Optimal Control of Markov Processes with Age-Dependent Transition Rates

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.

Simplified theory of carrier back-scattering in semiconducting carbon nanotubes: A Kane's model approach

We present a simplified yet analytical formulation of the carrier backscattering coefficient for zig-zag semiconducting single walled carbon nanotubes under diffusive regime. The electron-phonon scattering rate for longitudinal acoustic, optical, and zone-boundary phonon emissions for both inter- and intrasubband transition rates have been derived using Kane's nonparabolic energy subband model.The expressions for the mean free path and diffusive resistance have been formulated incorporating the aforementioned phonon scattering. Appropriate overlap function in Fermi's golden rule has been incorporated for a more general approach. The effect of energy subbands on low and high bias zones for the onset of longitudinal acoustic, optical, and zone-boundary phonon emissions and absorption have been analytically addressed. 90% transmission of the carriers from the source to the drain at 400 K for a 5 mu m long nanotube at 105 V m(-1) has been exhibited. The analytical results are in good agreement with the available experimental data. (c) 2010 American Institute of Physics.

Coherence factors in excitonic insulators

Results of a theoretical study on ultrasonic attenuation and NMR relaxation in excitonic insulators are reported. The transition rates derived have anomalous temperature dependence owing to the occurrence of coherence factors analogous to the case of superconductors. It is found that these coherence factors are characteristically different for the interband and the intraband scattering processes. It is suggested that experimental observation of these temperature-dependent coherence factors may help identify the existence of an excitonic phase.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Synthesis of Eu3+-activated BiOF and BiOBr phosphors: photoluminescence, Judd-Ofelt analysis and photocatalytic properties

A series of Bi1-xEuxOX (X = F and Br; x = 0, 0.01, 0.03 and 0.05) phosphors were synthesized at relatively low temperature and short duration (500 degrees C, 1 h). Rietveld refinement results verified that all the compounds were crystallized in the tetragonal structure with space group P4/nmm (no. 129). Photoluminescence spectra exhibit characteristic luminescence D-5(0) -> F-7(J) (J = 0-4) intra-4f shell Eu3+ ion transitions. The magnetic dipole (D-5(0) -> F-7(1)) transition dominates the emission of BiOF:Eu3+, while the electric dipole (D-5(0) -> F-7(2)) peak was stronger in BiOBr:Eu3+ phosphors. The evaluated CIE color coordinates for Bi0.95Eu0.05OBr (0.632, 0.358) are close to the commercial Y2O3:Eu3+ (0.645, 0.347) and Y2O2S:Eu3+ (0.647, 0.343) red phosphors. Intensity parameters (Omega(2), Omega(4)) and various radiative properties such as transition rates (A), branching ratios (beta), stimulated emission cross-section (sigma(e)), gain bandwidth (sigma(e) x Delta lambda(eff)) and optical gain (sigma(e) x tau) were calculated using the Judd-Ofelt theory. It was observed that BiOBr:Eu3+ phosphors have a long lifetime (tau) and better optical gain (sigma(e) x tau) as compared to reported Eu3+ doped materials. Furthermore, these compounds exhibit excellent photocatalytic activity for the degradation of rhodamine B dye under visible light irradiation. The determined radiative properties and photocatalytic results revealed that BiOBr:Eu3+ phosphors have potential applications in energy and environmental remedies, such as to develop red phosphors for white light-emitting diodes, red lasers and to remove toxic organic industrial effluents.

Dipolar reorientation and phase-transition in mixed alkali-halide crystals

We show that the results of Lüty and Ortiz-Lopez relating the cyanide reorientation rates to the high-temperature phase diagrams of alkali-halide-alkali-cyanide mixed crystals can be understood within simple mean-field theory.

Mechanistic studies on the pyrolysis and combustion of polystyrene/ammonium perchlorate propellants in the presence of transition metal oxides

The effect of transition metal oxides (Fe2O3, MnO2, Ni2O3 and Co2O3) on polystyrene/ammonium perchlorate propellant systems has been examined. The mechanism of action of the oxides in increasing the burning rate was examined by studying the effect of the oxides on the thermal decomposition and combustion of the oxidizer and the propellant. It has been concluded that one of the mechanisms by which the oxides act is by promoting the charge-transfer process, which is indicated by the enhancement of the electron-transfer process in ammonium perchlorate and by the correlation between the redox potential of the metal ions and the corresponding burning rates of the propellant.

Aromatic claisen rearrangements in carbohydrates: stereocontrol of rearrangement rates in unsaturated sugar substrates

A remarkable difference is observed in the rates of [3,3]-sigmatropic rearrangement of aryl 4,6-di-O-acetyl-2,3-dideoxy-D-erythro-hex-2-enopyranosides 1 and 2; the slower reactivity of the alpha-isomers is consistent with AM1 calculated transition state energetics of model systems.

