Distribution of Substituents along the Cellulose Chain on Cellulose Xanthate and Carboxymethyl Cellulose

The distribution of substituents of cellulose xanthogenate and carboxymethyl cellulose along the cellulose chains and therefore in relation to the molecular mass can be measured using size exclusion chromatography including a multi angle laser light scattering and mass detection for determining the molecular mass of the derivative assisted by an UV- detection for determining the xanthate groups and carboxymethyl groups after derivatisation, respectively. The results investigating cellulose xanthogenate show that the temperature used in dissolving xanthogenate and in ripening viscose influences the distribution of xanthate groups in a different way; but all steps processing viscose are connected with a loss in the degree of substitution in ripening the distribution of substitution additionally becomes more even. The investigated carboxymethyl cellulose revealed different distribution of carboxylic groups in dependence on the viscosity of the CMC.     

Time-dependent step–step correlations in a self-avoiding random walk

The space–time step–step correlations of a polymer chain, described by a self-avoiding random walk on a cubic lattice, are studied by simulating its behavior on a computer. Chains of N = 16 and N = 32 beads are studied. The short-time behavior of the correlations is characterized by peaks, which become depressed and broadened with increasing interstep distance. The long-time behavior is characterized by extremely slow decay, which goes to zero in about the same time for all interstep distances. The short-time behavior is a consequence of the rotation of parts of the chain smaller than or equal to the static coherence length ζ. These short-time processes also seem to be responsible for the relaxation of the square of the end-to-end distance, since in both cases the relaxation is of the order of 6N². The long-time behavior of the correlations is a consequence of the rotations of parts of the chain greater than the coherence length. The correlations vanish when the entire chain has had time to rotate in space. Our results suggest that this corresponds to the relaxation of the end-to-end vector.     

A random walk simulation of flow injection analysis

Dispersion and chemical reaction in a single-channel flow-injection system are modelled by a random walk (stochastic, Markovian chain) method using a microcomputer. The effects of various simulated physical variables are investigated. The model provides valuable insight into the mixing process in flow injection analysis.     

The change of aromaticity along a Diels-Alder reaction path

[reaction: see text] Quinodimethanes are highly reactive toward dienophiles since Diels-Alder cycloaddition results in an aromatic product. Density functional-based (13)C, (1)H NMR, NICS, and MO-NICS calculations indicate that the increase of aromatic character of the developing benzenoid ring along the reaction path is especially pronounced after the transition state is reached, even though the number of pi orbitals decreases. The forming aliphatic ring exhibits large ring current effects during the reaction.     

On describing the steady absorption of brownian particles by a restricted random walk

This paper is concerned with idealizing brownian motion as a random walk, using the diffusion equation, and finding the boundary condition at an absorbing surface - all with an eye towards chemical kinetics. Three models of random walk (due to Smoluchowski, Fermi, and Lorentz) are considered, and it is concluded that the lorentzian model is the most appropriate.     

A mathematical theory of the random walk model in chromatography

An exact mathematical treatment of the random walk model in chromatography is given in this paper. Various factors which can cause broadening of peaks, such as equilibium fluctuation, diffusion, size and structure of fixed phase particles, fluid velocity, flow around the particles, distribution ratio, column temperature and nonuniformity, etc., are all considered with a unified theory. Formulas of mean retention time and height of theoretical plate, containing all of the factors, are presented.     

A random walk through the dynamics of homogeneous vapor-liquid nucleation

A method of calculating rates of homogeneous vapor-liquid nucleation based on Langevin dynamics of a few relevant degrees of freedom on a free-energy surface is proposed. The surface is obtained here from simulation and from a semi empirical expression. The mass and friction coefficients are derived from atomistic umbrella-sampling molecular-dynamics simulations. The calculated nucleation rate agrees with atomistic simulations for one particular state point of the Lennard-Jones fluid. The present method is about four orders of magnitude more computationally efficient than the direct atomistic simulation of the transmission coefficient.     

Symmetric random walk on a regular lattice with an elastic barrier: diffusion equation and the boundary condition

We examine here the symmetric random-walk model in which a particle can jump only to adjacent sites on a regular lattice, and discuss, in the light of the works of Chandrasekhar, Goodrich, van Kampen, and Oppenheim, the reduction of the problem of random walk in the presence of an elastic barner to a boundary value problem.     

Energy difference space random walk to achieve fast free energy calculations

A method is proposed to efficiently obtain free energy differences. In the present algorithm, free energy calculations proceed by the realization of an energy difference space random walk. Thereby, this algorithm can greatly improve the sampling of the regions in phase space where target states overlap.     

On the random walk of energy to traps in disordered systems

Adams recently derived a theorem concerning solutions of the Schrödinger equation for an N-electron system. From this theorem he concludes that exact eigenvalues and (antisymmetric) eigenfunctions can be obtained by solving a different type of equation whose eigenfunctions are not antisymmetric. We critically discuss aspects of Adams' formalism.     

Laplacian normalization and random walk on heterogeneous networks for disease-gene prioritization

Random walk on heterogeneous networks is a recently emerging approach to effective disease gene prioritization. Laplacian normalization is a technique capable of normalizing the weight of edges in a network. We use this technique to normalize the gene matrix and the phenotype matrix before the construction of the heterogeneous network, and also use this idea to define the transition matrices of the heterogeneous network. Our method has remarkably better performance than the existing methods for recovering known gene–phenotype relationships. The Shannon information entropy of the distribution of the transition probabilities in our networks is found to be smaller than the networks constructed by the existing methods, implying that a higher number of top-ranked genes can be verified as disease genes. In fact, the most probable gene–phenotype relationships ranked within top 3 or top 5 in our gene lists can be confirmed by the OMIM database for many cases. Our algorithms have shown remarkably superior performance over the state-of-the-art algorithms for recovering gene–phenotype relationships. All Matlab codes can be available upon email request.     

