Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

Reversible dynamics and the macroscopic rate law for a solvable Kolmogorov system: The three bakers' reaction

We investigate a piecewise linear (area-preserving) mapT describing two coupled baker transformations on two squares, with coupling parameter 0c1. The resulting dynamical system is Kolmogorov for anyc0. For rational values ofc, we construct a generating partition on whichT induces a Markov chain. This Markov structure is used to discuss the decay of correlation functions: exponential decay is found for a class of functions related to the partition. Explicit results are given forc=2^–n. The macroscopic analog of our model is a leaking process between two (badly) stirred containers: according to the Markov analysis, the corresponding progress variable decays exponentially, but the rate coefficients characterizing this decay are not those determined from the one-way flux across the cell boundary. The validity of the macroscopic rate law is discussed.     

STRUCTURE EVOLUTION OF POLYMER CHAINS FOR NECKING FORMATION IN HIGH-SPEED FIBER SPINNING PROCESS

Finite element method is used to simulate the high-speed melt spinning process,based on the equation system proposed by Doufas et al.Calculation predicts a neck-like deformation,as well as the related profiles of velocity,diameter, temperature,chain orientation,and crystallinity in the fiber spinning process.Considering combined effects on the process such as flow-induced crystallization,viscoelasticity,filament cooling,air drag,inertia,surface tension and gravity,the simulated material flow behaviors are consistent with those observed for semi-crystalline polymers under various spinning conditions.The structure change of polymer coils in the necking region described by the evolution of conformation tensor is also investigated.Based on the relaxation mechanism of macromolecules in flow field different types of morphology change of polymer chains before and in the neck are proposed,giving a complete prospect of structure evolution and crystallization of semi-crystalline polymer in the high speed fiber spinning process.     

The circular chemistry conceptual framework: A way forward to sustainability in industry 4.0

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Green chemistry and sustainability metrics in the pharmaceutical manufacturing sector

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Using a process-centered approach to minimize the effort of compliance

 The complexity of different quality standards can, in principle, be covered by different approaches and strategies. In-depth process mapping of quality control (QC) work streams was used by the analytical laboratories of Lonza AG to show up the principle differences in being compliant to different quality systems. The results identified two main drivers for all necessary actions: process-related activities and infrastructure-related activities. In addition, a clear indication of the economic impact of these driving forces was gained, which led the laboratories to decide on a process-oriented approach. This approach has the advantage of being able to reflect the different demands of different quality assurance (QA) regulations within the same QC organizational structure. Following the process helps avoid unnecessary efforts in analytical work and represents a very economical approach, at the same time, providing high flexibility to react to different QA or customer demands. Received: 5 July 2002 Accepted: 12 November 2002 Acknowledgements The process-oriented approach resulted from many, very challenging discussions for which I would like to thank the staff of my organization (Analytics & QC), especially, the QA staff and the LIMS team. Presented at Analytica Conference, 23–26 April 2002, Munich, Germany Correspondence to B. Ciommer     

Probability theory and polymer physics

This study applies the theory of stochastic processes to the equilibrium statistical physics of polymers in solution. The topics treated include random copolymers and randomly branching polymers, with self-consistent mean field effects. A new and more natural way of dealing with Boltzmann weighting is discussed, which makes it possible from the beginning of a calculation to consider only the physical polymer conformations. We also show that in general the random copolymer problem can be reduced to the ordinary polymer problem, and treat the self-consistent field problem for a general branching polymer.     

Singular perturbed Markov chains and exact behaviors of simulated annealing processes

We study asymptotic properties of discrete and continuous time generalized simulated annealing processesX(·) by considering a class of singular perturbed Markov chains which are closely related to the large deviation of perturbed diffusion processes. Convergence ofX(t) in probability to a setS ₀ of desired states, e.g., the set of global minima, and in distribution to a probability concentrated onS ₀ are studied. The corresponding two critical constants denoted byd and withd are given explicitly. When the cooling schedule is of the formc/logt, X(t) converges weakly forc>0. Whether the weak limit depends onX(0) or concentrates onS ₀ is determined by the relation betweenc, d, and . Whenc>, the expression for the rate of convergence for each state is also derived.