].