Annihilation Dynamics Research Articles

Two-order-parameter model of the liquid–glass transition. II. Structural relaxation and dynamic heterogeneity

We propose that there exist two key temperatures relevant to glass transition: (i) a transition from the ordinary-liquid to the frustrated metastable-liquid (the Griffiths-phase-like) state at Tm∗, which is characterized by the appearance of metastable high-density solid-like islands and the resulting appearance of the cooperative nature of α relaxation, and (ii) another transition into the spin-glass-like state and the resulting divergence of the α relaxation time at T0. Tm∗ is a density-ordering (melting) point of the corresponding hypothetical pure system that is free from disorder effects. Below Tm∗, a system has a complex free-energy landscape characteristic of the frustrated metastable-liquid state; metastable solid-like islands with different densities coexist and fluctuate dynamically. In our model, the α mode is associated with dynamics of creation and annihilation of metastable islands below Tm∗. The metastable solid-like islands are the origin of dynamic heterogeneity. We propose a modified Vogel–Fulcher law, which can phenomenologically describe the Arrhenius/Vogel–Fulcher crossover induced by a transition from the ordinary-liquid to the frustrated metastable-liquid state around Tm∗. We also argue that the hidden crystalline ordering in metastable islands may cause the change in the structure factor of a supercooled liquid below Tm∗, which is more enhanced upon cooling.

Two-order-parameter model of the liquid–glass transition. III. Universal patterns of relaxations in glass-forming liquids

In the preceding companion papers (paper I and II), we propose a possible origin of the slow dynamics associated with the liquid–glass transition in the light of our two-order-parameter model of liquids. Our model suggests that there exist two levels of dynamic structural heterogeneity, namely, ‘locally favored structures and their clusters’ and ‘metastable solid-like islands’. On the basis of this picture, we consider how all the dynamic modes associated with a glass transition, covering from the boson peak to the structural relaxation (α) mode, can be explained within the same model. We assign the boson peak to (quasi-) localized vibrational modes characteristic of locally favored structures and their clusters and the ultrafast mode to their overdamped states. We assign the fast β mode to the restricted ‘translational’ motion, while the slow β mode to the restricted ‘rotational’ (librational) motion characteristic of molecules in metastable islands, which exist only below Tm∗. The α mode is associated with dynamics of creation and annihilation of metastable islands below Tm∗. The appearance and disappearance of the modes as a function of the temperature are discussed, focusing on the behavior of locally favored structures and metastable solid-like islands.

Static pairwise annihilation in complex networks

We study static annihilation on complex networks, in which pairs of connected particles annihilate at a constant rate during time. Through a mean-field formalism, we compute the temporal evolution of the distribution of surviving sites with an arbitrary number of connections. This general formalism, which is exact for disordered networks, is applied to Kronecker, Erdös-Rényi (i.e., Poisson), and scale-free networks. We compare our theoretical results with extensive numerical simulations obtaining excellent agreement. Although the mean-field approach applies in an exact way neither to ordered lattices nor to small-world networks, it qualitatively describes the annihilation dynamics in such structures. Our results indicate that the higher the connectivity of a given network element, the faster it annihilates. This fact has dramatic consequences in scale-free networks, for which, once the "hubs" have been annihilated, the network disintegrates and only isolated sites are left.

Annihilation dynamics of umbilical defects in nematic liquid crystals under applied electric fields

Umbilical defects were induced in a nematic liquid crystal with negative dielectric anisotropy, confined to Hele-Shaw cells with homeotropic boundary conditions, and their annihilation dynamics were investigated experimentally. Dynamic scaling laws, previously proposed for Schlieren defects, were verified also for electric field induced umbilical defects while varying external parameters, such as electric field amplitude, frequency, Hele-Shaw cell gap, and temperature. In all cases, scaling relations of rho(t) proportional to t(-1) for the defect density and D proportional to (t(0) - t)(1/2) for the defect pair separation were obtained, independent of external field parameters. The experimental results give evidence of the universality of scaling relations for the annihilation of topological defects in liquid crystals, extended to umbilical defects and their annihilation dynamics under applied external fields.

Excitation‐Energy Migration in Self‐Assembled Cyclic Zinc(II)–Porphyrin Arrays: A Close Mimicry of a Natural Light‐Harvesting System

The excitation-energy-hopping (EEH) times within two-dimensional cyclic zinc(II)-porphyrin arrays 5 and 6, which were prepared by intermolecular coordination and ring-closing metathesis reaction of olefins, were deduced by modeling the EEH process based on the anisotropy depolarization as well as the exciton-exciton annihilation dynamics. Assuming the number of energy-hopping sites N = 5 and 6, the two different experimental observables, that is, anisotropy depolarization and exciton-excition annihilation times, consistently give the EEH times of 8.0 +/- 0.5 and 5.3 +/- 0.6 ps through the 1,3-phenylene linkages of 5 and 6, respectively. Accordingly, the self-assembled cyclic porphyrin arrays have proven to be well-defined two-dimensional models for natural light-harvesting complexes.