Crystal structure of nonadentate tricompartmental ligand derived from pyridine-2,6-dicarboxylic acid: Spectroscopic, electrochemical and thermal investigations of its transition metal(II) complexes

The coordinating behavior of a new dihydrazone ligand, 2,6-bis(3-methoxysalicylidene) hydrazinocarbonyl]pyridine towards manganese(II), cobalt(II), nickel(II), copper(II), zinc(II) and cadmium(II) has been described. The metal complexes were characterized by magnetic moments, conductivity measurements, spectral (IR, NMR, UV-Vis, FAB-Mass and EPR) and thermal studies. The ligand crystallizes in triclinic system, space group P-1, with alpha=98.491(10)degrees, beta=110.820(10)degrees and gamma=92.228(10)degrees. The cell dimensions are a=10.196(7)angstrom, b=10.814(7)angstrom, c=10.017(7)angstrom, Z=2 and V=1117.4(12). IR spectral studies reveal the nonadentate behavior of the ligand. All the complexes are neutral in nature and possess six-coordinate geometry around each metal center. The X-band EPR spectra of copper(II) complex at both room temperature and liquid nitrogen temperature showed unresolved broad signals with g(iso) = 2.106. Cyclic voltametric studies of copper(II) complex at different scan rates reveal that all the reaction occurring are irreversible. (C) 2011 Elsevier B.V. All rights reserved.

Effective Mass-Driven Structural Transition in a Mn-Doped ZnS Nanoplatelet

Mn doping in ZnS nanoplatelets has been shown to induce a structural transition from the wurtzite to the zinc blende phase. We trace the origin of this transition to quantum confinement effects, which shift the valence band maximum of the wurtzite and zinc blende polyrnorphs of ZnS at different rates as a function of the nanocrystal size, arising from different effective hole masses in the two structures. This modifies the covalency associated with Mn incorporation and is reflected in the size-dependent binding energy difference for the two structures.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

Two-point correlation function of an exclusion process with hole-dependent rates

We consider an exclusion process on a ring in which a particle hops to an empty neighboring site with a rate that depends on the number of vacancies n in front of it. In the steady state, using the well-known mapping of this model to the zero-range process, we write down an exact formula for the partition function and the particle-particle correlation function in the canonical ensemble. In the thermodynamic limit, we find a simple analytical expression for the generating function of the correlation function. This result is applied to the hop rate u(n) = 1 + (b/n) for which a phase transition between high-density laminar phase and low-density jammed phase occurs for b > 2. For these rates, we find that at the critical density, the correlation function decays algebraically with a continuously varying exponent b - 2. We also calculate the two-point correlation function above the critical density and find that the correlation length diverges with a critical exponent nu = 1/(b - 2) for b < 3 and 1 for b > 3. These results are compared with those obtained using an exact series expansion for finite systems.

Lesion Detection in Breast Ultrasound Images Using Tissue Transition Analysis

Breast cancer is one of the leading cause of cancer related deaths in women and early detection is crucial for reducing mortality rates. In this paper, we present a novel and fully automated approach based on tissue transition analysis for lesion detection in breast ultrasound images. Every candidate pixel is classified as belonging to the lesion boundary, lesion interior or normal tissue based on its descriptor value. The tissue transitions are modeled using a Markov chain to estimate the likelihood of a candidate lesion region. Experimental evaluation on a clinical dataset of 135 images show that the proposed approach can achieve high sensitivity (95 %) with modest (3) false positives per image. The approach achieves very similar results (94 % for 3 false positives) on a completely different clinical dataset of 159 images without retraining, highlighting the robustness of the approach.

The high temperature mechanical characteristics of superplastic 3 mol% yttria stabilized zirconia

A detailed study was undertaken to characterize the deformation behavior of a superplastic 3 mol% yttria-stabilized tetragonal zirconia (3YTZ) over a wide range of strain rates, temperatures and grain sizes. The experimental data were analyzed in terms of the following equation for high temperature deformation: Image Full-size image ∞ σn d−pexp(−Q/RT), where Image Full-size image is the strain rate, σ is the flow stress, d is the grain size, Q is the activation energy, R is the gas constant, T is the absolute temperature, and n and p are constants termed the stress exponent and the inverse grain size exponent, respectively. The experimental data over a wide range of stresses revealed a transition in stress exponent. Deformation in the low and high stress regions was associated with n not, vert, similar 3 and p not, vert, similar 1, and n not, vert, similar 2 and p not, vert, similar 3, respectively. The transition stress between the two regions decreased with increasing grain size. The activation energy was similar for both regions with a value of not, vert, similar 550 kJ mol−1. Microstructural measurements revealed that grains remained essentially equiaxed after the accumulation of large strains, and very limited concurrent grain growths occurred in most experiments. Assessment of possible rate controlling creep mechanisms and comparison with previous studied indicate that in the n not, vert, similar 2 region, deformation occurs by a grain boundary sliding process whose rate is independent of impurity content. Deformation in the n not, vert, similar 3 region is controlled by an interface reaction that is highly sensitive to impurity content. It is concluded that an increase in impurity content increases yttrium segregation to grain boundaries, which enhances the rate of the interface reaction, thereby decreasing the apparent transition stress between the n not, vert, similar 2 and n not, vert, similar 3 regions. This unified approach incorporating two sequential mechanisms can rationalize many of the apparently dissimilar results that have been reported previously for deformation of 3YTZ.

Transition from disc to rod-like shape of 16-3-16 dimeric micelles in aqueous solutions

Small-angle neutron scattering (SANS) measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(3)-N+ (CH3)(2)C16H33 2Br(-) dimeric surfactant, referred to as 16-3-16, at different concentrations and temperatures, are reported. It is seen that micelles are disc-like for concentrations C = 2.5 and 10 mM at temperature T = 30 degrees C. At low concentration C = 0.5 mM micelles are rod-like. Similarly, there is a disc to rod-like transition of micelles on increasing the temperature. For C = 2.5 mM, micelles are rod-like at T = 45 and 70 degrees C.