Comtrans algebras, Thomas sums, and bilinear forms

A comtrans algebra is said to decompose as the Thomas sum of two subalgebras if it is a direct sum at the module level, and if its algebra structure is obtained from the subalgebras and their mutual interactions as a sum of the corresponding split extensions. In this paper, we investigate Thomas sums of comtrans algebras of bilinear forms. General necessary and sufficient conditions are given for the decomposition of the comtrans algebra of a bilinear form as a Thomas sum. Over rings in which 2 is not a zero divisor, comtrans algebras of symmetric bilinear forms are identified as Thomas summands of algebras of infinitesimal isometries of extended spaces, the complementary Thomas summand being the algebra of infinitesimal isometries of the original space. The corresponding Thomas duals are also identified. These results represent generalizations of earlier results concerning the comtrans algebras of finite-dimensional Euclidean spaces, which were obtained using known properties of symmetric spaces. By contrast, the methods of the current paper involve only the theory of comtrans algebras.Received: 30 March 2004     

Generic adjoints in comtrans algebras of bilinear spaces

As a first step towards a general structure theory for comtrans algebras (modeled loosely on the Cartan theory for Lie algebras), this paper investigates comtrans algebras of bilinear spaces. Attention focuses on invariants associated with comtrans algebras, and the extent to which these invariants may serve to specify the algebras up to isomorphism within certain classes. Over fields whose characteristic differs from two, comtrans algebras of symmetric forms are determined up to isomorphism by the eigenvalues of generic adjoints, while comtrans algebras of symplectic forms are determined by the dimensions of maximal abelian subalgebras. Examples show that the multiplicity of zero as a root of the characteristic polynomial is generally independent of the dimension of a maximal abelian subalgebra.     

A computational analysis of strained laminar flame propagation in a stratified CH4/H2/air mixture

Propagation of a H₂-added strained laminar CH₄/air flame in a rich-to-lean stratified mixture is numerically studied. The back-support effect, which is known to enhance the consumption speed of a flame propagating into a leaner mixture compared to that into a homogeneous mixture, is evaluated. A new method is devised to characterize unsteady reactant-to-reactant counterflow flames under transiently decreasing equivalence ratio, in order to elucidate the influence of flow strain on the back-support effect. In contrast to the conventional reactant-to-product configurations, the current configuration is more relevant to unsteady stratified flames back-supported by their own combustion products. Moreover, since H₂ distribution downstream of the flame is known to play a crucial role in back-supported CH₄/air flames, the influence of H₂ addition in the upstream mixture is examined. The results suggest that a larger strain rate leads to a larger equivalence ratio gradient at the reaction zone through increased flow divergence, which amplifies the back-support. Meanwhile, since H₂ addition in the upstream mixture does not affect the downstream H₂ content, the relative increase in the consumption speed, i.e. the back-support, is suppressed with larger H₂ addition. Especially, when the upstream H₂ content decreases with the equivalence ratio, the H₂ preferentially diffuses toward the unburned gas, which mitigates H₂ accumulation in the preheat zone and further weakens the back-support.     

Flame dynamics under various backpressures in a model scramjet with and without a cavity flameholder

Flame dynamics under various backpressure conditions were experimentally investigated using direct flame visualization, high-speed CH* chemiluminescence imaging, and wall pressure measurements. The stagnation pressure and temperature used in the present study were 100 kPa and 2500 K, respectively, with a freestream Mach number of 4.5. Rectangular scramjet models with and without a cavity were used to explore the effects of the cavity on flame dynamics when operating in scramjet mode, ramjet mode, and unstart. The flow rate of the ethylene jet was varied to impose backpressures corresponding to each operation mode. For both models, reverse flame propagation was observed for ramjet mode and unstart. For ramjet mode, flame fluctuation occurred within the isolator due to the coupling of fluid dynamics and combustion. The presence of a cavity enhanced combustion and reduced flame fluctuation in both scram and ramjet mode. The cavity promoted unstart because of the greater heat release from combustion. Further research using spatially resolved diagnostic techniques is needed to identify the flame locations for ramjet mode and unstart.     

Waterproof Light-Emitting Metal Halide Perovskite–Polymer Composite Microparticles Prepared via Microfluidic Device

Waterproof light-emitting perovskite–polymer composite microparticles are synthesized by a continuous one-step microfluidic reactor, which enables in situ production of metal halide perovskite nanoparticles (MHP-NPs) by the ligand-assisted reprecipitation process (LARP) and the encapsulation of MHP-NPs by UV cross-linking polymerization in the microfluidic channel. Successful encapsulation of MHP-NPs in polymer microparticles is attributed to the co-dispersion of an LARP solution and UV polymerizable solution in an aqueous continuous phase within the microfluidic channel, in which N,N-dimethylformamide, in co-dispersion droplets, is continuously extracted to the aqueous medium upon UV polymerization. MHP-NPs–polymer composite microparticles show enhanced stability against air and moisture.     

