Radiation reaction

I solve Maxwell's equation for a current produced by a classical, point electron. My solution, which represents the self electromagnetic field of the electron, can be found along the electron trajectory, where the conventional retarded-time solution is singular. The solution is in the form of an integral over all spectral frequencies of the field and has an Ehrenfest correspondence with the operator field of quantum electrodynamics (QED). Use of the field in the equation of motion for a harmonically-bound electron leads to an equation having the same form as the Schrödinger equation for a two-level atom interacting with the QED vacuum field.     

Interfacial reaction kinetics

We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. Coupled equations are derived for the hierarchy of many-body correlation functions. Postulating physically motivated bounds, closed equations result without the need for ad hoc decoupling approximations. We consider general dynamical exponent z, where is the rms diffusion distance after time t. At short times the number of reactions per unit area, , is 2nd order in the far-field reactant densities . For spatial dimensions dabove a critical value , simple mean field (MF) kinetics pertain, where Q_b is the local reactivity. For low dimensions , this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, , provided . Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs: . A density depletion hole grows on the more dilute A side. In the symmetric case (), when the long time decay of the interfacial reactant density, , is determined by fluctuations in the initial reactant distribution, giving . Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction . For fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and . We apply our results to simple molecules (Fickian diffusion, z=2) and to several models of short-time polymer diffusion (z>2). Received 8 June 1998 and Received in final form 10 September 1999     

Computing reaction paths of a bifurcation reaction: an action wave-front-based perspective

Application of Hamilton–Jacobi (HJ) equation to reaction systems which involve energy barrier(s) leading to the product is relatively new. Such problems are described by a new class of HJ equation, called the generalised HJ equation. This new HJ equation renders an anisotropic propagation for the wave front. In this paper, we describe the adaptation of the fast marching method (FMM) and the generalised HJ equation to understand a new class of reaction process where the energy barrier does not lead to the product; instead, a new class of states are detected along the reaction path of such reactions. These states are valley-ridge inflection point, branching point and potential energy ridge. Such reactions are characterised as bifurcation reactions. We have identified a new classical wave front, called the reaction action front (RAF) which distinctly separates the reaction system into a reactant zone and a product zone connected by a third zone, called ‘neck’. The RAF is an important tool to understand the bifurcation reaction and the associated reaction paths. We have also introduced a convenient way to compute the reaction path force (RPF) using the FMM. The RPF for a bifurcation reaction significantly differs from the reactions with energy barrier, and so, the RPF provides vital information about the occurrence of branching of a path. The method has been tested for the isomerisation reaction of methoxy radical (H₃C) to hydroxymethylene radical (H₂?OH).     

Dynamic regimes in a periodically forced reaction cell with oscillatory chemical reaction

Periodic and aperiodic regimes in a forced chemical system are studied experimentally and the observations are interpreted on the basis of phase transition curves evaluated both from the model equations and experimentally. The periodically oscillating system of the Belousov-Zhabotinski reaction in a flow-through stirred reaction cell exhibited phase transition curves both of the type 1 and 0 when a single pulse perturbation by bromide ions was used. This behaviour is only partly described by the mathematical models studied. Phase synchronization, intermittency and chaos were observed when the frequency and amplitude of concentration perturbations were varied in continuous forcing experiments. A one-dimensional deterministic model based on the experimental phase curves describes results of continuous forcing relatively well; better agreement was reached when effects of experimental noise were included in the model.     

The Gewald multicomponent reaction

The Gewald reaction of sulfur, cyanoacetic acid derivatives, and oxo-component (G-3CR) yielding highly substituted 2-aminothiophene derivatives has seen diverse applications in combinatorial and medicinal chemistry. Its products are of great use in pharmaceutical industry mainly as small molecular weight inhibitors. We herein review synthetic scope and variations, usage, and structural biology of Gewald products.     

Radiation reaction. II

Regularized classical field theory [B. Ritchie,Found. Phys. Lett. 4, 375 (1991)] is used to derive a new model for the Coulomb problem of an electron bound to an infinitely heavy nucleus. The model is solved numerically and interesting results are obtained, including the prediction of a stable ground state.     

