Scaling properties of diffusion-limited reactions on fractal and euclidean geometries

We review our scaling results for the diffusion-limited reactions A + A 0 and A+B0 on Euclidean and fractal geometries. These scaling results embody the anomalies that are observed in these reactions in low dimensions; we collect these observations under a single phenomenological umbrella. Although we are not able to fix all the exponents in our scaling expressions from first principles, we establish bounds that bracket the observed numerical results.     

Discrete to continuous-time crossover due to anisotropy in diffusion-limited two-particle annihilation reactions

The diffusion-limited reaction A + A inert with anisotropic hopping on thed=1 lattice is solved exactly for a simultaneous updating, discrete time-step dynamics. Diffusion-dominated processes slow down as the anisotropy increases. For large times or large anisotropy, one can invoke the appropriate continuum limits. In these limits the effects of the anisotropy on the variation of particle density can be absorbed in time rescaling. However, in other regimes, when the discreteness of the time steps is nonnegligible, the anisotropy effects are nontrivial, although they are always quite small numerically.     

Spatial structure in diffusion-limited two-particle reactions

We analyze the limiting behavior of the densities _A(t) and _B(t), and the random spatial structure(r) = ( _A(t)., _B(t)), for the diffusion-controlled chemical reaction A+Binert. For equal initial densities _B(0) = _b(0) there is a change in behavior fromd 4, where _A(t) = _B(t) C/t^d/4, tod 4, where _A(t) = _b(t) C/t ast ; the termC depends on the initial densities and changes withd. There is a corresponding change in the spatial structure. Ind < 4, the particle types separate with only one type present locally, and , after suitable rescaling, tends to a random Gaussian process. Ind >4, both particle types are, after large times, present locally in concentrations not depending on type or location. Ind=4, both particle types are present locally, but with random concentrations, and the process tends to a limit.     

变化电压下扩散限制电解沉淀过程对铜的分形维数的影响

研究了铜的二维电解沉淀物在限制条件下的分形维数.拍摄了铜沉淀物随时间变化的照片,使用盒维法分析了各种条件下的豪斯多夫分形维数,并建立了计算机评估模型,以证明电压对豪斯多夫维数的重要影响.根据照片显示沉淀物的欧几里德几何形状也有着规则的变化.     

Open problems in formation and decay of composite systems in heavy ion reactions

New highly exclusive experiments in the field of formation and decay of composite systems in heavy ion reactions are presented. Dynamical effects are reviewed in the light of recent works on the role of the N/Z asymmetry between projectile and target. The possibility of extracting directly from the experimental data the emission barrier of alpha particles emitted from highly excited nuclei is discussed. Finally, the first experimental evidence of double giant resonance excitation in fusion-evaporation reaction is presented.     

Space-and time-resolved diffusion-limited binary reaction kinetics in capillaries: experimental observation of segregation,anomalous exponents,and depletion zone

An experimental investigation of one-dimensional, diffusion-limited A+BC chemical reactions is reported. The persistence of reactant segregation and the formation of a depletion zone is observed and expressed in terms of the universal time exponents: (motion of the boundary zone), (width of instantaneous product formation zone), (rate of instantaneous local formation of product), (rate of instantaneous global formation of product), etc. There is good agreement with the recently predicted and/or simulated values:=1/2,=1/6,=2/3,=1/2, in contrast to classical predictions (=0,=1/2,=0,=–1/2). Furthermore, classically the segregation would not be preserved and there would be no formation of a depletion zone and no motion (just dissipation) of the reaction zone. We also discuss the relations to electrode oxidation-reduction reactions, i.e., A+CC where C is a catalyst, electrode, or trap.     

Screened Coulomb potentials for astrophysical nuclear fusion reactions

The electron-screening acceleration of laboratory fusion reactions at astrophysical energies is an unsolved problem of great importance to astrophysics. That effect is modeled here by considering the fusion of hydrogen-like atoms whose electron probability density is used in Poisson's equation in order to derive the corresponding screened Coulomb potential energy. That way atomic excitations and deformations of the fusing atoms can be taken into account. Those potentials are then treated semiclassically in order to obtain the screening (accelerating) factor of the reaction. By means of the proposed model the effect of a superstrong magnetic field on laboratory hydrogen fusion reactions is investigated here for the first time showing that, despite the considerable increase in the cross-section of the dd reaction, the pp reaction is still too slow to justify experimentation. The proposed model is finally applied on the H² d, pH³ fusion reaction describing satisfactorily the experimental data although some ambiguity remains regarding the molecular nature of the deuteron target. Notably, the present method gives a sufficiently high screening energy for hydrogen fusion reactions so that the take-away energy of the spectator nucleus can also be taken into account. Received: 19 May 2000 / Accepted: 4 September 2000     