Solvent-free synthesis of polyhydroquinoline and 1,8-dioxodecahydroacridine derivatives through the Hantzsch reaction catalyzed by a natural organic acid: A green method

Solvent-free and high yielding one-pot synthesis of 1,8-dioxodecahydroacridine and polyhydroquinoline derivatives have been described through Hantzsch condensation of various aldehydes, ammonium acetate with cyclic 1,3-dicarbonyl compounds and ethyl acetoacetate in a very simple, efficient, and environmentally benign method using ascorbic acid as a nontoxic organocatalyst.     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Influence of clay surface modification with urethane groups on the crystallization behavior of in situ polymerized poly(butylene succinate) nanocomposites

The crystallization behavior and fine structure of poly(butylene succinate) (PBS) nanocomposites with intercalation (30B20) and exfoliation (30BM20) morphologies, respectively, were investigated via isothermal crystallization testing and synchrotron small-angle X-ray scattering (SAXS). The dynamic viscosity of 30BM20 was markedly increased due to favorable interactions between the PBS matrix and the urethane group on the clay surface. However, 30BM20 showed similar crystallization rates to that of homo PBS because the surface urethane modification for 30BM20 precluded PBS matrix from the metallic group into clay to difficult in contact with each other, resulting in a reduced nucleation activity for the metallic group. SAXS profiles revealed that the long period and amorphous region size for 30B20 drastically decreased during isothermal crystallization. Meanwhile, 30BM20 was similar to those of homo PBS. This result also supports the above explanation for isothermal crystallization behavior. Considering all results in total, the introduction of a urethane modification considerably enhanced the physical properties of PBS but caused delayed crystallization rates.     

Protegrin‐1 orientation and physicochemical properties in membrane bilayers studied by potential of mean force calculations

Protegrin‐1 (PG‐1) belongs to the family of antimicrobial peptides. It interacts specifically with the membrane of a pathogen and kills the pathogen by releasing its cellular contents. To fully understand the energetics governing the orientation of PG‐1 in different membrane environments and its effects on the physicochemical properties of the peptide and membrane bilayers, we have performed the potential of mean force (PMF) calculations as a function of its tilt angle at four distinct rotation angles in explicit membranes composed of either DLPC (1,2‐dilauroylphosphatidylcholine) or POPC (1‐palmitoyl‐2‐oleoylphosphatidylcholine) lipid molecules. The resulting PMFs in explicit lipid bilayers were then used to search for the optimal hydrophobic thickness of the EEF1/IMM1 implicit membrane model in which a two‐dimensional PMF in the tilt and rotation space was calculated. The PMFs in explicit membrane systems clearly reveal that the energetically favorable tilt angle is affected by both the membrane hydrophobic thickness and the PG‐1 rotation angle. Local thinning of the membrane around PG‐1 is observed upon PG‐1 tilting. The thinning is caused by both hydrophobic mismatch and arginine‐lipid head group interactions. The two‐dimensional PMF in the implicit membrane is in good accordance with those from the explicit membrane simulations. The ensemble‐averaged Val16 ¹⁵N and ¹³CO chemical shifts weighted by the two‐dimensional PMF agree fairly well with the experimental values, suggesting the importance of peptide dynamics in calculating such ensemble properties for direct comparison with experimental observables. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Effect of heat treatment on ZrO2-embedded electrospun carbon fibers used for efficient electromagnetic interference shielding

ZrO₂-embedded carbon fibers were prepared for use as an electromagnetic interference (EMI) shielding material by electrospinning and heat treatment methods. Structural changes were observed in the ZrO₂ and in the carbon structures by XRD and Raman spectroscopy, respectively. During heat treatment, XRD analysis results revealed a transition from a monoclinic structure to a tetragonal structure in ZrO₂ and a graphitization in the structural formation of carbon fibers was observed by Raman spectroscopy. It was observed that these structural changes in the ZrO₂ and the carbon fibers improved the real and imaginary permittivities by a factor of more than 3.5. The EMI shielding efficiency (SE) improved along with the permittivity with higher treatment temperatures and greater amounts of embedded ZrO₂; the highest average EMI SE achieved was 31.79 dB in 800-8500 MHz. The heat treatment played an important role in the improvements in the permittivity and in the EMI SE because of the heat-induced structural changes of the ZrO₂-embedded electrospun carbon fibers. We suggest that the EMI shielding of the fibers is primarily due to the absorption of electromagnetic waves, which prevents secondary EMI by reflection of electromagnetic waves.