On the nonlinear stability and the existence of selective decay states of 3D quasi-geostrophic potential vorticity equation

In this article, we study the dynamics of large-scale motion in atmosphere and ocean governed by the 3D quasi-geostrophic potential vorticity (QGPV) equation with a constant stratification. It is shown that for a Kolmogorov forcing on the first energy shell, there exist a family of exact solutions that are dissipative Rossby waves. The nonlinear stability of these exact solutions are analyzed based on the assumptions on the growth rate of the forcing. In the absence of forcing, we show the existence of selective decay states for the 3D QGPV equation. The selective decay states are the 3D Rossby waves traveling horizontally at a constant speed. All these results can be regarded as the expansion of that of the 2D QGPV system and in the case of 3D QGPV system with isotropic viscosity. Finally, we present a geometric foundation for the model as a general equation for nonequilibrium reversible-irreversible coupling.     

The rigorous derivation of the T2 focusing cubic NLS from 3D

We derive rigorously the 2D periodic focusing cubic NLS as the mean-field limit of the 3D focusing quantum many-body dynamics describing a dilute Bose gas with periodic boundary condition in the x-direction and a well of infinite-depth in the z-direction. Physical experiments for these systems are scarce. We find that, to fulfill the empirical requirement for observing NLS dynamics in experiments, namely, that the kinetic energy dominates the potential energy, it is necessary to impose an extra restriction on the system parameters. This restriction gives rise to an unusual coupling constant.     

Heat Transfer in Rotor/Rotor and Rotor/Stator Cavity: Physics,Correlations and Numerical Modeling

The transitional and turbulent flow in the near wall sublayer is now mostly modeled based on the existing knowledge of simple 2D flows. To determine the effect of three dimensionality on the turbulent flow structures and turbulent heat transfer in the near wall areas the authors investigate numerically (SVV) turbulent flow in rotor/stator and rotor/rotor flows (with and without axial throughflow). These simple model flows contain most of the phenomena that are needed to understand more complex, 3D transitional and turbulent flows. Attention is focused on the turbulent characteristics which should have more universal character. To stabilize calculations for high Reynolds numbers (up to Re=800 000) the SVV operator is introduced into the Navier-Stokes and energy equations solver for cylindrical coordinate system without using complex numbers. Code optimization and parallelization have speeded up computations 20 times. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of a Hamiltonian conservative chaotic system and its mechanism routes from periodic to quasiperiodic,chaos and strong chaos

In this paper, the important role of 3D Euler equation playing in forced-dissipative chaotic systems is reviewed. In mathematics, rigid-body dynamics, the structure of symplectic manifold, and fluid dynamics, building a four-dimensional (4D) Euler equation is essential. A 4D Euler equation is proposed by combining two generalized Euler equations of 3D rigid bodies with two common axes. In chaos-based secure communications, generating a Hamiltonian conservative chaotic system is significant for its advantage over the dissipative chaotic system in terms of ergodicity, distribution of probability, and fractional dimensions. Based on the proposed 4D Euler equation, a 4D Hamiltonian chaotic system is proposed. Through proof, only center and saddle equilibrium lines exist, hence it is not possible to produce asymptotical attractor generated from the proposed conservative system. An analytic form of Casimir power demonstrates that the breaking of Casimir energy conservation is the key factor that the system produces the aperiodic orbits: quasiperiodic orbit and chaos. The system has strong pseudo-randomness with a large positive Lyapunov exponent (more than 10 K), and a large state amplitude and energy. The bandwidth for the power spectral density of the system is 500 times that of both existing dissipative and conservative systems. The mechanism routes from quasiperiodic orbits to chaos is studied using the Hamiltonian energy bifurcation and Poincaré map. A circuit is implemented to verify the existence of the conservative chaos.     

波浪上方飞行二维地效翼的非线性分析

针对二维波浪上方飞行的非定常二维地效翼进行了非线性分析．通过对二维奇点在规则波上方运动的Green函数的推导,利用离散涡方法解决了二维波浪上方飞行的非定常地效翼的升力问题．针对不同的几何参数和波浪参数对升力系数进行了研究．通过与定常情况的对比,验证了方法的有效性.     