Gravitationally Induced Decoherence in Macroscopic Systems

A quantum master equation for the time evolution of the center of mass (CM) of a macroscopic body is derived which takes into account the influence of the system's gravitational field over the CM wave function. As a consequence, all the relevant phenomenological features of the so-called GRW (Ghirardi, Rimini, and Weber) model are reproduced with no free parameters. The model presented here predicts also the existence of a transition region for the mass of the system—a kind of frontier between quantum (coherent) and classical (decoherent) behavior.     

Two-pion production in photon-induced reactions

Differences in the photoproduction of mesons on the free proton and on nuclei are expected to reveal changes in the properties of hadrons. Inclusive studies of nuclear photoabsorption have provided evidence of medium modifications. However, the results have not been explained in a model independent way. A deeper understanding of the situation is anticipated from a detailed experimental study of meson photoproduction from nuclei in exclusive reactions. In the energy regime above the Δ(1232) resonance, the dominant double pion production channels are of particular interest. Double pion photoproduction from nuclei is also used to investigate the in-medium modification of meson-meson interactions     

Pattern formation in reaction-diffusion system in crossed electric and magnetic fields

We consider a reaction-diffusion system in crossed electric and magnetic fields lying on the reaction plane. It is shown that a charge separation along the direction normal to the reaction plane resulting in a diffusional flux may cause a differential flow induced chemical instability and stationary pattern formation on a homogeneous steady state. This pattern is generically different from a Turing pattern modified by the crossed fields. The special role of magnetic field is emphasized. Our theoretical analysis is corroborated by numerical simulation on a reaction-diffusion system in three dimensions.     

Intrinsic fluctuations in explosive reactions

A reaction is called explosive when the amount of a reactant becomes infinite in a finite time. When the intrinsic stochastic character of the reaction is taken into account, the explosion time is a random quantity. We compute its probability distribution, or at least its average and variance, for various kinds of reactions. If a reaction is unstable, so that a reactant can either explode or disappear, one first has to compute the probability for an explosion to occur at all, and then the average explosion time. Finally, the same ideas are applied to more general Markov processes.     

Pattern formation,social forces,and diffusion instability in games with success-driven motion

A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner’s dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion.     

Transition states in Ei reactions

The pyrolysis of amine oxides, sulfoxides, selenoxides, and esters to form alkenes is believed to be a concerted reaction with a cyclic transition state. Phosphine oxides, sulfones, and nitro compounds are unreactive. This study seeks to identify reasons for the lack of reactivity of the latter. Transition states were located for all substrates progressing from RHF/3‐21G* to the MP2/6‐31+G(d,p) level (in certain cases). For sulfones and nitro compounds, two possible reasons for lack of reactivity were considered: (1) Atoms approaching one another in the transition state may be considered to participate in a local n_O → σ*_CH interaction. The second oxygen in the sulfone or nitro compound lowers the energy of the ‘non‐bonded electrons’ at oxygen leading to a greater mismatch in energy with the antibonding C? H orbital (in comparison to the sulfoxide or amine oxide). (2) The sulfone and nitro ‘lone pairs’ are not really ‘alone’, and available to react. In fact, complex bonding arrangements exist in the SO₂ and NO₂ groups. The situation is less clear for phosphine oxides, although ground state stability of bonds is important. Implications concerning the Hammond postulate are covered. Copyright © 2009 John Wiley & Sons, Ltd.     

Analysis of the spectator-angular distribution in the light-nuclei reactions

Angular distributions of spectator particles in dp and ⁴Hep reactions in the region of a few GeV have been studied. Significant asymmetries of the spectator particle distributions have been observed for reactions where π-mesons are produced in the final state. Results of calculations in the framework of a spectator model taking into account the nuclear wave function, flux factor and the energy dependence of the NN elementary cross-sections, have been compared to experimental data. A good agreement has been observed for the fragments momenta, where the one-pole mechanism dominates. Received: 11 February 2000 / Accepted: 29 June 2000     

Understanding oxygen reactions in aprotic Li-O_2 batteries

Although significant progress has been made in many aspects of the emerging aprotic Li-O_2 battery system, an indepth understanding of the oxygen reactions is still underway. The oxygen reactions occurring in the positive electrode distinguish Li-O_2 batteries from the conventional Li-ion cells and play a crucial role in the Li-O_2cell's performance(capacity, rate capability, and cycle life). Recent advances in fundamental studies of oxygen reactions in aprotic Li-O_2 batteries are reviewed, including the reaction route, kinetics, morphological evolution of Li_2O_2, and charge transport within Li_2O_2. Prospects are also provided for future fundamental investigations of Li-O_2 chemistry.     

