Relative frequencies of constrained events in stochastic processes: An analytical approach

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈104). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications

Relative frequencies of constrained events in stochastic processes: An analytical approach

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They rely on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least $\approx 10^4$). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications

Impact of competitive processes on controlled radical polymerization

The kinetics of radical polymerization have been systematically studied for nearly a century and in general are well understood. However, in light of recent developments in controlled radical polymerization many kinetic anomalies have arisen. These unexpected results have been largely considered separate, and various, as yet inconclusive, debates as to the cause of these anomalies are ongoing. Herein we present a new theory on the cause of changes in kinetics under controlled radical polymerization conditions. We show that where the fast, intermittent deactivation of radical species takes place, changes in the relative rates of the competitive reactions that exist in radical polymerization can occur. To highlight the applicability of the model, we demonstrate that the model explains well the reduction in branching in acrylic polymers in RAFT polymerization. We further show that such a theory may explain various phenomena in controlled radical polymerization and may be exploited to design precise macromolecular architectures

Ion cyclotron wall conditioning experiments on Tore Supra in presence of the toroidal magnetic field

Wall conditioning techniques applicable in the presence of the high toroidal magnetic field will be required for the operation of ITER for tritium removal, isotopic ratio control and recovery to normal operation after disruptions. Recently ion cyclotron wall conditioning (ICWC) experiments have been carried out on Tore Supra in order to assess the efficiency of this technique in ITER relevant conditions. The ICRF discharges were operated in He/H-2 Mixtures at the Tore Supra nominal field (3.8 T) and a RF frequency of 48 MHz, i.e. within the ITER operational space. RF pulses of 60 s (max.) were applied using a standard Tore Supra two-strap resonant double loop antenna in ICWC mode, operated either in pi or 0-phasing with a noticeable improvement of the RF coupling in the latter case. In order to assess the efficiency of the technique for the control of isotopic ratio the wall was first preloaded using a D-2 glow discharge. After 15 minutes of ICWC in He/H-2 gas mixtures the isotopic ratio was altered from 4% to 50% at the price of an important H implantation into the walls. An overall analysis comparing plasma production and the conditioning efficiency as a function of discharge parameters is given