Locally active Hindmarsh–Rose neurons

In this paper the locally active and the edge of chaos regions of the Hindmarsh–Rose (HR) model for neuron dynamics are studied. From these regions parameters are chosen to set emergent phenomena both in 2D and 3D grids of HR neurons.     

中厚度复合材料夹芯层板变分渐近精细模型

为准确预测对中厚度复合材料夹芯层板分层开裂至关重要的沿厚向应力/应变分布,利用板固有小参数将原三维板分析严格拆分为沿厚向的一维分析和二维板非线性分析,并将原三维能量渐近扩展为系列二维近似能量泛函;通过对近似能量泛函中主导变分项(含翘曲项)的渐近修正,得到与原三维模型尽可能接近的近似能量,从而构建无需任何场变量假设的精细模型,并转换为工程常用的Reissner模型形式．通过4层复合材料夹芯板柱形弯曲算例表明:基于所构建模型重构的三维场精度较一阶剪切变形理论和经典层合理论更好,与精确解基本一致;由于所构建的变分渐近模型为等效单层板模型,在保证足够精度的前提下,相比三维有限元计算可减少2~3阶计算量,在精确性和有效性间取得较好的折衷．     

Diffuse Interface Methods for Multiple Phase Materials: An Energetic Variational Approach

In this paper, we introduce a diffuse interface model for describing the dynamics of mixtures involving multiple (two or more) phases. The coupled hydrodynamical system is derived through an energetic variational approach. The total energy of the system includes the kinetic energy and the mixing (interfacial) energies. The least action principle (or the principle of virtual work) is applied to derive the conservative part of the dynamics, with a focus on the reversible part of the stress tensor arising from the mixing energies. The dissipative part of the dynamics is then introduced through a dissipation function in the energy law, in line with Onsager's principle of maximum dissipation. The final system, formed by a set of coupled time-dependent partial differential equations, reflects a balance among various conservative and dissipative forces and governs the evolution of velocity and phase fields. To demonstrate the applicability of the proposed model, a few two-dimensional simulations have been carried out, including (1) the force balance at the three-phase contact line in equilibrium, (2) a rising bubble penetrating a fluid-fluid interface, and (3) a solid particle falling in a binary fluid. The effects of slip at solid surface have been examined in connection with contact line motion and a pinch-off phenomenon.     

Interface boundary value problem for the Navier-Stokes equations in thin two-layer domains

We study a system of 3D Navier-Stokes equations in a two-layer parallelepiped-like domain with an interface coupling of the velocities and mixed (free/periodic) boundary condition on the external boundary. The system under consideration can be viewed as a simplified model describing some features of the mesoscale interaction of the ocean and atmosphere. In case when our domain is thin (of order ε), we prove the global existence of the strong solutions corresponding to a large set of initial data and forcing terms (roughly, of order ε^−2/3). We also give some results concerning the large time dynamics of the solutions. In particular, we prove a spatial regularity of the global weak attractor.     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part II—performance evaluation of draft tube model

Computational Fluids Dynamics (CFD) tools guide engineers and designers to estimate the performance of new designs. However, a CFD analysis can be very time-consuming depending mainly on the grid size and domain complexity. Thus, this paper aims to describe the tools used to evaluate and compare the performance of different 3D draft tube models for reducing the time-effort needed in an optimization procedure. The results presented here, are the second part of an overall research to establish a global optimization methodology to improve the performance of an hydraulic draft tube through the inlet velocity profile. Previously, three steps of optimization methodology to minimize the energy losses were studied: the inlet velocity profile parameterization, the numerical optimization set-up and the objective function validation. In the latter step, a global optimization method called Multi Island Genetic Algorithm (MIGA) was considered, which requires a large number of iterations before producing a reliable result. This step is able to identify an efficient inlet velocity profile to minimize the energy losses through the draft tube model. However, each iteration is expensive in terms of computational time due to the need for 3D Navier–Stokes (NS) computations to evaluate each profile’s fitness. Thus, in this work the methodology attempts to accelerate the optimization process with accurate results. In order to achieve the goal, the grid size of the 3D draft tube model was minimized, resulting in a much lower computational cost. Specifically, the draft tube calculations were performed on a sequence of five different grids each having approximately twice the number of elements compared to the previous. The measurements of the sensitivity of the draft tube performance quantities to the change of the inlet velocity parameters during the process showed that, in spite of the numerical difference between its performance, the results have the same tendency. Consequently, the 3D draft tube numerical model with a minimal grid size, is reliable and left record of its capabilities for being integrated in the optimization process.     