Selective tunnelling effects in collinear chemical reactions

Summary Tunnelling contributions to the reactive probability of both early- and late-barrier reactions are investigated. For the first class of reactions a new type of tunnelling effect taking place at high translational energy is discussed. For both reactions relations linking tunnelling features to the type of energy promoting reactivity are discussed with regard to the barrier location.

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Riassunto Si esamina il contributo dell'effetto tunnel alla probabilità reattiva per reazioni con barriera anticipata e con barriera posticipata. Per la prima classe di reazioni si discute un nuovo tipo di effetto tunnel che ha luogo ad alte energie traslazionali. Per ambedue i tipi di reazione si discute il nesso esistente tra le caratteristiche dell'effetto tunnel e la forma di energia che è capace di favorire la reazione in relazione alla posizione della barriera.

     

Pattern formation in Ferroelastic Transitions

We study pattern formation in ferroelastic materials using the Ginzburg–Landau approach. Since ferroelastic transitions are driven by strain, the nonlinear elastic free energy is expressed as an expansion in the appropriate (i.e., order parameter) strain variables. However, the displacement fields are the real independent variables, whereas the components of the strain tensor are related to each other through elastic compatibility relations. These constraints manifest as an anisotropic long-range interaction which drastically influences the underlying microstructure. The evolution of the microstructure is demonstrated for (i) a hexagonal-to-orthorhombic transition using a strain-based approach with explicit long-range interactions; and (ii) a cubic-to-tetragonal transition by solving the force-balance equations for the displacement fields.     

Pattern formation in the reaction with anisotropic lateral adsorbate-adsorbate interactions

We present Monte Carlo simulations of the formation of (1×2) islands in the case of the 2 A + B ₂ → 2 AB reaction occurring via the Langmuir-Hinshelwood mechanism on a square lattice under steady-state conditions. The model employed takes into account the effect of anisotropic lateral B-B interactions on the rates of B diffusion and elementary reaction events. The results obtained with qualitatively realistic ratio of the rate of elementary reaction steps indicate that the average island size depends on the details of diffusion and reaction dynamics in a similar way as in the earlier studied case of the simplest A + B reaction running via the Eley-Rideal mechanism. Received 4 January 2002 and Received in final form 2 April 2002 Published online 25 June 2002     

Exponential stability of states close to resonance in infinite-dimensional Hamiltonian systems

We develop canonical perturbation theory for a physically interesting class of infinite-dimensional systems. We prove stability up to exponentially large times for dynamical situations characterized by a finite number of frequencies. An application to two model problems is also made. For an arbitrarily large FPU-like system with alternate light and heavy masses we prove that the exchange of energy between the optical and the acoustical modes is frozen up to exponentially large times, provided the total energy is small enough. For an infinite chain of weakly coupled rotators we prove exponential stability for two kinds of initial data: (a) states with a finite number of excited rotators, and (b) states with the left part of the chain uniformly excited and the right part at rest.     

Structure and reactions of halo nuclei: An entangled approach

Halo nuclei are characterised by their weak binding, large spatial extent and hence a quite pronounced, yet highly correlated, few-body structure. This is typically in terms of a well-defined core plus one or more valence nucleons. Over the past decade the properties of halo nuclei have been studied theoretically using a range of reaction models, many of which having served us well for half a century or more in the study of less exotic, “mean-field”, nuclei. However, it is now clear that for many reactions with halo nuclei, it is not appropriate to disentangle (factorise out) the structure information from the reaction information. That is, the few-body nature of these systems requires few-body reaction models in which the nuclear structure and reaction mechanisms are necessarily entangled. This talk will briefly review the physical assumptions made by various reaction models, and point to areas where progress is being made to extend their range of applicability in order to provide further insights into halo structure. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: j.al-khalili@surrey.ac.uk