Statistics of numerically generated turbulence

This paper considers numerically generated turbulence obtained by integrating the complete time-dependent three-dimensional Navier-Stokes equations. The simulated unidirectional turbulent flow, bounded by two parallel planes, is strongly inhomogeneous in the direction normal to the planes but homogeneous in the parallel directions. The resulting flow field, which is considered a numerical realization of fully developed turbulent channel flow, contains detailed information on spatial coherent flow structures as well as on the time-dependency and statistics of the three-dimensional velocity and pressure fields. Focussing here on the statistics of the numerically generated turbulence, second-moments and higher-moments are presented and compared with the most recent PTV and LDV laboratory measurements. It is concluded that direct numerical simulations are an invaluable approach to turbulence which complements field studies and laboratory investigations. Numerical experiments are now becoming a principal source of detailed and reliable information, which play a key role in the deepening of our understanding of turbulent flow phenomena.     

Boundary Layer Heat Transport in turbulent Rayleigh-Bénard Convection in Air

We study the convective heat transfer in a large-scale Rayleigh-Bénard (RB) experiment which is called the “Barrel of Ilmenau”. We present the results of flow visualization and Particle Image Velocimetry (PIV) measurements of the near wall flow field in a plane perpendicular to the surface of the heated bottom plate. The experiment was run in a smaller rectangular inset that was placed inside the larger barrel. The Rayleigh number amounts to Ra = 1.4 × 10¹⁰. The aspect ratios were Γ_x = 1 in flow direction and Γ_y = 0.26 perpendicular to the vertical flow plane. The measurements have been undertaken using a 2 W continuous wave Laser in combination with a light sheet optics and various cameras. Due to the slender geometry of the cell, the mean wind is confined in one direction where the Laser light sheet is aligned parallel. The flow was seeded with droplets of 1...2 µm size generated using an ordinary fog machine. Flow visualization as well as the PIV data clearly show the intermittent character of the boundary layer flow field that permanently switches between “laminar” and “turbulent” phases. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can a metaphor of physics contribute to MEG neuroscience research? Intermittent turbulent eddies in brain magnetic fields

A common manifestation of nonlinear mathematical and experimental neurobiological dynamical systems in transition, intermittence, is currently being attended by concepts from physics such as turbulent eddy and the avalanche of critical systems. Do these concepts constitute an enticing poetry of dynamical universality or do these metaphors from physics generate more specific novel and relevant concepts and experiments in the neurosciences? Using six graphics and ten measures derived from the ergodic theory of dynamical systems, we study the magnetoencephalic, MEG, records of taskless, “resting” human subjects to find consistent evidence for turbulent (chaotic) dynamics marked by intermittent turbulent eddies. This brings up an apparent discrepancy via the juxtaposition of the superposition characteristics of magnetic fields and the non-superposition properties of turbulent flow. Treating this apparent inconsistency as an existent duality, we propose a physical model for how that might be the case. This leaves open the question: has the physical metaphor, turbulent eddy, contributed to a scientific understanding of the human resting MEG?     

Markov random fields,Markov cocycles and the 3-colored chessboard

The well-known Hammersley–Clifford Theorem states (under certain conditions) that any Markov random field is a Gibbs state for a nearest neighbor interaction. In this paper we study Markov random fields for which the proof of the Hammersley–Clifford Theorem does not apply. Following Petersen and Schmidt we utilize the formalism of cocycles for the homoclinic equivalence relation and introduce “Markov cocycles”, reparametrizations of Markov specifications. The main part of this paper exploits this to deduce the conclusion of the Hammersley–Clifford Theorem for a family of Markov random fields which are outside the theorem’s purview where the underlying graph is Z_d. This family includes all Markov random fields whose support is the d-dimensional “3-colored chessboard”. On the other extreme, we construct a family of shift-invariant Markov random fields which are not given by any finite range shift-invariant interaction.     

Convergence of finite element approximations of large eddy motion

Fluid motion in many applications occurs at higher Reynolds numbers. In these applications dealing with turbulent flow is thus inescapable. One promising approach to the simulation of the motion of the large structures in turbulent flow is large eddy simulation in which equations describing the motion of local spatial averages of the fluid velocity are solved numerically. This report considers “numerical errors” in LES. Specifically, for one family of space filtered flow models, we show convergence of the finite element approximation of the model and give an estimate of the error. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 689–710, 2002; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/num.10027.     