Stability of Tunnel Structure and Relationship between Peel Load and Spatiotemporal Pattern by Deformed Adhesive during Peeling

We investigated (i) the relationship between the spatiotemporal pattern of a deformed adhesive and peel load during peeling, and (ii) the dependence of the pattern formation on peel speed in the hard spring limit case. In the hard spring limit case, it is found that elastic and viscous peeling states coexist. It is also found that the occupation ratio of tunnel structures in a separation front is determined by the peel speed and is a monotonically decreasing function of peel speed. We experimentally confirmed that the value of peel load has a linear dependence on the occupation ratio of tunnel structures. An explanation of dynamical behavior is also given on the basis of the creation–annihilation dynamics of tunnel structures.

Probing Defect Sites on the CeO2 Surface with Dioxygen

In situ Raman spectroscopy of adsorbed dioxygen was used to characterize electron defects on the surface of nanocrystalline cerium oxide that was partially reduced with H2 and CO. Via 16O/18O isotope substitution, the bands in the range of 1135−1127 and 877−831 cm-1 were assigned to the O−O stretching vibration of dioxygen species bound to one- and two-electron defects on the CeO2 surface to form superoxide (O2-) and peroxide (O22-) species, respectively. A band at 357 cm-1 was attributed to the cerium−oxygen vibration of the adsorbed superoxides, O2-, whereas the bands at 538 and 340 cm-1 were assigned to the asymmetric and symmetric cerium−oxygen vibrations of the surface peroxides, O22-, respectively. The dynamics of the defect annihilation that results from surface reoxidation by adsorbed dioxygen species during temperature-programmed experiments allowed peroxide species adsorbed on isolated and aggregated two-electron defects to be distinguished. A general approach to investigate the reactivity of di...

Diffusion-controlled annihilationA+B→0with initially separated reactants: The death of anAparticle island in theBparticle sea

We consider the diffusion-controlled annihilation dynamics A+B-->0 with equal species diffusivities in the system where an island of particles A is surrounded by the uniform sea of particles B. We show that once the initial number of particles in the island is large enough, then at any system's dimensionality d the death of the majority of particles occurs in the universal scaling regime within which approximately 4/5 of the particles die at the island expansion stage and the remaining approximately 1/5 at the stage of its subsequent contraction. In the quasistatic approximation, the scaling of the reaction zone has been obtained for the cases of mean-field (d>or=d(c)) and fluctuation (d<d(c)) dynamics of the front.

Hedgehog–antihedgehog pair annihilation to a static soliton

We experimentally demonstrate that, for sufficiently small perturbations, a hedgehog ( H) and antihedgehog ( H ̄ ) point defect in nematic liquid crystals can be asymptotically free. For larger external perturbations, we find that the annihilation dynamics of an H H ̄ pair to a static soliton is asymmetric and shows two time regimes. A model for the experimental observations in the absence of smectic A fluctuations is proposed.

Some exact results for Boltzmann's annihilation dynamics.

The problem of ballistic annihilation for a spatially homogeneous system is revisited within Boltzmann's kinetic theory in two and three dimensions. Analytical results are derived for the time evolution of the particle density for some isotropic discrete bimodal velocity modulus distributions. According to the allowed values of the velocity modulus, different behaviors are obtained: power law decay with nonuniversal exponents depending continuously upon the ratio of the two velocities, or exponential decay. When one of the two velocities is equal to zero, the model describes the problem of ballistic annihilation in the presence of static traps. The analytical predictions are shown to be in agreement with the results of two-dimensional molecular dynamics simulations.

Dynamics of ballistic annihilation.

The problem of ballistically controlled annihilation is revisited for general initial velocity distributions and an arbitrary dimension. An analytical derivation of the hierarchy equations obeyed by the reduced distributions is given, and a scaling analysis of the corresponding spatially homogeneous system is performed. This approach points to the relevance of the nonlinear Boltzmann equation for dimensions larger than 1 and provides expressions for the exponents describing the decay of the particle density n(t) proportional, variant t(-xi) and the root-mean-square velocity v proportional, variant t(-gamma) in terms of a parameter related to the dissipation of kinetic energy. The Boltzmann equation is then solved perturbatively within a systematic expansion in Sonine polynomials. Analytical expressions for the exponents xi and gamma are obtained in arbitrary dimension as a function of the parameter mu characterizing the small velocity behavior of the initial velocity distribution. Moreover, the leading non-Gaussian corrections to the scaled velocity distribution are computed. These expressions for the scaling exponents are in good agreement with the values reported in the literature for continuous velocity distributions in d=1. For the two-dimensional case, we implement Monte Carlo and molecular dynamics simulations that turn out to be in excellent agreement with the analytical predictions.

Subdiffusion-limited reactions

Abstract We consider the coagulation dynamics A + A → A and the annihilation dynamics A + A →0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the “anomalous kinetics” and “anomalous diffusion” problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. We calculate both short-time and long-time concentrations, and compare and contrast the continuous and discrete cases. Our analysis is based on the fractional diffusion equation and its discrete analog.

