Unconditionally Energy Stable Numerical Schemes for Hydrodynamics Coupled Fluids Systems

The thesis consists of two parts. In the first part we propose several second order in time, fully discrete, linear and nonlinear numerical schemes to solve the phase-field model of two-phase incompressible flows in the framework of finite element method. The schemes are based on the second order Crank-Nicolson method for time disretizations, projection method for Navier-Stokes equations, as well as several implicit-explicit treatments for phase-field equations. The energy stability, solvability, and uniqueness for numerical solutions of proposed schemes are further proved. Ample numerical experiments are performed to validate the accuracy and efficiency of the proposed schemes thereafter. In the second part we consider the numerical approximations for the model of smectic-A liquid crystal flows. The model equation, that is derived from the variational approach of the de Gennes energy, is a highly nonlinear system that couples the incompressible Navier-Stokes equations and two nonlinear coupled second-order elliptic equations. Based on some subtle explicit-implicit treatments for nonlinear terms, we develop unconditionally energy stable, linear, decoupled time discretization scheme. We also rigorously prove that the proposed scheme obeys the energy dissipation law. Various numerical simulations are presented to demonstrate the accuracy and the stability thereafter

Polymerisable octahedral rhenium cluster complexes as precursors for photo/electroluminescent polymers

New polymerisable photoluminescent octahedral rhenium cluster complexes trans-[{Re₆Q₈}(TBP)₄VB)₂] (Q = S or Se; TBP – p-tert-butylpyridine; VB – vinyl benzoate) have been synthesised, characterised and used to construct rhe-nium cluster-organic polymer hybrid materials. These novel polymer systems are solution-processable and the rhenium clusters retain their photoluminescent properties within the polymer environment. Notably, when the rhenium cluster complexes are incorporated into the matrix of the electroluminescent polymer poly(N-vinylcarbazole), the resultant cluster polymer hybrid combined properties of both components and was used successfully in the construc-tion of a polymer light emitting diode (PLED). These prototype devices are the first PLEDs to incorporate octahedral rhenium clusters and provide the first direct evidence of the electroluminescent properties of rhenium clusters and indeed, to the best of our knowledge, of any member of the family of 24-electron hexanuclear cluster complexes of molybdenum, tungsten or rhenium

Hexaazide octahedral molybdenum cluster complexes: synthesis, properties and the evidence of hydrolysis

This article reports the synthesis, crystal structure of new molybdenum hexaazide cluster complex (ⁿBu₄N)₂[{Mo₆I₈}(N₃)₆] (3) and comparison of its photophysical and electrochemical properties to those of earlier reported analogues (ⁿBu₄N)₂[{M₆X₈}(N₃)₆] (X = Cl, Br). Additionally, the dimerisation of 3 as a result of hydrolysis was revealed by mass spectrometry and single crystal X-Ray diffraction. Indeed, the structurally characterised compound (ⁿBu₄N)₄[{Mo₆I₈}(N₃)₅)₂O] represents the first example of oxo-bridged dimer of octahedral molybdenum clusters complexes

Water-soluble hybrid materials based on {Mo₆X₈}⁴⁺ (X = Cl, Br, I) cluster complexes and sodium polystyrene sulfonate

Development of water-soluble forms of octahedral molybdenum clusters {Mo₆X₈}⁴⁺ (X = Cl, Br, I) is strongly motivated by the tremendous potential that these complexes have for biological applications, namely as agents for bioimaging and photodynamic therapy. In these work we report the first water-soluble hybrid materials, which represent sodium polystyrene sulfonate doped by molybdenum clusters, and evaluation of their photophysical and biological properties (dark and photoinduced cytotoxicity and cellular uptake) with the use of cervical cancer (HeLa) and human epidermoid larynx carcinoma (Hep-2) cell-lines as models

Problem of accident reconstruction mechanism using parameters of braking process of two-wheeled motor vehicles

Increase in the number of two-wheeled motor vehicles (motorcycles, vehicles of category L3) is observed in the traffic of almost all countries in the world. That is why the number of victims and people seriously injured in the road traffic accidents (RTA) has considerably increased. The majority of RTA is the result of many factors which form together sets of different causes and effects. Identification of actual reasons having led to a traffic accident, as well as their attendant circumstances, is one of the most important tasks in ensuring traffic safety. On the one hand, configurations of two-wheeled motor vehicles have been significantly improved over the last decades, so it is necessary to align the analytical apparatus of estimating parameters of the braking process with these configurations. On the other hand, the current practice of expert analysis and settlement of accidents still involves estimation of increase in braking time and steady deceleration of motorcycles manufactured domestically during the past years, which hardly participate in the modern traffic due to their age. Both of these circumstances require review and adjustment, as well as formation of an updated basis of estimate for assessment of braking processes of two-wheeled motor vehicles in order to increase the reliability of RTA examination and determine compliance or non-compliance of driver’s actions with the requirements of traffic rules, establish the causes of accidents, evaluate a technical capability of a driver of the two-wheeled motor vehicle to prevent the accident. Settlement of all these issues can be provided by effective methods of calculation (quantitative) assessment, which are not available at the present moment

