The effects of flow split ratio and flow rate in manifolds

This paper reports a combined experimental and numerical investigation of three-dimensional steady turbulent flows in inlet manifolds of square cross-section. Predictions and measurements of the flows were carried out using computational fluid dynamics and laser Doppler anemometry techniques respectively. The flow structure was characterized in detail and the effects of flow split ratio and inlet flow rate were studied. These were found to cause significant variations in the size and shape of recirculation regions in the branches, and in the turbulence levels. It was then found that there is a significant difference between the flow rates through different branches. The performance of the code was assessed through a comparison between predictions and measurements. The comparison demonstrates that all important features of the flow are well represented by the predictions.     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

Projector formalism of generalized Brownian motion theory applied to dissipative and noisy systems

The projector formalism of Zwanzig-Mori type is extended to obtain generalized Fokker-Planck and generalized nonlinear Langevin equations for coarse-grained variables when the underlying microscopic dynamics is dissipative and noisy (stochastic).     

一类周期种群系统的适定性及最优控制

本文研究了一类非线性周期种群系统的适定性及最优控制问题 .利用压缩不动点原理讨论了该种群系统的周期解的存在唯一性 .并用变分法给出了最优控制所满足的必要条件 .     

ULTIMATE BOUNDEDNESS FOR A DIFFERENTIAL DELAY MODEL

This paper considers the scalar differential delay equation x(t) = -μx(t)-f(x(t-Τ(t)), t). By using the mapping method we obtain that the solutionswill be ultimately in some interval.     

Hybrid systems: Modelling and analysis using emergent dynamics

In this paper, we discuss modelling and analysis of hybrid systems with physical interaction dynamics. Such systems are typically considered complex and they are modelled using abstractions. Abstractions may, however, unintentionally exclude critical details, leading to partial or false results. Therefore, we study here use of a particle system in modelling and analysis. The novelty of the particle system is that it is designed to reveal interaction dynamics as emergent dynamics; thus, supporting analysis of complex and intricate interaction dynamics with acceptable modelling effort. As the main contribution, we formalize the particle system, and use it to model and analyze hybrid systems, both mechanical and biological, with nontrivial interaction dynamics.     

Analogues of Coherent and Dissipative Structures in Social and Historical Processes

An analogy between social and hydrodynamic processes is developed. The relation of the state system to the passionarity theory suggested by L. N. Gumilev is discussed.     

Kinetics and equilibrium of small metallic clusters: Ab initio confinement molecular dynamics study of 4

The ab initio molecular dynamics (AIMD) [1] is combined with the heuristic, successive confinement method of surveying a potential energy surface (PES) [2], thereby offering a framework for the simulation study of kinetics and equilibrium properties of metallic clusters. This approach is applied to the study of Au₄, a cluster possessing a simple but specific PES, which consists of very shallow and deep basins and due to this presents a challenge to the conventional AIMD methods. Among other things, the probabilities of the transitions between isomers have been found, and on this basis, both the time-dependent and equilibrium populations of the isomers have been calculated for the conditions typical of the NeNePo experiments [3] in the femtosecond pump-probe spectroscopy.