Propagation of infinitesimal thermo-mechanical waves during the finite-deformation loading of a viscoelastic material: general theory

We study the theory of propagation of infinitesimal thermo-mechanical waves in a special class of nonlinear viscoelastic materials under homogeneous and inhomogeneous finite static and time-varying deformations. These results are based on a thermodynamically consistent finite-deformation nonlinear viscoelastic model that reduces to a general linear viscoelastic model of integral form. On a thermo-mechanically deforming body, we impose a thermo-mechanical perturbation history and obtain the equations to solve for the perturbation parameters from the constitutive model and the balance laws. We use these equations to study the characteristics of different perturbations. We develop the special equations for both time-harmonic and time-damping plane waves for homogeneous pre-loads.     

The effect of NaCl and Na2SO4 concentration in aqueous phase on the phase inversion temperature O/W nanoemulsions

The effect of NaCl and Na₂SO₄ concentrations in aqueous phase on the phase inversion temperature (PIT) in nanoemulsions of water/Brij30/n-hexadecane system has been studied separately, and then compared. The variation of conductivity with temperature was measured by Cyber Scan PC510 conductivity meter for emulsions with 20 wt% hexadecane and 8 wt% Brij30 concentration and different concentrations of NaCl and Na₂SO₄ in aqueous phase. The results showed that with increasing concentrations of NaCl and Na₂SO₄ in aqueous phase, the PIT of nanoemulsions decreases. The effect of the elevation of concentration on the decrease of PIT was more for Na₂SO₄ in aqueous phase than NaCl with equal concentrations.     

Three new [XC(O)NH]P(O)[N(CH2C6H5)2]2 phosphoric triamides (X = CClF2, 3‐F‐C6H4 and 3,5‐F2‐C6H3): a database analysis of tertiary N‐atom geometry in compounds with a C(O)NHP(O)[N]2 core

In the phosphoric triamides N,N,N′,N′‐tetrabenzyl‐N′′‐(2‐chloro‐2,2‐difluoroacetyl)phosphoric triamide, C₃₀H₂₉ClF₂N₃O₂P, (I), N,N,N′,N′‐tetrabenzyl‐N′′‐(3‐fluorobenzoyl)phosphoric triamide, C₃₅H₃₃FN₃O₂P, (II), and N,N,N′,N′‐tetrabenzyl‐N′′‐(3,5‐difluorobenzoyl)phosphoric triamide, C₃₅H₃₂F₂N₃O₂P, (III), the tertiary N atoms of the dibenzylamido groups have sp² character with minimal deviation from planarity. The sums of the three bond angles about the N atoms in (I)–(III) deviate by less than 8° from the planar value of 360°. The geometries of the tertiary N atoms in all phosphoric triamides with C(O)NHP(O)[N]₂ skeletons deposited in the Cambridge Structural Database [CSD; Allen (2002). Acta Cryst. B 58 , 380–388] have been examined and the bond‐angle sums at the two tertiary N atoms (SUM1 and SUM2) and the parameter ΔSUM (= SUM1 − SUM2) considered. It was found that in compounds with a considerable ΔSUM value, the more pyramidal N atoms are usually oriented so that the corresponding lone electron pair is anti with respect to the P=O group. In (I), (II) and (III), the phosphoryl and carbonyl groups, separated by an N atom, are anti with respect to each other. In the C(O)NHP(O) fragment of (I)–(III), the P—N bond is longer and the O—P—N angle is contracted compared with the other two P—N bonds and the O—P—N angles in the molecules. These effects are also seen in analogous compounds deposited in the CSD. Compounds with [C(O)NH]P(O)[N]X (X≠ N), such as compounds with a [C(O)NH]P(O)[N][O] skeleton, have not been considered here. Also, compounds with a [C(O)NH]₂P(O)[N] fragment have not been reported to date. In the crystal structures of all three title compounds, adjacent molecules are linked via pairs of P=O...H—N hydrogen bonds, forming dimers with C_i symmetry.     

