The Δ- Method for the Boltzmann Equation

A new numerical method is proposed to solve the Boltzmann equation. A frame is set up by using a discrete velocity approximation in the infinite velocity space, but by considering only those distribution function points which are not too small. The distribution function points may occur anywhere in the infinite discrete velocity space and are not constrained to a pre-specified region. A fourth-order finite difference is used for the convection terms. A Monte Carlo-like method is applied to the discrete velocity model of the collision integral. The effort of the method is proportional to the number of discrete points. Numerical examples are given for the full Boltzmann equation and results for some benchmark problems are compared with analytical or prior solutions.     

Determination of electrical and solar cell parameters of FTO/CuPc/Al Schottky devices

A Schottky structure is fabricated using CuPc sandwiched between fluorinated tin oxide (FTO) and aluminium electrodes. The electrical properties of the device are measured at room temperature. Permittivity of the device is calculated from capacitance measurements. The saturation current density, , diode ideality factor, n=3.02 and barrier height, are determined for the Schottky juction. Reverse bias versus is interpreted in terms of Schottky emission. Solar cell parameters are determined from the J-V characteristics. Power conversion efficiency, η of 0.0024% is obtained for the cell. Band gap energy of the material is determined from UV-visible absorption spectrum.     

DNA-directed artificial light-harvesting antenna

Designing and constructing multichromophoric, artificial light-harvesting antennas with controlled interchromophore distances, orientations, and defined donor-acceptor ratios to facilitate efficient unidirectional energy transfer is extremely challenging. Here, we demonstrate the assembly of a series of structurally well-defined artificial light-harvesting triads based on the principles of structural DNA nanotechnology. DNA nanotechnology offers addressable scaffolds for the organization of various functional molecules with nanometer scale spatial resolution. The triads are organized by a self-assembled seven-helix DNA bundle (7HB) into cyclic arrays of three distinct chromophores, reminiscent of natural photosynthetic systems. The scaffold accommodates a primary donor array (Py), secondary donor array (Cy3) and an acceptor (AF) with defined interchromophore distances. Steady-state fluorescence analyses of the triads revealed an efficient, stepwise funneling of the excitation energy from the primary donor array to the acceptor core through the intermediate donor. The efficiency of excitation energy transfer and the light-harvesting ability (antenna effect) of the triads was greatly affected by the relative ratio of the primary to the intermediate donors, as well as on the interchromophore distance. Time-resolved fluorescence analyses by time-correlated single-photon counting (TCSPC) and streak camera techniques further confirmed the cascading energy transfer processes on the picosecond time scale. Our results clearly show that DNA nanoscaffolds are promising templates for the design of artificial photonic antennas with structural characteristics that are ideal for the efficient harvesting and transport of energy.     

Synthesis, characterization, and electronic structure of new type of heterometallic boride clusters

The reaction of [Cp*TaCl(4)], 1 (Cp* = η(5)-C(5)Me(5)), with [LiBH(4)·THF] at -78 °C, followed by thermolysis in the presence of excess [BH(3)·THF], results in the formation of the oxatantalaborane cluster [(Cp*Ta)(2)B(4)H(10)O], 2 in moderate yield. Compound 2 is a notable example of an oxatantalaborane cluster where oxygen is contiguously bound to both the metal and boron. Upon availability of 2, a room temperature reaction was performed with [Fe(2)(CO)(9)], which led to the isolation of [(Cp*Ta)(2)B(2)H(4)O{H(2)Fe(2)(CO)(6)BH}], 3. Compound 3 is an unusual heterometallic boride cluster in which the [Ta(2)Fe(2)] atoms define a butterfly framework with one boron atom lying in a semi-interstitial position. Likewise, the diselenamolybdaborane, [(Cp*Mo)(2)B(4)H(4)Se(2)], 4 was treated with an excess of [Fe(2)(CO)(9)] to afford the heterometallic boride cluster [(Cp*MoSe)(2)Fe(6)(CO)(13)B(2)(BH)(2)], 5. The cluster core of 5 consists of a cubane [Mo(2)Se(2)Fe(2)B(2)] and a tricapped trigonal prism [Fe(6)B(3)] fused together with four atoms held in common between the two subclusters. In the tricapped trigonal prism subunit, one of the boron atoms is completely encapsulated and bonded to six iron and two boron atoms. Compounds 2, 3, and 5 have been characterized by mass spectrometry, IR, (1)H, (11)B, (13)C NMR spectroscopy, and the geometric structures were unequivocally established by crystallographic analysis. The density functional theory calculations yielded geometries that are in close agreement with the observed structures. Furthermore, the calculated (11)B NMR chemical shifts also support the structural characterization of the compounds. Natural bond order analysis and Wiberg bond indices are used to gain insight into the bonding patterns of the observed geometries of 2, 3, and 5.     

