Modeling of the dynamics of a well-stirred reactor with parallel exothermic reactions

The dynamics of a well-stirred reactor in which two parallel exothermic first-order reactions occur was modeled. Phase portraits of the system were plotted, the possibility of realization of oscillatory regimes was revealed, and the stability of the steady states involved was examined. Two types of limit cycle extinction, smooth and sharp, were demonstrated to exist.     

Soot particle size distributions in a well-stirred reactor/plug flow reactor

A well-stirred reactor (WSR) followed by a plug flow reactor (PFR) is being used to study polycyclic aromatic hydrocarbon (PAH) growth and soot inception. Soot size distributions were measured using a dilution probe followed by a nano-differential mobility analyzer (Nano-DMA). A rapid insertion probe was fabricated to thermophoretically collect particles from the reactor for transmission electron microscopy (TEM) imaging. Results are presented on the effect of equivalence ratio on the soot size distributions obtained for fixed dilution ratio, the effect of dilution ratio on the soot size distributions obtained for fixed equivalence ratio, and the effect of temperature on the soot size distributions obtained for fixed equivalence ratio. In addition to particle sizing measurements, gas samples were analyzed by a gas chromatograph to determine the concentration of gaseous species in the PFR thought to be important in soot formation. Our soot size distribution measurements demonstrate that the mixing conditions in the flame zone affect whether or not a nucleation mode was detected in the size distribution.     

Effects of benzene and naphthalene addition on soot inception in a well-stirred reactor/plug flow reactor

A well-stirred reactor (WSR) followed by a plug flow reactor (PFR) is being used to study soot inception. Soot size distributions were measured using two different dilution probes followed by a nano-differential mobility analyzer (nano-DMA). One of the dilution probes was developed for the PFR section, while the second probe was specifically developed for use in the WSR section. Results are presented on the effect of residence time on the soot size distributions obtained for fixed dilution ratio and equivalence ratio. In addition, a technique to inject aromatics and PAH species in the transition region between the WSR and PFR was developed. Results are presented on the effect of benzene and naphthalene on the soot size distributions obtained for differing seeding concentrations and residence times. The results demonstrate for the first time the sensitivity of the soot particle size distribution to the seeding of aromatic species in a WSR/PFR.     

Self-oscillations in a flow ideal mixing reactor in the region of multiplicity of stationary equilibrium states: a consecutive reaction

A model of a flow ideal mixing reactor for a consecutive two-stage exothermic first-order reaction was considered. The presence of a region of multiplicity of stationary states was established. This multiplicity region can contain regions of three and five stationary states; the region of five states always appears inside the region of three stationary states. Changes in the type of stationary state stability in each of these regions are analyzed. Numerical calculations of phase trajectories in the regions of stationary state stability and instability were performed. A mechanism of the creation of a stable limiting cycle was suggested for the case of three stationary states.     

On stability of steady states

Conditions of stability with respect to finite perturbations of a steady transport state are derived on the basis of a statistical theory for a very general type of equations of motion for the state change. Infinitesimal perturbations yield the stability condition of Glansdorff and Prigogine.     

A reduced mechanism for primary reactions of coal volatiles in a plug flow reactor

In the present paper, the authors study the primary reactions of coal volatiles and a detailed mechanism has been made for three different environments: thermal decomposition (pyrolysis), partial oxidation (O₂) and O₂/CO₂ gasification in a plug flow reactor to analyze the combustion component. The computed results have similar trend for three different environments with the experimental data. A systematically reduced mechanism for O₂/CO₂ gasification has also been derived by examination of Rate of Production (ROP) analysis from the detailed mechanism (255 species and 1095 reactions). The reduced mechanism shows similar result and has been validated by comparing the calculated concentrations of H₂, CH₄, H₂O, CO, CO₂ and polycyclic aromatic hydrocarbon (PAH) with those of the detailed mechanism in a wide range of operating conditions. The authors also predicted the concentration profiles of H₂, CO, CO₂ and PAH at high temperature and high pressure.     

NESS theory of random steady states

A theory is presented for the properties of random steady states based upon a generalization of existing theories of nonrandom steady states. A sample calculation is presented for the energy cascade in a weakly stirred system. The theory introduces multivariable time correlation functions, and a new method for evaluating such objects is also given.Research supported by NSF grant No. CHE78-09704.Dreyfus Teacher-Scholar.     

Exact steady states to a nonlinear surface growth model

We report on exact stationary solutions to a nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. 80, 4221 (1998)]. Firstly, attention is focused on periodic solutions (steady states) which admit vertical points (or diverging local slopes). Such solutions, which are determined by a theoretical analysis, reveal that the nonlinear evolution equation may admit a non stationary solution with spike singularities or/and caps (dead-core solution) at maxima or/and minima. In a second part, steady states are, mathematically, generalized to a family of evolution equations. Finally, the effect of smoothening by step-edge diffusion is also revisited.     

Chaotic mixing in a steady flow in a microchannel

We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree with theoretical and experimental results for the flows in the Batchelor regime of mixing that are chaotic in time. The proposed microchannel provides fast and efficient mixing and is simple to fabricate.     