Annihilation dynamics in the KPP-Fisher equation

We study the annihilation dynamics arising in the KPP-Fisher equation, proposed by Fisher in 1936 to model the propagation of a mutant gene and subsequently studied rigorously in the seminal work of Kolmogorov, Petrovskii and Piskunov. The approach is via a comparison theorem, where the comparison functions satisfy equations which are linearizable to the heat equation. In some sense, we have obtained a ‘linearization’ of the KPP-Fisher equation.

Subdiffusion-limited A+A reactions.

We consider the coagulation dynamics A+A-->A and A+A <==> A and the annihilation dynamics A+A-->0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation.

Dynamics of F-center annihilation in thermochemically reduced MgO single crystals

Optical absorption measurements were used to monitor the thermal annihilation of oxygen vacancies ( F-centers) in thermochemically reduced MgO crystals . The annihilation characteristics were sample-dependent and varied strongly with the F-center concentration. Different mechanisms for the destruction of F centers are suggested depending on their concentration.

Positron annihilation in simple molecular gases: A study of vibrational effects

The dynamics of positron annihilation in molecular gases containing simple diatomics is studied within a quantum formulation and is implemented by treating the positron–molecule interaction via an ab initio, nonempirical approach for all the forces at play. The process is analysed for room temperature conditions of the ambient gas and the behaviour of the corresponding annihilation rate coefficients, Z eff, is studied in detail by considering the role of the dynamical coupling between the positron motion and the vibrational degree of freedom of the molecular partner.

Anharmonic Oscillator Approach to the Exciton‐Exciton Annihilation Dynamics in Molecular Aggregates

AbstractThe dynamics of Frenkel excitons in aggregates of coupled electronic three‐level molecules in the presence of strong external fields is investigated. Particular emphasis is paid to the microscopic inclusion of exciton‐exciton annihilation. It appears as a combination of exciton fusion and internal conversion processes which are taken into account within perturbation theory. The influence of an environment on the exciton dynamics is treated by means of stochastic fluctuations of the electronic transition energies. A closed set of equations of motion is derived and it is shown how nonlinear optical spectra can be calculated nonperturbatively.

Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model

The Langevin equation for a particle ("random walker") moving in d-dimensional space under an attractive central force and driven by a Gaussian white noise is considered for the case of a power-law force, F(r) approximately -r(-sigma). The "persistence probability," P0(t), that the particle has not visited the origin up to time t is calculated for a number of cases. For sigma>1, the force is asymptotically irrelevant (with respect to the noise), and the asymptotics of P0(t) are those of a free random walker. For sigma<1, the noise is (dangerously) irrelevant and the asymptotics of P0(t) can be extracted from a weak noise limit within a path-integral formalism employing the Onsager-Machlup functional. The case sigma=1, corresponding to a logarithmic potential, is most interesting because the noise is exactly marginal. In this case, P0(t) decays as a power law, P0(t) approximately t(-straight theta) with an exponent straight theta that depends continuously on the ratio of the strength of the potential to the strength of the noise. This case, with d=2, is relevant to the annihilation dynamics of a vortex-antivortex pair in the two-dimensional XY model. Although the noise is multiplicative in the latter case, the relevant Langevin equation can be transformed to the standard form discussed in the first part of the paper. The mean annihilation time for a pair initially separated by r is given by t(r) approximately r(2) ln(r/a) where a is a microscopic cutoff (the vortex core size). Implications for the nonequilibrium critical dynamics of the system are discussed and compared to numerical simulation results.

Relaxation Paths and Dynamics of Photoexcited Polyene Chains: Evidence for Creation and Annihilation of Neutral Soliton Pairs

In recent work, we have demonstrated that the excited-state paths for radiationless deactivation and trans → cis isomerization for a series of polyenes involve a point of conical intersection between the covalent excited and ground states. In this paper we show how motion through this point can “trigger” the production of a transient π-diradical species (on the ground state) featuring an inverted double bond/single bond pattern. The computations have been carried out using an ab initio CAS−SCF approach and a hybrid molecular mechanics−valence bond (MM−VB) force field on three polyenes of increasing chain length: hexa-1,3,5-triene, octa-1,3,5,7-tetraene, and dodeca-1,3,5,7,9,11-hexaene (C12H14). Our computations show that production of the π-diradical must be a general feature of photoexcited polyenes. The investigation of the geometrical and electronic structure of these species indicates that they correspond to a pair of neutral solitons carrying unpaired electrons. Semiclassical trajectory computations on the “minimal” polyacetylene model C12H14 are used to model the creation, evolution, and annihilation dynamics of these transient entities.

Five years of antineutron physics at LEAR

For the first time the ( np ) system has been investigated in detail by using the unique n beam facility of the OBELIX experiment at LEAR. The advantages and usefulness of n beams, as complementary to the p ones, for studying the NN annihilations are discussed. After describing the n production techniques the most relevant results achieved during the last five years, on annihilation dynamics, meson spectroscopy and annihilation on nuclei are reported. The possibility to continue such a line of research in future at JHF is put forward.