Composite Control of a Hovering Helicopter Based on Optimized Sliding Mode Control

Journal of Optimization Theory and Applications - A composite control law for stabilizing a small-scale helicopter during hover flight mode is proposed in this paper. The proposed method is...     

From symmetry breaking to symmetry swapping: is Kasha's rule violated in multibranched phenyleneethynylenes?

The phenomenon of excited-state symmetry breaking is often observed in multipolar molecular systems, significantly affecting their photophysical and charge separation behavior. As a result of this phenomenon, the electronic excitation is partially localized in one of the molecular branches. However, the intrinsic structural and electronic factors that regulate excited-state symmetry breaking in multibranched systems have hardly been investigated. Herein, we explore these aspects by adopting a joint experimental and theoretical investigation for a class of phenyleneethynylenes, one of the most widely used molecular building blocks for optoelectronic applications. The large Stokes shifts observed for highly symmetric phenyleneethynylenes are explained by the presence of low-lying dark states, as also established by two-photon absorption measurements and TDDFT calculations. In spite of the presence of low-lying dark states, these systems show an intense fluorescence in striking contrast to Kasha''s rule. This intriguing behavior is explained in terms of a novel phenomenon, dubbed “symmetry swapping” that describes the inversion of the energy order of excited states, i.e., the swapping of excited states occurring as a consequence of symmetry breaking. Thus, symmetry swapping explains quite naturally the observation of an intense fluorescence emission in molecular systems whose lowest vertical excited state is a dark state. In short, symmetry swapping is observed in highly symmetric molecules having multiple degenerate or quasi-degenerate excited states that are prone to symmetry breaking.

Highly symmetric multibranched phenyleneethynylenes exhibit intense fluorescence despite the presence of low-lying dark states. The inversion of the energy order of excited states is explained in terms of a novel phenomenon dubbed “symmetry swapping”.     

The Novikov Conjecture for Low Degree Cohomology Classes

We outline a twisted analogue of the Mishchenko–Kasparov approach to prove the Novikov conjecture on the homotopy invariance of the higher signatures. Using our approach, we give a new and simple proof of the homotopy invariance of the higher signatures associated to all cohomology classes of the classifying space that belong to the subring of the cohomology ring of the classifying space that is generated by cohomology classes of degree less than or equal to 2, a result that was first established by Connes and Gromov and Moscovici using other methods. A key new ingredient is the construction of a tautological C* _r (, )-bundle and connection, which can be used to construct a C* _r (, )-index that lies in the Grothendieck group of C* _r (, ), where is a multiplier on the discrete group corresponding to a degree 2 cohomology class. We also utilise a main result of Hilsum and Skandalis to establish our theorem.     

Synthesis, Characterization, and X-Ray Diffraction Analysis of Triethylenetetraammonium Tetrathiomolybdate

The reaction of gaseous H₂S with aqueous ammonium heptamolybdate in the presence of triethylenetetramine (trien) gave a red complex. The complex was recrystallized in hot water and characterized by element analysis and UV, visible, IR, and ¹H NMR spectroscopy. PMR has revealed accidental magnetic equivalence, resulting from the proximity of [MoS₄]^2- species in one complex molecule to the open triethylenetetramine ligand of another molecule. (TrienH₂)[MoS₄] crystallizes in the orthorhombic crystal system, space group Pca2₁, a=13.045(2), b=16.461(3), c=13.754(2) , =90, =90, =90°, V=2953.5(9) ³, Z=8, R₁=0.0323, wR₂=0.0730. The structure consists of the tetrahedral tetrathiomolybdate anions, forming an extended 3D framework in solids due to the interactions with triene cations via Mo-S...H-N hydrogen bonds.