Random walk, solute

Prickett, T.A., T.G. Naymik and C.G. Lonnquist (19810. A random walk solute transport model for selected groundwater quality evaluations. Illinois State Water Survey, Bulletin 65. 

Prickett, T. A. Maymik, T. G. Lonnquist, C. G. A Random-Walk Solute Transport Model for Selected Groundwater Quality Evaluation. 1981, Illinois State Water Survey Bull. 65, 103... 

Prickett, T.A. Naymik, T.G. Lonnquist C.G. "A Random-Walk Solute Transport Model for Selected Groundwater Quality Evaluations" Bull. 65 111. State Water Survey Champaign,... 

Scalas, E., Gorenflo, R., Mainardi, R Uncoupled continuous-time random walks solution and limiting behavior of the master equation. Phys. Rev. E 69(1), 011107 (2004). http //dx.doi.org/10.1103/PhysRevE.69.011107... 

In the limit that the number of effective particles along the polymer diverges but the contour length and chain dimensions are held constant, one obtains the Edwards model of a polymer solution [9, 30]. Polymers are represented by random walks that interact via zero-ranged binary interactions of strength v. The partition frmction of an isolated chain is given by... 

There is an intimate connection at the molecular level between diffusion and random flight statistics. The diffusing particle, after all, is displaced by random collisions with the surrounding solvent molecules, travels a short distance, experiences another collision which changes its direction, and so on. Such a zigzagged path is called Brownian motion when observed microscopically, describes diffusion when considered in terms of net displacement, and defines a three-dimensional random walk in statistical language. Accordingly, we propose to describe the net displacement of the solute in, say, the x direction as the result of a r -step random walk, in which the number of steps is directly proportional to time ... 

Various mathematical concepts and techniques have been used to derive the functions that describe the different types of dispersion and to simplify further development of the rate theory two of these procedures will be discussed in some detail. The two processes are, firstly, the Random Walk Concept [1] which was introduced to the rate theory by Giddings [2] and, secondly, the mathematics of diffusion which is both critical in the study of dispersion due to longitudinal diffusion and that due to solute mass transfer between the two phases. The random walk model allows the relatively simple derivation of the variance contributions from two of the dispersion processes that occur in the column and, so, this model will be the first to be discussed. 

MMT (32) is a 1- or 2-dimensional solute transport numerical groundwater model, to be driven off-line by a flow transport, such as VTT (Variable Thickness Transport). MMT employs the random-walk numerical method and was originally developed for radionuclide transport. The model accounts for advection, sorption and decay. 

This expression accounts for the configurational entropy of an ideal binary mixture with identical molecular sizes, but not for that of a polymer solution, since polymer chains are large and flexible. For that case, more contributions arise from the chain conformational entropy, first considered by Meyer [19] and then derived by Huggins [20] and Flory [21]. In analogy with a nonreversing random walk on a lattice, the conformational contribution of polymer chains to the partition function is given by... 

The characteristic feature of a macromolecule in solution is its high degree of conformational freedom. The simplest possible model for an isolated macromolecule is the random walk (or... 

Conformation and Deformation of Linear Macromolecules in Concentrated Solutions and Melts in the Self-Avoiding Random Walks Statistics... 

Polymeric chains in the concentrated solutions and melts at molar-volumetric concentration c of the chains more than critical one c = (NaR/) ] are intertwined. As a result, from the author s point of view [3] the chains are squeezed decreasing their conformational volume. Accordingly to the Flory theorem [4] polymeric chains in the melts behave as the single ones with the size R = aN112, which is the root-main quadratic radius in the random walks (RW) Gaussian statistics. 

In presented work the analysis of osmotic pressure of the polymeric solutions has been done with taken into account the thermodynamics of conformation state of macromolecules following from the self-avoiding random walks statistics [13, 14],... 

Medvedevskikh Yu. G. Conformation and deformation of linear macromolecules in concentrated solutions and melts in the self-avoiding random walks statistics (see paper in presented book)... 

A point that has not been investigated is the possibility of considering u(k) a coloured noise instead of white noise, and therefore a non diagonal E. For example, the choice of a tridiagonal Ey would imply the assumption of u(k) a random walk process. On the one hand, by imposing a correlation among successive values of u(k), the flexibility of the output is reduced, and for example a delta function could not be recuperated. On the other hand, smoother outputs and better solutions could be obtained if good "a priori" estimations of the real autocorrelations of u(k) could be provided. 

The mathematical translation of the plane-source problem is as follows. Initially, there is a finite amount of mass M but very high concentration at a = 0, i.e., the density or concentration at a = 0 is defined to be infinite (which is unrealistic but merely an abstraction for the case in which initially the mass is concentrated in a very small region around a = 0). The initial condition is not consistent with that required for Boltzmann transformation. Hence, other methods must be used to solve the case of plane-source diffusion. Because this is the classical random walk problem, the solution can be found by statistical treatment as the following Gaussian distribution ... 

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