Phase diagrams of decomposing nanoalloys

The thermodynamics of nucleation and decomposition in small isolated particles are considered. There exist three possibilities: phase separation, prohibition of decomposition and a metastable state. We investigate the peculiarities of phase diagrams related to depletion of the nanosize parent phase even at the nucleation stage. For small particles the equilibrium diagram becomes split (and shifted and size dependent). Concentration, size and temperature hystereses take place. Size-dependent ‘critical supersaturation’, increasing with decreasing size, has been analysed.     

Coupled Intervals in the Discrete Optimal Control

In this paper, we investigate the nonnegativity and positivity of a quadratic functional ? with variable (i.e. separable and jointly varying) endpoints in the discrete optimal control setting. We introduce a coupled interval notion, which generalizes (i) the conjugate interval notion known for the fixed right endpoint case and (ii) the coupled interval notion known in the discrete calculus of variations. We prove necessary and sufficient conditions for the nonnegativity and positivity of ? in terms of the nonexistence of such coupled intervals. Furthermore, we characterize the nonnegativity of ? in terms of the (previously known notions of) conjugate intervals, a conjoined basis of the associated linear Hamiltonian system, and the solvability of an implicit Riccati equation. This completes the results for the nonnegativity that are parallel to the known ones on the positivity of ?. Finally, we define partial quadratic functionals associated with ? and a (strong) regularity of ?, which we relate to the positivity and nonnegativity of ?.     

Optimal control for a parabolic problem in a domain with highly oscillating boundary

In this article we study the homogenization of an optimal control problem for a parabolic equation in a domain with highly oscillating boundary. We identify the limit problem, which is an optimal control problem for the homogenized equation and with a different cost functional.     

Quantized fracture mechanics

A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at ‘quantized’ stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, β-SiC nanorods, α-Si₃N₄ whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agreement with Orowan's prediction. In contrast to LEFM, QFM has no restrictions on treating defect size and shape. The different fracture Modes (opening I, sliding II and tearing III), and the stability of the fracture propagations, are treated in a simple way.     

Perturbation Theory for Discrete Volterra Equations

Fixed point theory is used to investigate nonlinear discrete Volterra equations that are perturbed versions of linear equations. Sufficient conditions are established (i) to ensure that stability (in a sense that is defined) of the solutions of the linear equation implies a corresponding stability of the zero solution of the nonlinear equation and (ii) to ensure the existence of asymptotically periodic solutions.     

Experimental investigations of the normal loading of elastic spherical and conical indenters on to elastic flats

Results obtained from a series of experimental investigations are described in which an elastic polyisoprene hemisphere and elastic rubber cones of included angles 60°, 90°, 120° and 150° were loaded normally on to smooth blocks of soda–lime glass and polydimethylsiloxane (PDMS) containing 10% and 20% by volume of the curing agent. The load versus displacement data were continuously recorded with an instrumented indentation machine. It is shown that, whereas the loading behaviour of the hemisphere on to the blocks of the soda–lime glass and PDMS closely follows the theory of Hertz (see equation (1)), the load versus displacement behaviour of the rubber cones of included angles 60°, 90° and 120° could not be fitted by the Sneddon equation (see equation (5)) for rigid conical indenters loading on to an elastic half-space or by the modified Sneddon equation (see equation (6)) employing the combined moduli of the indenter and the half-space. The discrepancy between the predictions of the modified Sneddon equation and the experimental measurements is very significant, thus confirming our recent concern about the validity of using the modified Sneddon equation for analysing the experimental data obtained from nanoindentation experiments. Estimates of the errors caused by the use of the modified Sneddon equation have been made to further illustrate our contention. On the other hand, the behaviour of the 150° included angle cone loading on to the blocks of rubber, PDMS (1?:?10) and PDMS (1?:?20), has been shown to be particularly striking, as the rubber cone behaved as if it were rigid; moreover, the experimental data are well fitted by the Sneddon equation corresponding to a 150° rigid cone loading on to an elastic half-space. Finally, it has been proposed that, in order to determine the elastic modulus of a very stiff solid (i.e. Young's modulus close to that of the indenter) correctly using the technique of instrumented indentation, including nanoindentation, the included angle of the indenter, made of diamond, should be 150° and the measured load versus displacement data should be analysed using the Sneddon equation corresponding to a rigid cone of an included angle of 150°.     