The mechanics of contentious politics: an agent-based modeling approach

ABSTRACT

“Contentious politics” has become the main label to define a wide range of previously separated fields of research encompassing topics such as collective action, radicalization, armed insurgencies, and terrorism. Over the past two decades, scholars have tried to bring these various strands together into a unified field of study. In so doing, they have developed a methodology to isolate and analyze the common social and cognitive mechanisms underlying several diverse historical phenomena such as “insurgencies,” “revolutions,” “radicalization,” or “terrorism.” A multidisciplinary approach was adopted open to contributions from diverse fields such as economics, sociology, and psychology. The aim of this paper is to add to the multidisciplinarity of the field of Contentious Politics (CP) and introduce the instruments of Agent-Based Modeling and network game-theory to the study of some fundamental mechanisms analyzed within this literature. In particular, the model presented in this paper describes the dynamics of one process, here defined as “the radicalization of politics,” and its main underlying mechanisms. Their mechanics are analyzed in diverse social contexts differentiated by the values of four parameters: the extent of repression, inequality, social tolerance, and interconnectivity. The model can be used to explain the basic dynamics underlying different phenomena such as the development of radicalization, populism, and popular rebellions. In the final part, different societies characterized by diverse values of the aforementioned four parameters are tested through Python simulations, thereby offering an overview of the different outcomes that the mechanics of our model can shape according to the contexts in which they operate.     

On time‐dependent behaviour of controlled turbulent flow with separation and reattachment

Results from numerical simulations of separating and reattaching turbulent boundary layer flow over a backwardfacing step are analysed with respect to the time‐dependent flow behaviour. Beside the well‐known roll‐up of the separated shear‐layer (“Kelvin‐Helmholtz instability”) and the ejection of subsequently formed large‐scale structures (denoted as “shedding”), another unsteady phenomenon which is commonly called “flapping” can be observed. Additionally, the effects of open‐loop passive and active flow control methods are investigated.     

Noise Prevents Collapse of Vlasov‐Poisson Point Charges

We elucidate the effect of noise on the dynamics of N point charges in a Vlasov‐Poisson model with a singular bounded interaction force. A too simple noise does not affect the structure inherited from the deterministic system and, in particular, cannot prevent coalescence of point charges. Inspired by the theory of random transport of passive scalars, we identify a class of random fields generating random pulses that are chaotic enough to disorganize the structure of the deterministic system and prevent any collapse of particles. We obtain the strong unique solvability of the stochastic model for any initial configuration of distinct point charges. In the case where there are exactly two particles, we implement the “vanishing noise method” for determining the continuation of the deterministic model after collapse. © 2014 Wiley Periodicals, Inc.     

The Number of Seymour Vertices in Random Tournaments and Digraphs

Seymour’s distance two conjecture states that in any digraph there exists a vertex (a “Seymour vertex”) that has at least as many neighbors at distance two as it does at distance one. We explore the validity of probabilistic statements along lines suggested by Seymour’s conjecture, proving that almost surely there are a “large” number of Seymour vertices in random tournaments and “even more” in general random digraphs.     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Systems of conservation laws of mixed type

A local theory of weak solutions of first-order nonlinear systems of conservation laws is presented. In the systems considered, two of the characteristic speeds become complex for some achieved values of the dependent variable. The transonic “small disturbance” equation is an example of this class of systems. Some familiar concepts from the purely hyperbolic case are extended to such systems of mixed type, including genuine nonlinearity, classification of shocks into distinct fields and entropy inequalities. However, the associated entropy functions are not everywhere locally convex, shock and characteristic speeds are not bounded in the usual sense, and closed loops and disjoint segments are possible in the set of states which can be connected to a given state by a shock. With various assumptions, we show (1) that the state on one side of a shock plus the shock speed determine the state on the other side uniquely, as in the hyperbolic case; (2) that the “small disturbance” equation is a local model for a class of such systems; and (3) that entropy inequalities and/or the existence of viscous profiles can still be used to select the “physically relevant” weak solution of such a system.     

A study of bounded cascade models of random fields on a plane

Cascade models of random processes and fields are extensively used in mathematical modeling of various objects and phenomena. This paper treats of properties of bounded cascade models on a plane as well as their one-dimensional distributions and correlation structure. The results obtained are helpful in analyzing the suitability of cascade models for solving various practical problems.     

Magnetization formula in the bounded XYZ spin chain

The bounded XYZ spin chain is studied. We construct the vacuum states by the vertex operators of the level one modules of the elliptic algebra, and compact them through a geometric symmetry of the model called the turning symmetry. From these simplified expressions, the “magnetization formula” for magnetizations at a boundary in the bounded chain and in the half-infinite chains is derived. Applying this formula we calculate the spontaneous magnetization at a boundary in the bounded XYZ spin chain.     