The double H‐atom acceptability of the P=O group in new XP(O)(NHCH2C6H4‐2‐Cl)2 phosphoramidates [X = C6H5O– and CF3C(O)NH–]: a database analysis of compounds having a P(O)(NHR) group

In the hydrogen‐bond patterns of phenyl bis(2‐chlorobenzylamido)phosphinate, C₂₀H₁₉Cl₂N₂O₂P, (I), and N,N′‐bis(2‐chlorobenzyl)‐N′′‐(2,2,2‐trifluoroacetyl)phosphoric triamide, C₁₆H₁₅Cl₂F₃N₃O₂P, (II), the O atoms of the related phosphoryl groups act as double H‐atom acceptors, so that the P=O...(H—N)₂ hydrogen bond in (I) and the P=O...(H—N_amide)₂ and C=O...H—N_C(O)NHP(O) hydrogen bonds in (II) are responsible for the aggregation of the molecules in the crystal packing. The presence of a double H‐atom acceptor centre is a result of the involvement of a greater number of H‐atom donor sites with a smaller number of H‐atom acceptor sites in the hydrogen‐bonding interactions. This article also reviews structures having a P(O)NH group, with the aim of finding similar three‐centre hydrogen bonds in the packing of phosphoramidate compounds. This analysis shows that the factors affecting the preference of the above‐mentioned O atom to act as a double H‐atom acceptor are: (i) a higher number of H‐atom donor sites relative to H‐atom acceptor centres in molecules with P(=O)(NH)₃, (N)P(=O)(NH)₂, C(=O)NHP(=O)(NH)₂ and (NH)₂P(=O)OP(=O)(NH)₂ groups, and (ii) the remarkable H‐atom acceptability of this atom relative to the other acceptor centre(s) in molecules containing an OP(=O)(NH)₂ group, with the explanation that the N atom bound to the P atom in almost all of the structures found does not take part in hydrogen bonding as an acceptor. Moreover, the differences in the H‐atom acceptability of the phosphoryl O atom relative to the O atom of the alkoxy or phenoxy groups in amidophosphoric acid esters may be illustrated by considering the molecular packing of compounds having (O)₂P(=O)(NH) and (O)P(=O)(NH)(N)groups, in which the unique N—H unit in the above‐mentioned molecules almost always selects the phosphoryl O atom as a partner in forming hydrogen‐bond interactions. The P atoms in (I) and (II) are in tetrahedral coordination environments, and the phosphoryl and carbonyl groups in (II) are anti with respect to each other (the P and C groups are separated by one N atom). In the crystal structures of (I) and (II), adjacent molecules are linked via the above‐mentioned hydrogen bonds into a linear arrangement parallel to [100] in both cases, in (I) by forming R₂²(8) rings and in (II) through a combination of R₂²(10) and R₂¹(6) rings.     

Numerical solution of Fokker‐Planck equation using the cubic B‐spline scaling functions

In this article a numerical technique is presented for the solution of Fokker‐Planck equation. This method uses the cubic B‐spline scaling functions. The method consists of expanding the required approximate solution as the elements of cubic B‐spline scaling function. Using the operational matrix of derivative, the problem will be reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Third Order Lagrangians, Weyl Invariants and Classical Trace Anomaly in Six Dimensions

We have proceeded the analogy (represented in our previous works) of the Einstein tensor and the alternative form of the Einstein field equations for the generic coefficients of the eight terms in the third order of the Lovelock Lagrangian. We have found the constraint between the coefficients into two forms, an independent and a dimensional dependent versions. Each form has three degrees of freedom, and not only the exact coefficients of the third order Lovelock Lagrangian do satisfy the two forms of the constraints, but also the two independent cubic of the Weyl tensor satisfy the independent constraint in six dimensions and yield the dimensional dependent version identically independent of the dimension. Then, we have introduced the most general effective expression for a total third order type Lagrangian with the homogeneity degree number three which includes the previous eight terms plus the new three ones among the all seventeen independent terms. We have proceeded the analogy for this combination, and have achieved the relevant constraint. We have shown that the expressions given in the literature as the third Weyl-invariant combination in six dimensions do satisfy this constraint. Thus, we suggest that these constraint relations to be considered as the necessary consistency conditions on the numerical coefficients that a Weyl-invariant in six dimensions should satisfy. Finally, we have calculated the “classical” trace anomaly (an approach that was presented in our previous works) for the introduced total third order type Lagrangian and have achieved a general expression with four degrees of freedom in more than six dimensions (three degrees in six dimensions). Then, we have demonstrated that the resulted expression contains exactly the relevant coefficient of the Schwinger–DeWitt proper time method (that linked with the relevant heat kernel coefficient) in six dimensions, as a particular case. Of course, this result is a necessary consistency check, nevertheless our approach can be regarded as an alternative (perhaps simpler, and classical) derivation of the trace anomaly which also gives a general expression with the relevant degrees of freedom.     