Continuous-time random walk models of DNA electrophoresis in a post array: part I. Evaluation of existing models

Several continuous-time random walk (CTRW) models exist to predict the dynamics of DNA in micropost arrays, but none of them quantitatively describes the separation seen in experiments or simulations. In Part I of this series, we examine the assumptions underlying these models by observing single molecules of λ DNA during electrophoresis in a regular, hexagonal array of oxidized silicon posts. Our analysis takes advantage of a combination of single-molecule videomicroscopy and previous Brownian dynamics simulations. Using a custom-tracking program, we automatically identify DNA-post collisions and thus study a large ensemble of events. Our results show that the hold-up time and the distance between collisions for consecutive collisions are uncorrelated. The distance between collisions is a random variable, but it can be smaller than the minimum value predicted by existing models of DNA transport in post arrays. The current CTRW models correctly predict the exponential decay in the probability density of the collision hold-up times, but they fail to account for the influence of finite-sized posts on short hold-up times. The shortcomings of the existing models identified here motivate the development of a new CTRW approach, which is presented in Part II of this series.     

Interpretation of diffusion coefficients in nanostructured materials from random walk numerical simulation

We make use of the numerical simulation random walk (RWNS) method to compute the "jump" diffusion coefficient of electrons in nanostructured materials via mean-square displacement. First, a summary of analytical results is given that relates the diffusion coefficient obtained from RWNS to those in the multiple-trapping (MT) and hopping models. Simulations are performed in a three-dimensional lattice of trap sites with energies distributed according to an exponential distribution and with a step-function distribution centered at the Fermi level. It is observed that once the stationary state is reached, the ensemble of particles follow Fermi-Dirac statistics with a well-defined Fermi level. In this stationary situation the diffusion coefficient obeys the theoretical predictions so that RWNS effectively reproduces the MT model. Mobilities can be also computed when an electrical bias is applied and they are observed to comply with the Einstein relation when compared with steady-state diffusion coefficients. The evolution of the system towards the stationary situation is also studied. When the diffusion coefficients are monitored along simulation time a transition from anomalous to trap-limited transport is observed. The nature of this transition is discussed in terms of the evolution of electron distribution and the Fermi level. All these results will facilitate the use of RW simulation and related methods to interpret steady-state as well as transient experimental techniques.     

Cellulose pyrolysis kinetics: An historical review on the existence and role of intermediate active cellulose

Cellulose pyrolysis, studied since more than one century, has been the object of a great number of papers. Several related kinetic models have been established in large experimental conditions, from slow to fast pyrolysis. Unfortunately, no actual consensus is reached. The primary formation of intermediate species accompanied or not with phase change phenomena are amongst the main matters of concerns. The purpose of the present review is to report the controversies, well-established knowledges and unresolved questions concerning the existence and role of intermediate species (often called “active cellulose”). After a general discussion, a few research topics are suggested at the end of the paper.     

Continuous-time random walk models of DNA electrophoresis in a post array: part II. Mobility and sources of band broadening

Using the two-state, continuous-time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1 μm posts with a 3 μm center-to-center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. On the contrary, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well described by a single post rope-over-pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device.     

Design, synthesis, and operation of small molecules that walk along tracks

The synthesis and system dynamics of a series of small-molecule walker-track conjugates, 3,4-C(n) (n = 2, 3, 4, 5, and 8), based on dynamic covalent linkages between the "feet" of the walkers and the "footholds" of the track, is described. Each walker has one acyl hydrazide and one sulfur-based foot separated by a spacer chain of "n" methylene groups, while the track consists of four footholds of alternating complementary functionalities (aldehydes and masked thiols). Upon repeatedly switching between acid and base, the walker moiety can be exchanged between the footholds on the track, primarily through a "passing-leg gait" mechanism, until a steady state, minimum energy, distribution is reached. The introduction of a kinetically controlled step in the reaction sequence (redox-mediated breaking and reforming of the disulfide linkages) can cause a directional bias in the distribution of the walker on the track. The different length walker molecules exhibit very different walking behaviors: Systems n = 2 and 3 cannot actually "walk" along the track because their stride lengths are too short to bridge the internal footholds. The walkers with longer spacers (n = 4, 5, and 8) do step up and down the track repeatedly, but a directional bias under the acid-redox conditions is only achieved for the C(4) and C(5) systems, interestingly in opposite directions (the C(8) walker has insufficient ring strain with the track). Although they are extremely rudimentary systems, the C(4) and C(5) walker-track conjugates exhibit four of the essential characteristics of linear molecular motor dynamics: processive, directional, repetitive, and progressive migration of a molecular unit up and down a molecular track.     

A reweighted random series method for stereographic projection path integrals

A set of general reweighted random series methods for metric affine spaces is developed. The extension of the theorems to metric affine spaces demands the introduction of a configuration-independent reference metric tensor; this geometric object is used to treat the path expansion coefficients beyond the core path, in both the partial averaging and the reweighted random series approach. Numerical tests are conducted by simulating a particle in a ring. The reweighted random series results show better convergence properties and better statistical quality at a fraction of the cost compared with the related partial averaging simulation.