Perturbative approach to anA+B→C reaction-diffusion system

The hierarchy of kinetic equations for diffusion-reaction processes are rederived using a Fock space formalism for the Master equation. In the diffusion dominated case the reactive part can be analyzed perturbationally. In according to the experimental situation the behaviour of the system is governed by one space dimension. The summation of a whole class of terms in a perturbative serie yields the scaling behaviour of the production rate of the C particle. The solution depends on the ratio of the diffusion constantsD=D _A /D _B and the ratio of the characteristic time scales for reaction and diffusion, respectively. Various special cases and approximations are discussed in terms ofD. The analytical results can be supported by numerical simulations.     

Influence of sublayer atoms on Si(100) surface reconstructions

Influence of sublayer atoms on Si(100) surface reconstruction has been examined with density functional theory and molecular dynamic simulation. We found that the displacements of sublayer atoms under the buckled dimer affect the motions of their neighboring atoms and thus play an important role in determining the surface reconstructions. The present results reveal the relationship between the surface dimer reconstruction and the motion of the sublayer atoms and provide an account for experimental observations of Si(100) surface reconstructions at very low temperatures.     

Hybrid functions for nonlinear initial-value problems with applications to Lane-Emden type equations

A numerical method for solving nonlinear initial-value problems is proposed. The Lane-Emden type equations which have many applications in mathematical physics are then considered. The method is based upon hybrid function approximations. The properties of hybrid of block-pulse functions and Lagrange interpolating polynomials are presented and are utilized to reduce the computation of nonlinear initial-value problems to a system of non-algebraic equations. The method is easy to implement and yields very accurate results.     

Interaction of electronic structure and nuclear dynamics on the S1 reaction surface for the ring opening of cyclohexadiene

For the ultrafast photoinduced ring opening of cyclohexadiene the S₁ state plays a central role, providing the possibility to rapidly decay to the ground state. In this paper we follow the path of a wavepacket propagating in the reactive coordinate space of the S₁ surface. We present a detailed analysis of the corresponding electronic and nuclear motions. With the help of a projection method and a normal-mode analysis, the vibrational modes driving the reaction might be detected experimentally. Received: 10 November 1999 / Published online: 13 July 2000     

Visualisation of a supersonic free-jet expansion using laser-induced fluorescence spectroscopy: Application to the measurement of rate constants at ultralow temperatures

2 Σ⁺, v^′=0) by air at 26±4 K. A value of 2.56±0.40×10^-10 molecule^-1 cm³ s^-1 was obtained, a factor of more than four higher than at room temperature, and consistent with attractive forces dominating the quenching of OH(A²Σ⁺). A d etailed computational fluid dynamics (CFD) simulation of the supersonic free-jet expansion was performed, providing a two-dimensional visualisation of temperature and density variations throughout the expansion. The CFD calculations reproduced the salient features of the experimental temperature and density profiles along the centreline. Comparison between experiment and computation has allowed validation of CFD codes. Received: 31 January 1997/Revised version: 24 March 1997     

Escape by diffusion from a square well across a square barrier

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.     

Transitions between wells and escape by diffusion in a one-dimensional potential landscape

The time-dependence of the occupation probabilities of neighboring wells due to diffusion in one dimension is formulated in terms of a set of generalized rate equations describing transitions between neighboring wells and escape across a final barrier. The equations contain rate coefficients, memory coefficients, and a long-time coefficient characterizing the amplitude of long-time decay. On a more microscopic level the stochastic process is described by a Smoluchowski equation for the one-dimensional probability distribution. A numerical procedure is presented which allows calculation of the transport coefficients in the set of generalized rate equations on the basis of the Smoluchowski equation.     

Isotope effects in the kinetics of simultaneous H and D thermal desorption from Pd

The kinetics of simultaneous hydrogen and deuterium thermal desorption from PdH_xD_y has been investigated. A novel experimental approach for the study of the transition state (TS) characteristics of the surface recombination reaction is proposed based on the analysis of the H and D partitioning into H₂, HD and D₂ molecules. It has been found that the hydrogen molecular isotopes distribution is determined by the energy differences of the corresponding TS of the atom-atom recombination reactions. On the other hand, the mechanisms and activation energies of the desorption process have been obtained. At 420 K, the desorption reaction changes from a surface recombination limiting mechanism during desorption from β-PdH_xD_y to a reaction limited by the rate of β to α phase transformation during the two phase coexistence. Surface recombination reaction becomes again rate limiting above 480 K, due to a change in the catalytic properties of the Pd surface. TS energies obtained from the kinetic analysis of the thermal desorption spectra are in good accordance with those obtained from the analysis of the H₂, HD and D₂ distributions. Anomalous TS energies have been observed for the H-D recombination reaction, which may be related to the heteronuclear character of this molecule.     

Diffusion and convection after escape from a potential well

The escape by diffusion of a particle from a potential well in one dimension is strongly influenced by the application of a field in the adjacent half-space. At long times the probability distribution becomes a uniformly moving and steadily broadening gaussian in this half-space. The mean time of escape from the well is given by a simple expression in terms of the mean first passage time and the coefficient of the long-time tail in the occupation probability of the well in the absence of the field. Transient effects in space and time are studied in explicit form for a parabolic potential well.     

Diffusion in a bistable potential

The problem of diffusion of a particle in a bistable potential is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. The potential is modeled as two parabolic wells separated by a parabolic barrier. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in one of the wells. In the limit of a high barrier the rate of transition to the other well is given by an asymptotic result due to Kramers. For a potential barrier of moderate height there are significant corrections to the asymptotic result.     

