Quantum dynamics through conical intersections in macrosystems: Combining effective modes and time-dependent Hartree

We address the nonadiabatic quantum dynamics of (macro)systems involving a vast number of nuclear degrees of freedom (modes) in the presence of conical intersections. The macrosystem is first decomposed into a system part carrying a few, strongly coupled modes, and an environment, comprising the remaining modes. By successively transforming the modes of the environment, a hierarchy of effective Hamiltonians for the environment can be constructed. Each effective Hamiltonian depends on a reduced number of effective modes, which carry cumulative effects. The environment is described by a few effective modes augmented by a residual environment. In practice, the effective modes can be added to the system’s modes and the quantum dynamics of the entire macrosystem can be accurately calculated on a limited time-interval. For longer times, however, the residual environment plays a role. We investigate the possibility to treat fully quantum mechanically the system plus a few effective environmental modes, augmented by the dynamics of the residual environment treated by the time-dependent Hartree (TDH) approximation. While the TDH approximation is known to fail to correctly reproduce the dynamics in the presence of conical intersections, it is shown that its use on top of the effective-mode formalism leads to much better results. Two numerical examples are presented and discussed; one of them is known to be a critical case for the TDH approximation.     

Locating conical intersections relevant to photochemical reactions

A new computerized method for locating conical intersections of interest in photochemistry is presented. The search is based on the Longuet-Higgins phase change theorem (Berry phase) which provides the subspace required for the initial search. The subspace is approximated as a plane containing three stable structures lying on a Longuet-Higgins loop. The search is conducted for a minimum of ΔE, the energy difference between two electronic states. It is started using up to three points within the circle defined by the three structures; symmetry, if relevant, is helpful but not essential. Since a two-dimensional subspace of the large 3N − 6 space is used, the search that uses either Cartesian or internal coordinates is efficient and yields a degeneracy after a few iterations. Given that not all degrees of freedom are included in the search, usually a high lying part of the conical intersection is initially located. The system is subsequently optimized along all coordinates keeping ΔE as close to zero as desired. The method is demonstrated for the symmetric H₃ system and also for the butadiene–cyclobutene–bicyclobutane system in which the three stable structures are not equivalent. The method is general and can be extended to any photochemical system.     

Combined complex-source beam and spherical-multipole analysis for the electromagnetic probing of conical structures

The paper addresses the combination of the spherical-multipole analysis in sphero-conal coordinates with a uniform complex-source beam (CSB) in order to analyze the scattering of a localized electromagnetic plane wave by any desired part of a perfectly conducting elliptic cone. The concept of uniform CSB is introduced and rigorously applied to the diffraction by a semi-infinite elliptic cone. The analysis takes into account the fact that the incident CSB does not satisfy the radiation condition. A new modal form of the Green's function for the elliptic cone is derived based on the principle that there is no energy loss to infinity. The numerical evaluation includes the scattered far fields of a CSB incident on the corner of a plane angular sector with different opening angles.     

Excited‐State Dynamics of Isolated DNA Bases: A Case Study of Adenine

We present a summary of recent advances in the understanding of the UV photophysics of the isolated DNA base adenine, emphasizing a discussion of the mechanisms behind the ultrafast relaxation following excitation to the ππ* band. Drawing on our femtosecond time‐resolved photoelectron spectroscopy experiments, we discuss differences in the ultrafast relaxation of adenine and 9‐methyladenine and consider the relative merits of the various proposed mechanisms.     

Characterization of the Graded Betti Numbers for Almost Complete Intersections

Using standard mapping cone procedure of the inclusion map of an ideal generated by a suitable regular sequence inside a Gorenstein ideal and by a deep analysis of possible cancellations, we give a numerical characterization of the graded Betti sequences admissible for almost complete intersections of height three.     

Numerical study of rheological behaviors of a compound droplet in a conical nozzle

The dynamics of compound droplets is more and more attractive because of their applications in a wide range of industrial and natural processes. This study aims to improve the understanding of dynamical rheological behaviors of a compound droplet moving in a nozzle with a conical shape in the downstream region via front-tracking-based simulations. The numerical results show that the compound droplet experiences three stages of deformation: the entrance stage (in front of the conical region), the transit stage (within the conical region), and the exit stage (in the exit of the nozzle). The droplet receives the maximum deformation in the axial direction during the transit stage, and the radially maximum deformation occurs during the exit stage. Because of the acceleration induced by the conical region, the inner droplet of the compound droplet can break up into smaller droplets during the exit stage. To reveal the transition between the finite deformation and the breakup, many parameters including the Capillary number Ca (varied in the range of 0.0125–1.6), the droplet size relative to the nozzle size R₁/R₀ (varied in the range of 0.2–0.9), the droplet radius ratio R₂₁ (varied in the range of 0.3–0.8), the viscosity ratios μ₂₁ and μ₃₁ (varied in the range of 0.05–3.2), the interfacial tension ratio σ₂₁ (varied in the range of 0.125–8.0), the conical angle α (varied in the range of 4°–34°) and the initial location of the inner droplet (i.e. the droplet eccentricity) are considered. From the finite deformation mode, the transition to the breakup mode of the inner droplet occurs when increasing any of Ca, R₁/R₀, R₂₁ and α, or decreasing any of μ₂₁ and σ₂₁. The breakup mode is also enhanced when the inner droplet is initially located closer to the leading side of the outer droplet. However, varying μ₃₁ induces no transition between these modes. The regime diagrams of these modes, based on these parameters, are also proposed.     

Hydrodynamics of gas-solid fluidization of a homogeneous ternary mixture in a conical bed： Prediction of bed expansion and bed fluctuation ratios

Hydrodynamic characteristics of fluidization in a conical or tapered bed differ from those in a columnar bed because the superficial velocity in the bed varies in the axial direction. Fixed and fluidized regions could coexist and sharp variations in pressure drop could occur, thereby giving rise to a noticeable pressure drop-flow rate hysteresis loop under incipient fluidization conditions. To explore these unique properties, several experiments were carried out using homogeneous, well-mixed, ternary mixtures with three dif- ferent particle sizes at varying composition in gas-solid conical fluidized beds with varying cone angles. The hydrodynamic characteristics determined include the minimum fluidization velocity, bed fluctuation, and bed expansion ratios. The dependence of these quantities on average particle diameter, mass fraction of the fines in the mixture, initial static bed height, and cone angle is discussed. Based on dimensional analysis and factorial design, correlations are developed using the system parameters, i.e. geometry of the bed （cone angle）, particle diameter, initial static bed height, density of the solid, and superficial velocity of the fluidizing medium. Experimental values of minimum fluidization velocity, bed fluctuation, and bed expansion ratios were found to agree well with the developed correlations.