Advances in the Engineering of Near Infrared Emitting Liquid Crystals and Copolymers, Extended Porous Frameworks, Theranostic Tools and Molecular Junctions Using Tailored Re6 Cluster Building Blocks

International audienceAt the occasion of the fiftieth birthday of the introduction of the term 'metal atom cluster' by F. A. Cotton in inorganic chemistry, it is the good time to make a review on the advances in the engineering of molecular assemblies and nanomaterials based on octahedral Re6 metal atom clusters. The latter exhibit unique intrinsic structural and physicochemical properties (orthogonal disposition of metallic sites that can be selectively functionalized, photoluminescence, redox, generation of singlet oxygen) that make them relevant building blocks for the structuration at the nanometric scale and functionalization of hybrid organic-inorganic materials and supramolecular frameworks. After synthesis by solid state chemistry techniques at high temperature, inorganic precursors built up on face-capped [(Re6Yi8)Ya6] cluster units (Y = chalcogen and/or halogen) can be functionalized via solution chemistry techniques or organic melts to form [(Re6Yi8)La6] (L = CN, OH, various organic ligands...). This work reports advances in the synthesis of [(Re6Yi8)Ya6] and [(Re6Yi8)La6] cluster units as well as on their use in the elaboration of supramolecular frameworks, nanoparticles, hybrid nanomaterials (co-polymers and liquid crystals) and active molecular junctions

A highly emissive inorganic hexamolybdenum cluster complex as a handy precursor for the preparation of new luminescent materials

The synthesis and characterisation of a new, highly luminescent inorganic cluster complex, (Bu4N)2[Mo6I 8(NO3)6], are described. The complex possesses labile nitrato ligands and is therefore a useful precursor for the design of new luminescent materials. To exemplify this, functionalised polystyrene beads have been utilised as "polymeric ligands" to immobilise the molybdenum cluster complex. This journal i

Luminescent coordination polymers based on Ca²⁺ and octahedral cluster anions [{M₆Clⁱ₈}Clᵃ₆}²⁻ (M = Mo, W) : synthesis and thermal stability studies

Luminescent coordination polymers (CPs) based of inexpensive stable precursors are attractive materials for applications. Here we report the synthesis and evaluation of the stability and photophysical characteristics of the first examples of phosphorescent CPs based on octahedral molybdenum and tungsten cluster anions. Specifically 1D CP trans-[{Ca(OPPh₃)₄}{{M₆Clⁱ₈}Clᵃ₆}]∞ (M = Mo, W) can be obtained either directly at increased temperature or via intermediate phases [cis-Ca(OPPh₃)₄(H₂O)₂][{M₆Clⁱ₈}Clᵃ₆]∙2CH₃CN that are stable at room-temperature, but convert to the titled CP at temperatures above 100 °C

Cellular internalisation, bioimaging and dark and photodynamic cytotoxicity of silica nanoparticles doped by {Mo₆I₈}⁴⁺ metal clusters

Silica nanoparticles (SNPs) doped by hexanuclear molybdenum cluster complexes [{Mo₆X₈}L₆]n (X = Cl, Br, or I; L = various inorganic or organic ligands) have been recently suggested as materials with a high potential for biomedical applications due to both the outstanding photoluminescent properties and the ability to efficiently generate singlet oxygen upon photoirradiation. However, no studies were undertaken so far to prove this concept. Therefore, here we examined the potential of photoluminescent SNPs doped by {Mo₆I₈}⁴⁺ for such applications as bioimaging and photodynamic therapy using human epidermoid larynx carcinoma (Hep-2) cell line as a model. Our results demonstrated both: (i) significant luminescence from cells with internalised molybdenum cluster doped SNPs combined with the low cytotoxicity of particles in the darkness and (ii) significant cytotoxicity of the particles upon photoirradiation. Thus, this research provides strong experimental evidence for high potential of molybdenum cluster doped materials in such biomedical applications as optical bioimaging, biolabeling and photodynamic therapy

A comparative study of hydrophilic phosphine hexanuclear rhenium cluster complexes’ toxicity

Octahedral rhenium cluster compound Na2H8[{Re6Se8}(P(C2H4CONH2)(C2H4COO)2)6] has recently emerged as a very promising X-ray contrast agent for biomedical applications. However, the synthesis of this compound is rather challenging due to difficulty to control the hydrolysis of initial P(C2H4CN)3 ligand during the reaction process. Therefore, in this report we compare the in vitro and in vivo toxicity of Na2H8[{Re6Se8}(P(C2H4CONH2)(C2H4COO)2)6] with those of related compounds featuring fully hydrolysed form of the phosphine ligand, namely Na2H14[{Re6Q8}(P(C2H4COO)3)6] (Q = S or Se). Our results demonstrate that cytotoxicity and acute in vivo toxicity of the complex Na2H8[{Re6Se8}(P(C2H4CONH2)(C2H4COO)2)6] solutions were considerably lower than those of compounds with fully hydrolysed ligand P(C2H4COOH)3. Such behavior can be explained by the higher osmolality of Na2H14[{Re6Q8}(P(C2H4COO)3)6] versus Na2H8[{Re6Se8}(P(C2H4CONH2)(C2H4COO)2)6]