Estimation of intrinsic processes affected by additive fractal noise

Fractal Gaussian models have been widely used to represent the singular behavior of phenomena arising in different applied fields; for example, fractional Brownian motion and fractional Gaussian noise are considered as monofractal models in subsurface hydrology and geophysical studies Mandelbrot [The Fractal Geometry of Nature, Freeman Press, San Francisco, 1982 [13]]. In this paper, we address the problem of least-squares linear estimation of an intrinsic fractal input random field from the observation of an output random field affected by fractal noise (see Angulo et al. [Estimation and filtering of fractional generalised random fields, J. Austral. Math. Soc. A 69 (2000) 1-26 [2]], Ruiz-Medina et al. [Fractional generalized random fields on bounded domains, Stochastic Anal. Appl. 21 (2003a) 465-492], Ruiz-Medina et al. [Fractional-order regularization and wavelet approximation to the inverse estimation problem for random fields, J. Multivariate Anal. 85 (2003b) 192-216]. Conditions on the fractality order of the additive noise are studied to obtain a bounded inversion of the associated Wiener-Hopf equation. A stable solution is then obtained in terms of orthogonal bases of the reproducing kernel Hilbert spaces associated with the random fields involved. Such bases are constructed from orthonormal wavelet bases (see Angulo and Ruiz-Medina [Multiresolution approximation to the stochastic inverse problem, Adv. in Appl. Probab. 31 (1999) 1039-1057], Angulo et al. [Wavelet-based orthogonal expansions of fractional generalized random fields on bounded domains, Theoret. Probab. Math. Stat. (2004), in press]). A simulation study is carried out to illustrate the influence of the fractality orders of the output random field and the fractal additive noise on the stability of the solution derived.     

Quantum Transport in Degenerate Systems

Transport in nonequilibrium degenerate quantum systems is investigated. The transfer rate depends on the parameters of the system. In this paper we investigate the dependence of the flow (transfer rate) on the angle between “bright” vectors (which define the interaction of the system with the environment). We show that in some approximation for the system under investigation the flow is proportional to the cosine squared of the angle between the “bright” vectors. Earlier the author has shown that in this degenerate quantum system excitation of nondecaying quantum “dark” states is possible; moreover, the effectiveness of this process is proportional to the sine squared of the angle between the “bright” vectors (this phenomenon was discussed as a possible model of excitation of quantum coherence in quantum photosynthesis). Thus quantum transport and excitation of dark states are competing processes; “dark” states can be considered as a result of leakage of quantum states in a quantum thermodynamic machine which performs the quantum transport.     

Direct numerical simulation of the laminar–turbulent transition at hypersonic flow speeds on a supercomputer

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar–turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier–Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton–Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar–turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar–turbulent transition.     

Spatial decay bounds for time dependent magnetohydrodynamic geophysical flow

This article is concerned with spatial decay bounds for the time dependent magnetohydrodynamic geophysical flow in an infinite pipe when homogeneous lateral surface boundary conditions are applied. Assuming that the entrance velocity and magnetic field data are small enough and the fluid flow converges to laminar flow as the distance down the pipe tends to infinity, we derive a second order differential inequality that leads to an exponential decay estimate for the “energy” associated with the velocity and magnetic field represented by the difference between the entrance flow and fully developed laminar flow. We also show how to establish the explicit decay bounds for the total energy.     

A method for optimal control in boundary-layer flow

A methodology for active flow control which couples unsteady flow fields and controls is described. Active-control methods are used to maintain laminar flow in a region in which the natural instabilities lead to turbulent flow. The simplest form of control which might achieve this objective is the wave-cancellation approach. The case of boundary layer instability suppression is considered as the initial validation and test case. Control is effected through the injection or suction of fluid through a single orifice on the boundary. The optimal control theory provides an approach which does not require a priori knowledge of the flow. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum rule for detection probability from Brownian motion in the space of classical fields

We obtain Born’s rule from the classical theory of random waves in combination with the use of thresholdtype detectors. We consider a model of classical random waves interacting with classical detectors and reproducing Born’s rule. We do not discuss complicated interpretational problems of quantum foundations. The reader can select between the “weak interpretation,” the classical mathematical simulation of the quantum measurement process, and the “strong interpretation,” the classical wave model of the real quantum (in fact, subquantum) phenomena.