Random obstacles

D. Wu, K. Hui, D. Chandler. Monte Carlo study of polymers in equilibrium with random obstacles. J Chem Phys 96.-835-841, 1991. 

LOCALIZATION OF POLYMERS IN A MEDIUM WITH FIXED RANDOM OBSTACLES... 

Random obstacles which prevent the chain from visiting certain sites. 

We have compared our analytical results with numerical simulations performed by Dayantis et al. [30], and also comment on the relation to earlier simulations done by Baumgartner and Muthukumar [28]. Dayantis et al. carried out simulations of free chains (random-flight walks) confined to cubes of various linear dimensions 6 — 20, in units of the lattice constant. These chains can intersect freely and lie on a cubic lattice. They introduced random obstacles with concentrations r = 0,0.1,0.2 and 0.3. The length of the chains vary between 18 — 98 steps. They also simulated self-avoiding chains that we will not discuss here. They measured the quenched entropy, the end-to-end distance, and also the radius of gyration which is a closely related quantity. Unfortunately, these... 

The crossover regime occurs at obstacle density C bs when the size of the random polymer coil becomes equal to the size of the pores, Rg =, obs-From Eqs. (46) and (47) in this regime follows... 

Random Coding. We now turn to the subsidiary developments and theorems necessary in order to prove Theorem 4-11. The first obstacle in the path of deriving an upper bound to the probability of decoding error for a particular channel is the difficulty of finding good codes. Even if we could find such codes, the problem of evaluating their error probability would be extremely tedious if M and N were large both... 

Time intervals permitting displacement values in the scaling window a< )tortuous flow as a result of random positions of the obstacles in the percolation model [4]. Hydrodynamic dispersion then becomes effective. For random percolation clusters, an anomalous, i.e., time dependent dispersion coefficient is expected according to... 

The spatial temperature distribution established under steady-state conditions is the result both of thermal conduction in the fluid and in the matrix material and of convective flow. Figure 2. 9.10, top row, shows temperature maps representing this combined effect in a random-site percolation cluster. The convection rolls distorted by the flow obstacles in the model object are represented by the velocity maps in Figure 2.9.10. All experimental data (left column) were recorded with the NMR methods described above, and compare well with the simulated data obtained with the aid of the FLUENT 5.5.1 [40] software package (right-hand column). Details both of the experimental set-up and the numerical simulations can be found in Ref. [8], The spatial resolution is limited by the same restrictions associated with spin... 

As seen above, the randomness of the Mobius strip approach and numerous difficult steps in Schill s directed approach were highly limiting factors in a trefoil knot synthesis. Both these major obstacles might be circumvented by the use of an unambiguous templated synthesis procedure. 

Sznitman, Alain-Sol Brownian Motion, Obstacles, and Random Media, Springer-Verlag. Inc., New York, NY, 1998. 

One of the obstacles in this aim is the lack of experimental thermodynamic data for activity coefficients in ionic liquids, which could be a basis for such solvent selection. In the past years several groups have started to measure such data however, there is a lack of data because the number of suitable anions and cations, and even more the number of ionic liquids, are rapidly increasing compared to the rate (or speed) of measurements. Reliable inter- and extrapolation schemes and group contribution methods are still missing. Thus the search for an appropriate ionic liquid for a certain task can, at present, only be made randomly or by systematic measurements. 

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