Fractional Differential Equations

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

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Heat and Mass Transfer

Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

Experimental study of the pressure drop after fractal-shaped orifices in turbulent pipe flows

Three different approaches are used for evaluating some Lagrangian properties of homogeneous turbulence containing anisotropy due to the application of a stable stratification and a solid-body rotation. The two external frequencies are the magnitude of the system vorticity 2Q, chosen vertical here, and the Brunt-Vaisala frequency N, which gives the strength of the vertical stratification. Analytical results are derived using linear theory for the Eulerian velocity correlations (single-point, two-time) in the vertical and the horizontal directions, and Lagrangian ones are assumed to be equivalent, in agreement with an additional Corrsin assumption used by Kaneda. They are compared with results from the kinematic simulation model (KS) by Nicolleau & Vassilicos, which also incorporates the wave-vortex dynamics inherited from linear theory, and directly yields Lagrangian correlations as well as Eulerian ones. Finally, results from direct numerical simulations (DNS) are obtained and compared for the rotation-dominant case B = 2Ω/N = 10, the stratification-dominant case B = 1/10, the non-dispersive case B = 1, and pure stratification B = 0 and pure rotation N = 0

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Turbulent diffusion in rapidly rotating flows with and without stable stratification

The fractal flow conditioner for orifice plate flow meters

Enhancing the thermal performance of PCM in a shell and tube latent heat energy storage system by utilizing innovative fins

We develop a Lagrangian model of both one-particle In this paper ‘particle’ and ‘fluid element’ are synonymous. and two-particle turbulent diffusion in high Reynolds number and low Froude number stably stratified non-
 decaying turbulence. This model is a kinematic simulation (KS) that obeys both the linearized Boussinesq equations and incompressibility. Hence, turbulent diffusion is anisotropic and is studied in all three directions concurrently with incompressibility satisfied at the level of each and every trajectory. Horizontal one-particle and two-particle diffusions are found to be independent of the buoyancy (Brunt–Vaissala) frequency N . For one-particle diffusion we find that formula here and formula here where i = 1,2 and u ′ and L are a r.m.s. velocity and a length-scale of the energy-containing motions respectively, and formula here This capping of one-particle vertical diffusion requires the consideration of the entire three-dimensional flow, and we show that each and every trajectory is vertically bounded for all times if the Lagrangian vertical pressure acceleration a 3 is bounded for all times. Such an upper bound for a 3 can be derived from the linearized Boussinesq equations as a consequence of the coupling between vertical pressure acceleration and the horizontal and vertical velocities. Two-particle vertical diffusion exhibits two plateaux. The first plateau's scaling is different according to whether the initial separation Δ 0 between the two particles is larger or smaller than η, the smallest length-scale of the turbulence: formula here The second plateau is reached when the two particles become statistically independent, and therefore formula here The transition between the two plateaux coincides with the time when the two particles start moving significantly apart in the horizontal plane.

Franck C. G. A. Nicolleau

Papers

Experimental study of the pressure drop after fractal-shaped orifices in turbulent pipe flows

Turbulent diffusion in rapidly rotating flows with and without stable stratification

The fractal flow conditioner for orifice plate flow meters

Enhancing the thermal performance of PCM in a shell and tube latent heat energy storage system by utilizing innovative fins

Turbulent diffusion in stably stratified non-decaying turbulence