Competition of interactions and a new high-temperature phase of selenourea.

The aggregation of molecules is usually associated with a specific type of interaction, which can be altered by thermodynamic conditions. Under normal conditions, the crystal structure of selenourea, SeC(NH2)2, phase α is trigonal, space group P31, Z = 27. Its large number of independent molecules (Zα' = 9) can be associated with the formation of an NH...N hydrogen bond substituting one of 36 independent NH...Se hydrogen bonds, which prevail among intermolecular interactions. Phase α approximates the trigonal structure with a threefold smaller unit cell (Z = 9), which in turn approximates another still threefold smaller unit cell (Z = 3). The temperature-induced transformations of selenourea have been characterized by calorimetry and by performing 21 single-crystal X-ray diffraction structural determinations as a function of temperature. At 381.0 K, phase α undergoes a first-order displacive transition to phase γ, with space group P3121 and Z reduced to 9, when the NH...N bond is broken and an NH...Se bond is formed in its place. Previously, an analogous competition was observed between NH...N and NH...O hydrogen bonds in high-pressure phase III of urea. The lattice vectors along the (001) plane in low- and high-temperature phases of selenourea are related by a similarity rule, while the lattice dimensions along direction c are not affected. This similarity rule also applies to the structures of phase γ and hypothetical phase δ (Z = 3). The thermally controlled transition between enantiomorphic phases of selenourea contrasts with its high-pressure transition at 0.21 GPa to a centrosymmetric phase ß, where both the NH...Se and NH...N bonds are present. The compression and heating reduce the number of independent molecules from Z' = 9 in phase α, to Z' = 2 in phase ß and to Z' = 1.5 in phase γ.

Analytic similarity solutions for fully resolved unsteady laminar boundary layer flow and heat transfer in the presence of radiation.

In this paper, we have compared a new type of similarity transformation derived systematically by using Lie point symmetries with the existing similarity transformations for unsteady fluid flow and heat transfer in the boundary layer in the presence of radiation. It is observed that the existing transformations map the steady and marginally accelerating flows only, while the Lie similarity transformations provide solutions for all types of accelerating flows and are independent of unsteadiness in the fluid. The previous transformations are valid for a specific time interval which depends on a range of unsteadiness parameter, however the Lie similarity transformations provide valid solutions at any given time. This implies that the Lie similarity transformations yield solutions for previously unexplored ranges of unsteadiness in the fluid. Boundary layer flow physics for both types of transformations is discussed by employing the Homotopy analysis method. We show that for accelerating fluids, in the developing region, the boundary layer thickness first increases and than starts to decrease with increase in unsteadiness for fully developed flow. Detailed comparison of velocity and temperature profiles in the boundary layer is made using the tables and graphs which show that with Lie similarity transformations the region of study of the considered flow extends significantly for the unsteadiness parameter. The effect of the Prandtl number and radiation parameter on temperature distribution is also compared for both types of similarity transformations. The Lie symmetry similarity transformations are shown to explain the unsteady laminar boundary layer flow and heat transfer to an extent where the existing similarity transformations do not work.

Theoretical analysis of unsteady squeezing nanofluid flow with physical properties.

Theoretical analysis of physical characteristics of unsteady, squeezing nanofluid flow is studied. The flow of nanofluid between two plates that placed parallel in a rotating system by keeping the variable physical properties: viscosity and thermal conductivity. It is analyzed by using Navier Stokes Equation, Energy Equation and Concentration equation. The prominent equations are transformed by virtue of suitable similarity transformation. Nanofluid model includes the important effects of Thermophoresis and Brownian motion. For analysis graphical results are drawn for verity parameters of our interest i.e., Injection parameter, Squeezing number, Prandtle number and Schmidt number are investigated for the Velocity field, Temperature variation and Concentration profile numerically. The findings underline that the parameter of skin friction increases when the Squeezing Reynolds number, Injection parameter and Prandtle number increases. However, it shows inverse relationship with Schmidt number and Rotation parameter. Furthermore, direct relationship of Nusselt number with injection parameter and Reynolds number is observed while its relation with Schmidt number, Rotation parameter, Brownian parameter and Thermophoretic parameter shows an opposite trend. The results are thus obtained through Parametric Continuation Method (PCM) which is further validated through BVP4c. Moreover, the results are tabulated and set forth for comparison of findings through PCM and BVP4c which shows that the obtained results correspond to each other.

BAYESIAN ALIGNMENT OF SIMILARITY SHAPES.

We develop a Bayesian model for the alignment of two point configurations under the full similarity transformations of rotation, translation and scaling. Other work in this area has concentrated on rigid body transformations, where scale information is preserved, motivated by problems involving molecular data; this is known as form analysis. We concentrate on a Bayesian formulation for statistical shape analysis. We generalize the model introduced by Green and Mardia for the pairwise alignment of two unlabeled configurations to full similarity transformations by introducing a scaling factor to the model. The generalization is not straight-forward, since the model needs to be reformulated to give good performance when scaling is included. We illustrate our method on the alignment of rat growth profiles and a novel application to the alignment of protein domains. Here, scaling is applied to secondary structure elements when comparing protein folds; additionally, we find that one global scaling factor is not in general sufficient to model these data and, hence, we develop a model in which multiple scale factors can be included to handle different scalings of shape components.