Model-based parameter optimization for arc welding process simulation

This paper presents a model-based parameter optimization for simulating a metal-inert gas welding process. The computational model used in this study is based on computational fluid dynamics methods and implemented using the finite volume approach on a 3D computational domain. The wire electrode, the arc plasma and the workpiece are treated as a self-consistent system. Important welding parameters, including arc current, wire feed rate, workpiece thickness, welding speed and geometry, as well as the metal alloy types used for the wire and workpiece, were implemented as adjustable parameters. By tuning these parameters, the performance of the arc welding can be predicted, and different settings can be compared to optimize welding performance.A benchmarking study of the arc model against experimental measurements is presented to demonstrate the model's capabilities in the prediction of the weld pool changes and thermal dynamics involved in the welding process. Two numerical case studies are presented to demonstrate the use of the model-based optimization to quantify welding pool variations with the change in welding parameters. The first case study is the determination of the optimal arc current and welding speed settings for different workpiece thicknesses. The optimization process shows that the predictions are not only in agreement with established experimental welding experience on the direct relationship between workpiece thickness and arc current, but more importantly quantify this relationship for a given workpiece thickness. The second case study focuses on the welding parameters optimization for different metal alloys. The comparison suggests that the welding parameters suitable for some aluminium alloys are less likely to be successful in welding magnesium alloys. A further model validation of Mg alloy AZ31 welding shows an agreement with experimental measurements. The work presented shows the potential of model-based parameter optimization to assist process engineers in the practical improvement of the welding process.     

Stochastic modeling and optimization of garbage collection algorithms in solid-state drive systems

Markov chains and mean-field analysis are powerful tools and widely used for performance analysis in large-scale computer and communication systems. In this paper, we consider the application of Markov modeling and mean-field analysis to solid-state drives (SSDs). SSDs are now widely deployed in mobiles, desktops, and data centers due to their high I/O performance and low energy consumption. In particular, we focus on characterizing the performance–durability tradeoff of garbage collection (GC) algorithms in SSDs. Specifically, we first develop a stochastic Markov chain model to capture the I/O dynamics of large-scale SSDs, then adapt mean-field analysis to derive the asymptotic steady state, based on which we are able to easily analyze the performance–durability tradeoff of a large family of GC algorithms. We further prove the model convergence and generalize the model for all types of workload. Inspired by this model, we also propose a randomized greedy algorithm (RGA) which has a single tunable parameter to trade between performance and durability. Using trace-driven simulation on DiskSim with SSD add-ons, we demonstrate how RGA can be parameterized to realize the performance–durability tradeoff.     

Critical damping in nonviscously damped linear systems

In structural dynamics, energy dissipative mechanisms with nonviscous damping are characterized by their dependence on the time-history of the response velocity, mathematically represented by convolution integrals involving hereditary functions. Combination of damping parameters in the dissipative model can lead the system to be overdamped in some (or all) modes. In the domain of the damping parameters, the thresholds between induced oscillatory and non-oscillatory motion are named critical damping surfaces (or critical manifolds, since several parameters can be involved). In this paper the theoretical foundations to determine critical damping surfaces in nonviscously damped systems are established. In addition, a numerical method to obtain critical curves is developed. The approach is based on the transformation of the algebraic equations, which define implicitly the critical curves, into a system of differential equations. The derivations are validated with three numerical methods covering single and multiple degree of freedom systems.     