Torque-balanced high-density steady states of single-component plasmas

Electron plasmas in a Penning-Malmberg trap are compressed radially using a rotating electric field (the "rotating-wall technique"). For large electric fields, plasmas can be compressed over a broad range of frequencies. This permits access to a novel high-density regime in which outward transport is insensitive to plasma density. The limiting density occurs when the plasma rotation frequency equals the rotating-wall frequency. Characteristics of the resulting torque-balanced steady states are described, and implications for high-density electron and positron plasma confinement are discussed.     

Multiple-valued steady states and their stability in a saturable-absorber laser

We present the results of a theoretical consideration of steady states in a saturable-absorber laser for different frequencies of transition in the active medium, the absorber, and the cavity. The conditions for the coexistence of several (up to five) stationary values of intensity are obtained. The stability of such states is analytically studied, and the possible regimes of generation and switching for the parameters corresponding to solid-state lasers with a saturable absorber are shown. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 3, pp. 322–326, May–June, 2000.     

On the solutions and the steady states of a master equation

A complete characterization of the time behavior of the means and variance of a stochastic process which is generated by a finite number of independent systems is presented based on the master equation for the conditional probability. It is found that the means and variance relax to a steady state and that the steady state will be independent of the initial state if and only if a matrix related to the transition matrix is nonsingular. Finally, the result that the variance approaches its steady-state form at twice the rate of the means is shown to depend on the nonsingularity of the same matrix.     

All-optical noninvasive control of unstable steady states in a semiconductor laser

All-optical noninvasive control of a multisection semiconductor laser by means of time-delayed feedback from an external Fabry-Perot cavity is realized experimentally. A theoretical analysis, in both a generic model as well as a device-specific simulation, points out the role of the optical phase. Using phase-dependent feedback we demonstrate stabilization of the continuous-wave laser output and noninvasive suppression of intensity pulsations.     

Selection of steady states in planar Darcy convection

The planar natural convection of an incompressible fluid in a porous medium is considered. We study the selection of steady states under temperature perturbations on the boundary. A selection map is introduced in order to analyze the selection of a steady state from a continuous family of equilibria which exists under zero boundary conditions. The results of finite-difference modeling for a rectangular enclosure are presented.     

Properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von Kármán flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e., a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in nonhomogeneous nonisotropic turbulent flow.     

The localization properties of a random steady flow on a lattice

We consider a random stationary vector field on a multidimensional lattice and investigate flow-connected subsets of the lattice invariant under the action of the associated flow. The subsets of primary interest are cycles, and vortices each of which is the set of orbits terminating in the same cycle. We prove that with probability 1 each vortex only involves a finite number of sites of the lattice. Under the assumption of independence of the vector field in different sites, we find that with probability 1 the vortices exhaust all possible maximal flowconnected invariant subsets of the lattice if and only if the probability of existence of a cycle is positive. Thus, if cycles exist, a particle under the action of the flow only moves within a bounded region, i.e., it is completely localized.     

Multiple steady states for the Degn-Harrison reaction scheme of a bacterial culture

Spatially non-homogeneous steady states of a model reaction-diffusion scheme containing an inhibitory step are constructed explicitly in a one-dimensional geometry for the case when one component migrates very rapidly. In this approximation and by a convenient choice of boundary conditions the problem is reduced to one dynamical variable only.     

用时序探测事件模拟提升中子多重性计算效率

提出基于时序处理探测事件的中子多重性计数统计方法。在JMCT粒子输运数值模拟程序的基础上研发了用于统计中子多重性计数的专用数值模拟程序JMCT_NMC,实现在线的中子多重性计数模拟功能。展示了利用中子多重性计数算例检验程序,比较了JMCT_NMC与传统算法计算时间消耗的结果。时序探测事件处理方法不需大量存储粒子信息,在解决中子多重性计数模拟受内存限制问题的同时,提升了计算效率。在JMCT_NMC程序中,时序探测事件模拟手段在探测器关联事件模拟、本底分析等领域还有着更广泛的应用前景。     

Statistical reactions with memory and thermalized-nonequilibrated nuclear states

Starting from the Feshbach S-matrix pole expansion we modify the standard statistical model for compound reactions by introducing correlations between fluctuating S-matrix elements with different J (total spin) and π (parity) values. The S-matrix (J, π)-correlations are obtained at the expense of introducing infinitesimally small entrance-exit channel off-diagonal (J, π)-correlations between the random variables of the statistical model. Although later on these correlations are switched off by means of a properly applied limiting procedure, the S-matrix (J, π)-correlations do not vanish and can be strong. The physical origin of the S-matrix (J, π)-correlations resembles the effect of spontaneous symmetry breaking while S-matrix (J, π)-decoherence is due to quantum chaos. Novel reaction mechanism results in the excitation of peculiar nuclear states: The intermediate system is thermalized so that the shape of the spectrum is angle-independent and Maxwellian with angle-independent slope, yet the intermediate nucleus is not equilibrated since the angular distribution is forward-peaked, i.e., memory of the direction of the initial beam is not lost. The existence of thermalized-nonequilibrated nuclear states is supported by data on the 50–100% forward peaking of neutrons in the typically evaporation (1–3.5 MeV) part of the spectrum observed in the ⁹³ N b(n, n′) scattering with E _n = 7 MeV.