Neutrino-nucleus reaction in supernovae

Neutrino reactions play an important role at various stages of core-collapse supernova. During infall, neutrinos are produced by electron capture mainly on nuclei and contribute significantly to the cooling of the collapsing core. After core bounce the nascent neutron star cools by neutrino emission. It is a major goal to observe such neutrinos from a future supernova by earthbound detectors and to establish their spectra. Recently it has been shown that the spectrum of electron neutrinos from the early neutrino burst is significantly altered if inelastic neutrino-nucleus scattering is considered in supernova simulations. Finally spallation reactions induced by neutrinos when passing through the outer burning shells can produce certain nuclides in what is called neutrino nucleosynthesis.     

The nuclear reaction matrix

Different difinitions of the reaction matrix G appropriate to the calculation of nuclear structure are reviewed and discussed. Qualitative physical arguments are presented in support of a two-step calculation of the G-matrix for finite nuclei. In the first step the high-energy excitations are included using orthogonalized plane-wave intermediate states, and in the second step the low-energy excitations are added in, using harmonic oscillator intermediate states. Accurate calculations of G-matrix elements for nuclear structure calculations in the A ≈ 18 region are performed following this procedure and treating the Pauli exclusion operator Q_2ν by the method of Tsai and Kuo. The treatment of Q_2ν, the effect of the intermediate-state spectrum and the energy dependence of the reaction matrix are investigated in detail. The present matrix elements are compared with various matrix elements given in the literature. In particular, close agreement is obtained with the matrix elements calculated by Kuo and Brown using approximate methods.     

Quasi-elastic reaction cross sections

Starting from the idea that a critical phenomenon separates deep-inelastic from quasi-elastic reactions, we introduce a simple procedure to calculate quasi-elastic cross sections. The results are compared with experimental data.     

Neck fragmentation reaction mechanism

Based on a microscopic transport model, we study the origin of nonstatistical intermediate mass fragment (IMF) production in semicentral heavy ion collisions at the Fermi energies. We show that a fast, dynamical IMF formation process, the neck fragmentation mechanism, can explain the experimentally observed features: deviations from Viola systematics and anisotropic, narrow angular distributions. It may be regarded as the continuation of the multifragmentation mechanism towards intermediate impact parameters. Its relation to other dynamical mechanisms, the induced fission and the abrasion of the spectator zones, that can also contribute to mid-rapidity IMF production, is discussed. The dependence on beam energy and centrality of the collision is carefully analysed. The competition between volume and surface instabilities makes this mechanism very sensitive to the in-medium nucleon-nucleon interactions, from the cross sections for hard collisions to the compressibility and other equation of state (EOS) properties.

For charge asymmetric collisions the sensitivity of various observables to the symmetry energy is investigated. Of particular interest appears the isospin diffusion dynamics with no signal of isospin equilibration. However, in spite of the short time scales and of the dynamical aspects, we notice isoscaling features of the neck mechanism. We observe that isospin enrichment of the neck zone as well as the isoscaling parameters are sensitive to the density dependence of asymmetry term of EOS around and below saturation value.     

Synthesis of neoproteoglycans using the transglycosylation reaction as a reverse reaction of endo-glycosidases

A method for the synthesis of carbohydrate chains (glycosaminoglycans) and their coupling to peptides was investigated using proteoglycans. Glycosidases generally catalyze a hydrolytic reaction, but can also mediate the reverse reaction, which in this case is a transglycosylation. In the transglycosylation reaction of bovine testicular hyaluronidase, which is an endoglycosidase, glycosaminoglycans (hyaluronan and chondroitin sulfates) release disaccharide (uronic acid-N-acetylhexosamine) moieties from non-reducing terminal sites, and then the liberated disaccharides are transferred immediately to the non-reducing termini of other glycosaminoglycan chains. Using such continuous reactions, it is possible to synthesize glycosaminoglycan chains according to a specific design. It then becomes possible to transfer glycosaminoglycan chains synthesized on a peptide to other peptides using the transglycosylation reaction of endo-β-xylosidase acting on the linkage region between a peptide and glycosaminoglycan chains of proteoglycans. We believe this approach will open a new field for the synthesis of homogeneous proteoglycans or their corresponding analogues.(Communicated by Takao SEKIYA, M.J.A.).     