Luminescence behavior as a probe for phase transitions and excimer formation in liquid crystals: dodecylcyanobiphenyl

The luminescence behavior of a liquid crystal, dodecylcyanobiphenyl, as a function of temperature, is reported. The fluorescence intensity exhibits discontinuities at temperatures which correspond to the phase transitions: crystalline — smectic — isotropic. The results are interpreted in terms of singlet monomer and excimer formation.     

PHOTOPHYSICS IN LIQUID CRYSTALS. FLUORESCENCE BEHAVIOR OF CHLOROPHYLL-a IN DODECYLCYANOBIPHENYL

Abstract— Fluorescence behaviour of chlorophyll- a in a liquid crystalline medium, dodecyl cyanobiphenyl, has been investigated as a function of temperature and concentration. At concentrations of 6 times 10^-4 M , emission in the Q-band region exhibited peaks in the crystal at 650,695 and 735 nm as well as the monomer band at 675 nm. Dilution studies indicate that these additional bands probably arise from aggregation of the chlorophyll.     

THE PHOTOEXCITED TRIPLET STATE OF TETRAPHENYL CHLORIN, MAGNESIUM TETRAPHENYL PORPHYRIN AND WHOLE CELLS OF CHLAMYDOMONAS REINHARDI. A LIGHT MODULATION-EPR STUDY

Abstract— The photoexcited triplet states of frozen solutions of tetraphenyl chlorin (TPC), magnesium tetraphenyl porphyrin (MgTPP) and whole cells of Chlamydomonas reinhardi have been studied by light modulation-EPR spectroscopy. The porphyrins were chosen to be studied as model compounds for chlorophyll molecules, From EPR spectra the zero field splitting parameters (ZFS) were calculated. For TPC, |D| = 0.0364 ± 0.0002 cm^-1, |E| = 0.0063 ± 0.0002 cm^-1. For MgTPP, |D| = 0.0310 ± 0.0002 cm^-1. For chloroplasts, |D| = 0.0280 ± 0.0004 cm^-1, |E| = 0.0032 ± 0.0004 cm^-1. In all compounds studied, except MgTPP, electron spin polarization (ESP) was observed. From the analysis of the kinetic curves at each canonical orientation we evaluated the spin lattice relaxation rate W, the depopulation rate constants k_p, and the ratio between the population rate constants, A_p, at zero magnetic field. For TPC in ethanol-toluene (5:1) k_x= (0.70 ± 0.10) × 10³ s^-1, k_y= (0.40 ± 0.07) × 10³ s^-1, k_x= (0.24 ± 0.05) × 10³ s^-1; A_x:A_y:A_z? 1.0:0.6:0.4; W= (2.60 ± 0.40) × 10³ s^-1. For MgTPP, only the total decay rate constant, k_T, was calculated: (1.5 ± 0.2) × 10 s^-1 in n-octane and (4.8 ± 0.8) × 10 s^-1 in ethanol. The results for TPC and MgTPP are compared to those reported previously for chlorophyll. It is concluded that the dynamics of the photoexcited triplet state in chlorophylls are mainly governed by the chlorin macrocycle. From the EPR spectrum and ZFS parameters of chloroplasts, we propose that both chlorophyll a and chlorophyll b are the main constituents of the EPR spectrum. From the analysis of the kinetic curves we obtain separately the kinetic parameters for chlorophylls a and b, k^a_x= (1.30 ± 0.20) × 10³ s^-1, k^a_y;= (0.85 ± 0.15) × 10³ s^-1k^a_x= (0.32 ± 0.05) × 10³ s^-1; A^a_x:A^a_y:A^a_z? 1.0:0.7:0.2; W^a= (1.20 ± 0.20) × 10³ s^-1; k^b_x= (0.56 ± 0.09) × 10³ s^-1, k^b_y= (0.30 ± 0.04) × 10³ s^-1, k^b_z= (0.06 ± 0.01) × 10³ s^-1; A^b_x:A^b_y:A^b_x? 1.0:0.6:0.1; W^b= (5.00 ± 0.80) × 10³ s^-1. These results are very close to those found separately for chlorophyll a and chlorophyll b oligomers in vitro.