Optical Soliton Bullets in (2+1)D Nonlinear Bragg Resonant Periodic Geometries

We consider light propagation in a Kerr-nonlinear 2D waveguide with a Bragg grating in the propagation direction and homogeneous in the transverse direction. Using Newton's iteration method we construct both stationary and travelling solitary wave solutions of the corresponding mathematical model, the 2D nonlinear coupled mode equations (2D CME). We call these solutions 2D gap solitons due to their similarity with the gap solitons of 1D CME (fiber grating). Long-time stable evolution preserving the solitary fashion is demonstrated numerically despite the fact that, as we show, for the 2D CME no local constrained minima of the Hamiltonian functional exist. Building on the 1D study of [ 1 ], we demonstrate trapping of slow enough 2D gap solitons at localized defects. We explain the mechanism of trapping as resonant transfer of energy from the soliton to one or more nonlinear defect modes. For a special class of defects, we construct a family of nonlinear defect modes by numerically following a bifurcation curve starting at analytically or numerically known linear defect modes. Compared to 1D the dynamics of trapping are harder to fully analyze and the existence of many defect modes for a given defect potential causes that slow solitons store a part of their energy for virtually all of the studied attractive defects.     

装药驱动飞片引爆炸药性能影响参数分析

扩爆装药结构对爆轰波传播、飞片驱动过程以及对主炸药引爆性能有直接的影响。为分析装药结构对飞片威力参数的影响,针对装药直径、飞片厚度、飞片拱起高度等主要结构参数,利用正交实验原理设计了数值实验方案,并采用动力学有限差分程序建立了相应的数值模拟模型。通过对数值实验结果的对比和统计分析,获得了影响飞片速度、动量、比动能等引爆炸药威力指标的主要装药结构参数及其影响规律。其结果可为相关扩爆装药设计提供理论依据。     

Evolving to the edge of chaos: Chance or necessity?

We show that ecological systems evolve to edges of chaos (EOC). This has been demonstrated by analyzing three diverse model ecosystems using numerical simulations in combination with analytical procedures. It has been found that all these systems reside on EOC and display short-term recurrent chaos (strc). The first two are non-linear food chains and the third one is a linear food chain. The dynamics of first two is dictated by deterministic changes in system parameters. In contrast to this, dynamics of the third model system (the linear food chain) is governed by both deterministic changes in system parameters as well as exogenous stochastic perturbations (unforeseen changes in initial conditions) of these dynamical systems.     

Evolving to the edge of chaos: Chance or necessity?

We show that ecological systems evolve to edges of chaos (EOC). This has been demonstrated by analyzing three diverse model ecosystems using numerical simulations in combination with analytical procedures. It has been found that all these systems reside on EOC and display short-term recurrent chaos (strc). The first two are non-linear food chains and the third one is a linear food chain. The dynamics of first two is dictated by deterministic changes in system parameters. In contrast to this, dynamics of the third model system (the linear food chain) is governed by both deterministic changes in system parameters as well as exogenous stochastic perturbations (unforeseen changes in initial conditions) of these dynamical systems.     

Vacuum Polarization Effects in a System of Two Three-Phase Chiral Bags

In the model of three-phase chiral quark bags in 1+1 dimensions, we obtain self-consistent solutions describing the system of two interacting bags. Attention is focused on investigating the role played by the fermionic vacuum polarization inside the bags in the dynamics of the system; the bosonic field interrelating the bags is taken into account only at the one-meson exchange level. The renormalized total energy of the system is investigated as a function of parameters characterizing the geometry of the problem and of the additional bag characteristics arising in 1+1 dimensions. We show that in the system of two three-phase bags, vacuum polarization yields a strong nonlinear interaction at small distances, which can be either repulsive or attractive depending on the bag characteristics.     

On the Lagrangian dynamics of the axisymmetric 3D Euler equations

We study the dynamics along the particle trajectories for the 3D axisymmetric Euler equations. In particular, by rewriting the system of equations we find that there exists a complex Riccati type of structure in the system on the whole of R³, which generalizes substantially the previous results in [5] (D. Chae, On the blow-up problem for the axisymmetric 3D Euler equations, Nonlinearity 21 (2008) 2053-2060). Using this structure of equations, we deduce the new blow-up criterion that the radial increment of pressure is not consistent with the global regularity of classical solution. We also derive a much more refined version of the Lagrangian dynamics than that of [6] (D. Chae, On the Lagrangian dynamics for the 3D incompressible Euler equations, Comm. Math. Phys. 269 (2) (2007) 557-569) in the case of axisymmetry.