The application of a new technique for zeolite framework structure solution is described that exhaustively enumerates every possible topology consistent with known unit-cell dimensions and space-group symmetry. It is shown that computer-generated on-line databases of hypothetical crystal structures can radically augment structure building in the pre-refinement stage.

In a previous study, we developed a database of periodic 4-connected graphs [Zeit. Kristallogr. 212 (1997) 768]. The database was built using a symmetry constrained intersite bonding search (SCIBS) method. This method enumerates all possible 4-connected nets within each space group type given the number of unique tetrahedral vertices, n(T). Approximately 107 graphs were obtained, mostly for n(T) = 1, 2. n(T) = 4 was achieved for some space groups that were rich in mirror symmetry. There was a combinatorial explosion of graphs with increasing n(T) in some space groups, which ultimately limited the method. The uninodal graphs, n(T) = 1, were refined by simulated annealing. A simple cost function was used that favoured a regular tetrahedral arrangement of neighbouring silicon atoms to emulate zeolite frameworks. Many plausible hypothetical uninodal zeolitic frameworks were reported.Since that report, we have improved the efficiency of the combinatorial search, and extended the range of our graph database to n(T) = 7 for some high mirror symmetry space groups. We have also implemented a more sophisticated Monte Carlo strategy for imbedding graphs in real space as an SiO2 Composition. Plausible refinements are then further optimized using the GULP program. Presently, there are almost 10(10) graphs in our database, and the number of plausible regular tetrahedral SiO2 frameworks identified now exceeds 100,000. (C) 2004 Elsevier Inc. All rights reserved.

We investigate high-Reynolds-number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number, which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible, so they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the statistics of the polymer elongations. The second state is realized when the Reynolds number is larger than the critical value. This regime is characterized by the strong back reaction of polymers on the flow. We establish some properties of the statistics of the stress and velocity in this regime and discuss its relation to the drag reduction phenomenon.

We consider inertial particles suspended in an incompressible turbulent flow. Because of particles' inertia their flow is compressible, which leads to fluctuations of concentration significant for heavy particles. We show that the statistics of these fluctuations is independent of details of the velocity statistics, which allows us to predict that the particles cluster on the viscous scale of turbulence and describe the probability distribution of concentration fluctuations. We discuss the possible role of the clustering in the physics of atmospheric aerosols, in particular, in cloud formation.

We consider inertial particles suspended in an incompressible turbulent flow. Due to inertia of particles, their velocity field acquires small compressible component. Its presence leads to a new qualitative effect --- possibility of clustering. We show that this effect is significant for heavy particles, leading to strong fluctuations of the concentration.

We consider statistics of the passive scalar on distances much larger than the pumping scale. Such statistics is determined by statistics of Lagrangian contraction that is by probabilities of initially distant fluid particles to come close. At the Batchelor limit of spatially smooth velocity, the breakdown of scale invariance is established for scalar statistics.

We consider the transport of dynamically passive quantities in the Batchelor regime of a smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity, we formulate the statistics of relevant characteristics of Lagrangian motion. This allows us to generalize many results obtained previously for strain delta correlated in time, thus answering a question about the universality of these results.

We consider inertial particles suspended in an incompressible turbulent flow. Due to inertia of particles, their velocity field acquires small compressible component. Its presence leads to a new qualitative effect --- possibility of clustering. We show that this effect is significant for heavy particles, leading to strong fluctuations of the concentration.

We describe two complementary formalisms designed for the description of the probability density function (PDF) of the gradients of turbulent fields. The first approach, we call it adiabatic, describes the PDF at the values much less than dispersion. The second, instanton, approach gives the tails of the PDF at the values of the gradient much larger than dispersion. Together, both approaches give a satisfactory description of gradient PDFs, as illustrated here by an example of a passive scalar advected by a one-dimensional compressible random how. [S1063-651X(98)50602-2].

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents zeta(n) of the structure functions S-n for n much greater than 1 under the additional condition d zeta(2) much greater than 1 (where d is the dimensionality of space). At n < n(c) [where n(c) = d zeta(2)/2(2 - zeta(2))] the exponents are zeta(n) = (zeta(2)/4)(2n - n(2)/n(c)), while at n > n(c) they are n independent: zeta(n) = zeta(2)n(c)/4. We also estimate n-dependent factors in S-n, particularly their behavior at n close to n(c). [S1063-651X(98)04011-2].

We consider high-order correlation functions of passive scalar in the Kraichnan model [I]. Using the instanton formalism we find the exponents zeta(n) of the structure functions S-n for n much greater than 1 at the condition d zeta(2) much greater than 1 (d is the dimensionality of space). At n < n(c) (where n(c) = d zeta(2)/[2(2 - zeta(2))]) the exponents are zeta(n) = (zeta(2)/4)(2n - n(2)/n(c)), whereas at n > n(c) they are n-independent: zeta(n) = zeta(2)n(c)/4. We also estimate n-dependent factors in S-n and critical behavior of S-n at n close to n(c).

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism, we find the scaling exponents ζn of the structure functions S n for n≫1 under the additional condition dζ2≫1 (where d is the dimensionality of space).At nn c they are n-independent: ζ n=ζ2n c /4. We also estimate the n-dependent factors in S n .

We demonstrate that if the exponent $\gamma$ that measures non-smoothness of the velocity field is small then the isotropic zero modes of the scalar's triple correlation function have the scaling exponents proportional to $\sqrt{\gamma}$. Therefore, zero modes are subleading with respect to the forced solution that has normal scaling with the exponent $\gamma$.

We consider the tails of probability density functions (PDF) for different characteristics of velocity that satisfies Burgers equation driven by a large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. We calculate high moments of the velocity gradient ∂xu and find out that they correspond to the PDF with [Formula: see text] where [Formula: see text] is the Reynolds number. That stretched exponential form is valid for negative ∂xu with the modulus much larger than its root-mean-square (rms) value. The respective tail of PDF for negative velocity differences w is steeper than Gaussian, ln ℘(w) ~-(w/u rms )3, as well as single-point velocity PDF ln ℘(u)~-(|u|/u rms )3. For high velocity derivatives [Formula: see text], the general formula is found: [Formula: see text].

We find explicitly a zero mode of the Kraichnan operator at two dimensions.

Advection of a passive scalar theta in d=2 by a large-scale velocity field rapidly changing in time is considered. The Gaussian feature of the passive scalar statistics in the convective interval was discovered in Ref. 1. Here we examine the deviations from the Gaussian behavior: The simultaneous fourth-order correlation function of theta is obtained analytically. Explicit expressions for fourth-order objects, like((theta(1)-theta(2))(4)), are derived. (C) 1995 American Institute of Physics.

We show that an arbitrary periodic flow of ideal incompressible fluids can be represented by means of three pairs of periodic Clebsch variables.