Dipotassium Hydrogen Phosphate Powder Catalyzed Synthesis of Alkyl 2-(2-Alkoxy-2-oxoethyl)dinaphtho[2,1-d:1,2-f][1,3]-dioxepin-2-Carboxylates from Stabilized Phosphorus Ylides in Solvent-Free Conditions

The protonation of the highly reactive 1:1 intermediates, produced in the reaction of triphenylphosphine and dialkyl acetylenedicarboxylates, by 1,1-binaphthyl-2,2′-diol leads to vinyltriphenylphosphonium salts, which undergo a Michael addition reaction to produce the corresponding stabilized phosphonium ylides. Dipotassium hydrogen phosphate powder was found to catalyze the conversion of the stabilized phosphonium ylides to alkyl 2-(2-alkoxy-2-oxoethyl)dinaphtho[2,1-d:1,2-f][1,3]-dioxepin-2-carboxylates under solvent-free conditions using microwave (0.6 KW, 3 min) and thermal (100°C, 60 min) conditions.     

Numerical study of electroosmotic micromixing of non-Newtonian fluids

Biofluids which exhibit non-Newtonian behavior are widely used in microfluidic devices which involve fluid mixing in microscales. In order to study the effects of shear depending viscosity of non-Newtonian fluids on characteristics of electroosmotic micromixing, a numerical investigation of flow of power-law fluid in a two-dimensional microchannel with nonuniform zeta potential distributions along the channel walls was carried out via finite volume scheme. The simulation results confirmed that the shear depending viscosity has a significant effect on the degree of mixing efficiency. It was shown as the fluid behavior index of power-law fluid, n, decreases, more homogeneous solution can be achieved at the microchannel outlet. Hence, electroosmotic micromixing was found more practical and efficient in microscale mixing of pseudoplastic fluids rather than those Newtonian and dilatant ones. Furthermore, it was found that increase in Reynolds number results in lower mixing efficiency while electroosmotic forces are kept constant.     

Horizon problem remediation via deformed phase space

We investigate the effects of a special kind of dynamical deformation between the momenta of the scalar field of the Brans–Dicke theory and the scale factor of the FRW metric. This special choice of deformation includes linearly a deformation parameter. We trace the deformation footprints in the cosmological equations of motion when the BD coupling parameter goes to infinity. One class of the solutions gives a constant scale factor in the late time that confirms the previous result obtained via another approach in the literature. This effect can be interpreted as a quantum gravity footprint in the coarse grained explanation. The another class of the solutions removes the big bang singularity, and the accelerating expansion region has an infinite temporal range which overcomes the horizon problem. After this epoch, there is a graceful exiting by which the universe enters in the radiation dominated era.     

Generalized framework for auxiliary extra dimensions

The theory of gravity with an auxiliary extra dimension is known to give the ghost-free cubic completion of the Fierz-Pauli mass term in the decoupling limit. Our work generalizes the boundary condition in the auxiliary dimension that avoids ghosts order-by-order, and to all orders, in the decoupling limit. Furthermore, we extend the formalism to the case of many auxiliary dimensions, and we show that the multi-dimensional extension with the rotationally invariant boundaries of the bulk, is equivalent to the model with a single auxiliary dimension. The above constructions require the appropriate adjustment of the boundary condition, which we discuss in detail. The other possible extension of the original model by the Gauss-Bonnet term is studied as well.