Small rafts of xenon physisorbed on Pt(111)

The behavior of small rafts of xenon (<50 particles) is illustrated. Events which involve collective motion of raft atoms are shown to occur. These events are persistent below a transition temperature and are not persistent above this temperature. A video of the events is available.     

Computer simulation study of the Levy flight process

The random walk simulation of a Levy flight shows a linear relation between the mean square displacement 〈r²〉 and time. We have analyzed different aspects of this linearity. It is shown that the restriction of jump length to a maximum value (l_m) affects the diffusion coefficient, even though it remains constant for l_m greater than 1464. So, this factor has no effect on the linearity. In addition, it is shown that the number of samples does not affect the results. We have demonstrated that the relation between the mean square displacement and time remains linear in a continuous space, while continuous variables just reduce the diffusion coefficient. The results also imply that the movement of a Levy flight particle is similar to the case in which the particle moves in each time step with an average jump length 〈l〉. Finally, it is shown that the non-linear relation of the Levy flight will be satisfied if we use a time average instead of an ensemble average. The difference between the time average and ensemble average results shows that the Levy distribution may be a non-ergodic distribution.     

Silicon etching in Cl2 environment

The ion-beam-assisted etching of silicon in Cl₂ environment is considered. The theoretically calculated dependences of silicon etching rate on the flux of Cl₂ molecules at different ion current densities are compared with experimentally measured. The composition of the adsorbed layer is determined. It is found that SiCl₂ molecules prevail in the adsorbed layer. The reciprocal of relative concentration of SiCl₂ molecules in the adsorbed layer linearly depends on the ion-to-neutral flux ratio.     

A Scheme for Information Erasure in a Double-Well Potential

We design an experimental scheme to realize one-bit information erasure and restoring processes by considering an overdamped colloidal particle in a double-well optical trap, which is added by a controllable laser tweezer. Using the Monte Carlo method, we simulate numerically the Langevin equation to calculate the mean work spent during the entire process and validate the entropy production fluctuation theory. Our result shows that the distribution of entropy production becomes narrow with increasing temperature and becomes stationary, represents the diminishing extent of irreversibility.     

Signal propagation in stem-cell niches

Stem cells, maintaining tissue homeostasis, are nurtured in microscopic niches formed of so-called environmental cells. The kinetics of proliferation and differentiation of stem cells in such niches depend on their interaction with the messenger proteins secreted by environmental cells. We propose a generic mean-field kinetic model of the propagation of such signals. To motivate our study, we briefly describe a stem-cell niche in the Drosophila ovary. Our model is however applicable to other niches as well. In particular, it helps one to understand the necessary conditions for the niche function. For example, the model predicts that in the case of the Drosophila ovary each germline stem cell should have in the external membrane at least 700 receptors interacting with the signaling Dpp and Gpp proteins emanating from the cap cells.     

Molecular dynamics simulation about porous thin-film growth in secondary deposition

The thin film growth has been confirmed to be assembled by an enormous number of clusters in experiments of CVD. Sequence of clusters’ depositions proceeds to form the thin film at short time as gas fluids through surface of substrate. In order to grow condensed thin film using series of cluster deposition, the effect of initial velocity, substrate temperature and density of clusters on property of deposited thin film, especially appearance of nanoscale pores inside thin film must be investigated. In this simulation, three different cluster sizes of 203, 653, 1563 atoms with different velocities (0, 10, 100, 1000 and 3000 m/s) were deposited on a Cu(0 0 1) substrate whose temperatures were set between 300 and 1000 K. Four clusters and one cluster were used in primary deposition and secondary deposition, respectively. We have clarified that adhesion between clusters and substrate is greatly influenced by initial velocity. As a result, the exfoliation pattern of deposited thin film is dependent on initial velocity and different between them. One borderline dividing whole region into porous region and nonporous region are obtained to show the effect of growth conditions on appearance of nanoscale pores inside thin film. Moreover, we have also shown that the likelihood of porous thin film is dependent on the point of impact of a cluster relative to previously deposited clusters.     

Fourier-transform sensitivity analysis

Fourier-transform sensitivity analysis has been applied to a simplified model of a XeCl self-sustained discharge laser. Sensitivity coefficients have been calculated for chemical, electron and photon densities and for the discharge current and voltage. The role of preionization instability on model sensitivity has also been investigated. The sensitivity analysis has been coupled to a statistical analysis of the output data (mean, maximum and minimum values), which can help to better understand the behaviour of the tested model.     

Experimental verification of a zero-dimensional model of the ionization kinetics of XeCl discharges

An improved 0-dimensional model for XeCl high-pressure glow discharges is presented. Calculated discharge voltages are compared with precise measurements at a small, very homogeneous discharge. Excellent agreement in a wide parameter field demonstrates that this model may serve as a reference for simpler models describing the ionization kinetics.     

Detailed balance and phonon assisted sticking in adsorption and desorption of H2/Si

Recent experimental results on the desorption of D₂ from Si show practically no translational heating indicating a low barrier for adsorption. This seems to be at variance with the extremely low sticking coefficient found in adsorption experiments indicating a very high barrier. In order to understand this apparent discrepancy we consider a simple model of local lattice relaxation allowing for different barriers in adsorption and desorption processes. After taking the dynamics of this relaxation into account it turns out that detailed balance in principle is valid. In practice, however, it can not be applied for very large energy releases from lattice distortions. Our model predicts very strong phonon assisted sticking.