Shape and phase transitions in quantum-Hall skyrmions

The shape deformability of quantum-Hall skyrmions leads to a rich phase diagram in the –g space. We study the long-wavelength physics of a collection of interacting skyrmions using a nonlinear sigma model. At zero temperature the ground state is crystalline with generalized Nèel order. As a function of the filling factor , the skyrmion crystal undergoes a sequence of structural transitions driven by a change of shape of the individual skyrmions. Quantum effects lead to melting and orientational disordering transitions at high and low skyrmion densities, respectively. We show that moment of inertia of skyrmions also arises from the shape deformability of the skyrmions.     

Inlet length by laminar flow of elastico-viscous liquids through straight channel and circular tube

The inlet lengths in a straight channel and a circular tube by the laminar flow of an elastico-viscous liquid have been determined in this paper. Expressions for the inlet lengths have been obtained by the kinetic energy end correction method. For a given pressure drop, the elasticity of the liquid increases the inlet length only if the liquid possesses cross-viscosity. But cross-viscosity which decreases the inlet length has an independent effect on it.     

Flow engendered by the time-varying motion of a porous plate in the presence of a magnetic field

The problem of flow of an electrically conducting viscous liquid due to the time-varying motion of an infinite porous plate has been studied. There is a uniform magnetic field imposed transversely to the plate and the magnetic lines of force are taken to be fixed relative to the fluid. Exact solutions for the velocity field and the skin-friction have been obtained and some particular cases have been discussed. The effect of suction parameter and magnetic field strength on the flow characteristics have been depicted through several graphs and tables.     

Inhomogeneous quantum diffusion and decay of a meta-stable state

We consider the quantum stochastic dynamics of a system whose interaction with the reservoir is considered to be linear in bath co-ordinates but nonlinear in system co-ordinates. The role of the space-dependent friction and diffusion has been examined in the decay rate of a particle from a meta-stable well. We show how the decay rate can be hindered by inhomogeneous dissipation due to nonlinear system–bath coupling strength.     

A new approach to find project characteristics and multiple possible critical paths in a fuzzy project network

Graphs are widely used to represent data and relationships. Among all graphs, a particularly useful family is the family of trees. In this paper, we utilize a rooted tree to describe a fuzzy project network as it enables simplification in finding earliest starting times and trapezoidal fuzzy numbers to express the operation times for all activities in project network. As there is an increasing demand that the decision maker needs “Multiple possible critical paths” to decrease the decision risk for project management, in this paper, we introduce an effective graphical method to compute project characteristics such as total float, earliest and latest times of activities in fuzzy project network and a new ranking to find possible critical paths. Numerical example is provided to explain the proposed procedure in detail; the results have shown that the procedure is very useful and flexible in finding total floats. By comparing the critical paths obtained by this method with the previous methods, it is shown that the proposed method is effective in finding possible critical paths.     

Functional Data Analysis of Tree Data Objects

Data analysis on non-Euclidean spaces, such as tree spaces, can be challenging. The main contribution of this article is establishment of a connection between tree-data spaces and the well-developed area of functional data analysis (FDA), where the data objects are curves. This connection comes through two tree representation approaches, the Dyck path representation and the branch length representation. These representations of trees in the Euclidean spaces enable us to exploit the power of FDA to explore statistical properties of tree data objects. A major challenge in the analysis is the sparsity of tree branches in a sample of trees. We overcome this issue by using a tree-pruning technique that focuses the analysis on important underlying population structures. This method parallels scale-space analysis in the sense that it reveals statistical properties of tree-structured data over a range of scales. The effectiveness of these new approaches is demonstrated by some novel results obtained in the analysis of brain-artery trees. The scale-space analysis reveals a deeper relationship between structure and age. These methods are the first to find a statistically significant gender difference. Supplementary materials for this article are available online.     

A new pH and thermo-responsive chiral hydrogel for stimulated release

Chirality of the amphiphile to promote gelation in the given solvent medium is narrated in a new catanionic surfactant mixture from a twin-chiral, twin-tailed surfactant derived from tartaric acid and cetyltrimethylammonium bromide (CTAB). The surfactant bis(decyloxy) succinic acid (BDSA), a chiral Gemini-type surfactant with a rigid spacer, in association with CTAB formed pH and temperature responsive vesicles and hydrogels. Molecular chirality gave rise to supertwisted fibrillar hydrogels at a BDSA:CTAB molar ratio of 1:2 and in 31% water content. The hydrogels from enantiomeric BDSA were reversibly pH and irreversibly temperature responsive at pH<6.2 and at 55 degrees C, respectively, whereas the corresponding sodium succinates formed transparent clear gels reversible to both pH and temperature. The hydrogels were able to entrap and release model dye molecules, Rhodamine B, and Congo red, responding to thermal and pH stimuli. Circular dichroism unraveled the chiro-optical behavior of the assembled fibers, allowing monitoring of aggregation and packing. The presence and the relative configuration of the stereogenic centers in the structure of this low molecular weight gelator have been observed to be critical to form gels. The high curvature Gaussian gel network was modeled based on the chiral elastic membrane approach and the pitch angle of the Gaussian twist was estimated to be 45 degrees.