The Ti/c-Si solid state reaction III. The low-temperature reaction kinetics

Thin Ti layers (≈10nm) are grown on top of a clean Si(111) substrate. Heating these layers initiates a solid state reaction, yielding a monosilicide phase at ≈350°C and a C49 disilicide at ≈450°C. The present study concerns the growth kinetics of both phases by means of ellipsometry. A diffusion-limited growth kinetics is found for the monosilicide formation. However, two growth rates are observed, a fast initial one and a slow terminal growth rate. An enhanced Si diffusion in atomically disordered regions as compared to well ordered regions (grains or clusters) could be an explanation. From the measurements we have found a value of 2×10^-15 cm²/s for the diffusion coefficient at ≈370°C and an activation energy of 0.62 ± 0.1 eV. Both values correspond to the fast process. Subsequently increasing the temperature to ≈450°C permits the growth of the homogeneous C49 TiSi₂ phase. For this process, both planar layer growth and intermixing are observed, however, quantitative results could not be derived from the present study.     

Toward cell circuitry: Topological analysis of enzyme reaction networks via reaction route graphs

The first step toward developing complete cell circuitry is to build quantitative networks for enzyme reactions. The conventional King-Altman-Hill (KAH) algorithm for topological analysis of enzyme networks, adapted from electrical networks, is based on “Reaction Graphs” that, unlike electrical circuits, are not quantitative, being straightforward renderings of conventional schematics of reaction mechanisms. Therefore, we propose the use of “Reaction Route (RR) Graphs” instead, as a more suitable graph-theoretical representation for topological analysis of enzyme reaction networks. The RR Graphs are drawn such that they are not only useful for visualizing the various reaction routes or pathways, but unlike Reaction Graphs possess network properties consistent with requisite kinetic, mass balance, and thermodynamic constraints. Therefore, they are better than the conventional Reaction Graphs for topological representation and analysis of enzyme reactions, both via the KAH methodology as well as via numerical matrix inversion. The difference between the two is highlighted based on the example of a single enzyme reaction network for the conversion of 7,8-dihydrofolate and NADPH into 5,6,7,8-tetrahydrofolate and NADP⁺, catalyzed by the enzyme dihydrofolate reductase.     

The water-forming reaction on palladium

The water-forming reaction on Pd has been studied on a PdSiO₂Si (Pd-MOS) structure in the temperature range 323–473 K. The reaction is found to be of the Langmuir-Hinshelwood type with the formation of OH beeing rate limiting. Since the Pd-MOS structure works as a sensitive hydrogen detector unique information on the behaviour of hydrogen during this catalytic reaction has been obtained. The reaction can be described in a model where the hydrogen atoms on the Pd surface have a large temperature activated lateral mobility and with no evidence of beeing in hot precursor states. At T = 473 K this means that for oxygen coverages ? 0.01 monolayers all hydrogen adsorbed will also react with oxygen. For smaller oxygen coverages unreacted hydrogen will not initially desorb towards the vacuum but towards the internal Pd surface of the Pd-MOS structure. Futhermore, hydrogen adsorption is blocked by adsorbed oxygen. The sticking coefficient for hydrogen on the bare Pd surface is, however, close to one and only weakly temperature dependent. An effect giving rise to a hysteresis in the work function versus oxygen coverage curve during oxygen adsorption - desorption is also discussed.     

Dual charges and radiation reaction

We offer a non-covariant derivation of the equation of motion for a dual charge, taking into account the radiation reaction, by means of a simple model of charge: a dumbbell. In the derivation we handle retarded quantities avoiding some of the usual approximations, in particular we do not restrict our calculations to first order inv/c nor overlook thet dependence ofR=|x–r(t)|. The differences with the radiation reaction problem for pure electric or magnetic charges are exhibited.     

Dynamics of traveling reaction pulses

The growth of activator losses is accompanied by the decay of a traveling reaction pulse. In a ring reactor, this propagation threshold is present simultaneously with a threshold related to the ring diameter. The results of numerical experiments with pulses of an exothermal reaction reveal the transition from pulse propagation to a homogeneous hot regime, established regimes with periodic variations of the pulse velocity, and oscillatory decay of the pulse. When the medium becomes “bistable” as a result of the variation in parameters, this factor does not prevent the propagation of pulses, but leads to changes in the pulse structure.     

Radiative reaction and quantum mechanics

According to the principles of quantum mechanics, the classical Lorentz-Dirac equations of the electron should follow from quantum electrodynamics in the classical limit. We show this is indeed true for the special case in which the charge does not radiate, provided the momentum operators in the Dirac theory are identified, in the classical limit, with the effective momenta of the Lorentz-Dirac equations.