Effect of ferroelectric liquid crystalline quaterphenyl structure and handedness on helical pitch length in bicomponent mixtures

The aim of this paper is characterisation of mesomorphic properties and helical structure parameters: handedness and helical pitch, of two laterally substituted ferroelectric compounds and mixtures based on them. These compounds have the same quaterphenyl rigid core and the same length of non-chiral chain – eight carbon atoms, as well as the absolute configuration of chiral centre (‘R’). Base compounds differ in the kind of a substituent in a rigid core (–Cl, –CH₃). Both of them have rather low melting temperature in comparison to most of quaterphenyls, and it affects the lowering of this temperature in binary mixtures. Thus they can be used for preparation of multicomponent ferroelectric mixtures useful for application.     

Swelling behaviors of poly(dodecyl methacrylate-co-methyl eugenol) and poly(dodecyl methacrylate-co-methyl chavicol) gels in essential oil components

Poly(dodecylmethacrylate-co-methyleugenol) P(DDMA-co-Meu) and poly(dodecylmethacrylate-co-methylchavicol) P(DDMA-co-Mch) gels were synthesized in ethanol using free radical cross-linking polymerization method at 60 °C for 24 h in the presence of azobisisobutyronitrile (AIBN) and triethylene glycol dimethacrylate (TEGDMA) as initiator and cross-linker, respectively. Scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) were used to characterize the gels. These gels were used to investigate swelling behaviors in linalool and methyl eugenol, in essential oil mixture of phenyl propanoid and terpenoid, and also in various solvents. While the equilibrium swelling values (ESV) of both gels were higher in linalool than in methyl eugenol, the result was vice versa in the case of essential oil mixture. ESVs of both gels were also obtained in various solvents with different functional groups and the highest ESV of both gels were obtained in toluene, and the lowest ESV of P(DDMA-co-Meu) and P(DDMA-co-Mch) was in methanol and in ethylene glycol, respectively. While P(DDMA-co-Meu) is sensitive to carbon number change in alcohol, P(DDMA-co-Mch) is less sensitive. In the case of esters, increase of carbon number in functional group causes a more significant change in ESV than an increase of carbon number in aliphatic chain. Experimental results were correlated by the first-order and second-order models. The second-order model was more suitable than the other. While P(DDMA-co-Meu) gel swelled in linalool exhibits a Fickian diffusion character, the diffusion mechanism of the gel in methyl eugenol is a non-Fickian one. In the case of P(DDMA-co-Mch), the result is vice versa.     

In Metric-measure Spaces Sobolev Embedding is Equivalent to a Lower Bound for the Measure

We study Sobolev inequalities on doubling metric measure spaces. We investigate the relation between Sobolev embeddings and lower bound for measure. In particular, we prove that if the Sobolev inequality holds, then the measure μ satisfies the lower bound, i.e. there exists b such that μ(B(x,r))≥b r ^α for r∈(0,1] and any point x from metric space.     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

Matrix-analytic solution of infinite,finite and level-dependent second-order fluid models

This paper presents a matrix-analytic solution for second-order Markov fluid models (also known as Markov-modulated Brownian motion) with level-dependent behavior. A set of thresholds is given that divide the fluid buffer into homogeneous regimes. The generator matrix of the background Markov chain, the fluid rates (drifts) and the variances can be regime dependent. The model allows the mixing of second-order states (with positive variance) and first-order states (with zero variance) and states with zero drift. The behavior at the upper and lower boundary can be reflecting, absorbing, or a combination of them. In every regime, the solution is expressed as a matrix-exponential combination, whose matrix parameters are given by the minimal nonnegative solution of matrix quadratic equations that can be obtained by any of the well-known solution methods available for quasi birth death processes. The probability masses and the initial vectors of the matrix-exponential terms are the solutions of a set of linear equations. However, to have the necessary number of equations, new relations are required for the level boundary behavior, relations that were not needed in first-order level dependent and in homogeneous (non-level-dependent) second-order fluid models. The method presented can solve systems with hundreds of states and hundreds of thresholds without numerical issues.     

Optimization method in problems of acoustic cloaking of material bodies

Optimization problems for a three-dimensional model of acoustic scattering are formulated and studied. These problems arise in designing tools for cloaking material bodies by applying the wave flow method. The cloaking effect is achieved due to an optimal choice of variable parameters of the inhomogeneous isotropic medium occupying the sought shell. The solvability of direct and optimization problems for the acoustic scattering model is proved, and sufficient conditions ensuring the uniqueness and stability of optimal solutions are established.     

New polymer composites based on keratin and polyethylene

New biodegradable composites based on keratin and polyethylene have been produced under shear deformation. It has been demonstrated that the introduction of keratin leads to an increase in elastic modulus and to a decrease in ultimate tensile strength and elongation at break of the compositions. Elongation at break ε_b depends on the keratin dispersity; the highest ε_b values are observed for the compositions containing the smallest keratin particles. It has been shown that the compositions are susceptible to mold fungi; i.e., they are biodegradable.     

Drying of colloidal solutions of fluoroalkyl oligomers

The change in the supramolecular structure upon drying (solvent removal) of colloidal solutions of fluoroalkyl oligomers at atmospheric pressure has been studied using atomic force microscopy. In an initial colloidal solution, micrometer-sized particles of the dense phase consist of randomly oriented oligomers in the form of rigid rods of a 3–5 nm length forming a porous framework filled with solvent molecules, which solvate the oligomer chains. The drying-induced capillary pressure, which in nanosized pores is of the same order of magnitude as the solvation energy, leads to framework deformation, collapse of the pores, and the formation of lamellar and dendritic structures on a 50–100 nm scale. The ordering of these structures (formation of blocks of parallel oriented fibers typical of a fluoroplastic) increases as the heat-treatment temperature and the drying rate are increased, increasing the roughness of the surface (ratio of real to smooth surface area) and its hydrophobicity.     

Changes in luminescence of semiconductor colloidal quantum dots CdSe@CdS by replacement of hydrophobic ligands with 1-thioglycerol

Luminescent properties of CdSe@CdS colloidal quantum dots upon replacement of hydrophobic stabilizing ligands with water-soluble 1-thioglycerol have been studied. The data obtained have made it possible to optimize the ligand replacement procedure and significantly decrease the loss of the fluorescence quantum yield of the resulting hydrophilic quantum dots.