Three-dimensional compressible-incompressible turbulent flow simulation using a pressure-based algorithm

In this work, we extend a finite-volume pressure-based incompressible algorithm to solve three-dimensional compressible and incompressible turbulent flow regimes. To achieve a hybrid algorithm capable of solving either compressible or incompressible flows, the mass flux components instead of the primitive velocity components are chosen as the primary dependent variables in a SIMPLE-based algorithm. This choice warrants to reduce the nonlinearities arose in treating the system of conservative equations. The use of a new Favre-averaging like technique plays a key role to render this benefit. The developed formulations indicate that there is less demand to interpolate the fluxes at the cell faces, which is definitely a merit. To impose the hyperbolic behavior in compressible flow regimes, we introduce an artificial hyperbolicity in pressure correction equation. We choose k-ω turbulence model and incorporate the compressibility effect as a correction. It is shown that the above considerations grant to achieve a robust algorithm with great capabilities in solving both flow regimes with a reasonable range of Mach number applications. To evaluate the ability of the new pressure-based algorithm, three test cases are targeted. They are incompressible backward-facing step problem, compressible flow over a wide range of open to closed cavities, and compressible turbulent flow in a square duct. The current results indicate that there are reliable agreements with those of experiments and other numerical solutions in the entire range of investigation.     

Methods for first-order kernel estimation: simple-cell receptive fields from responses to natural scenes

Recent studies have recovered receptive-field maps of simple cells in visual cortex from their responses to natural scene stimuli. Natural scenes have many theoretical and practical advantages over traditional, artificial stimuli; however, the receptive-field estimation methods are more complex than for white-noise stimuli. Here, we describe and justify several of these methods-spectral correction of the reverse correlation estimate, direct least-squares solution, iterative least-squares algorithms and regularized least-squares solutions. We investigate the pros and cons of the different methods, and evaluate them in a head-to-head comparison for simulated simple-cell data. This shows that, at least for quasilinear simulated simple cells, a regularized solution ('reginv') is most efficient, requiring fewer stimulus presentations for high-resolution reconstruction of the first-order kernel. We also investigate several practical issues that determine the success of this kind of experiment-the effects of neuronal nonlinearities, response variability and the choice of stimulus regime.     

Non-Darcy flow in disordered porous media: A lattice Boltzmann study

It is well known that the Darcy law is insufficient for describing high-rate flows in porous media. However, it is still an open problem to establish a universal form for the nonlinear correction to Darcy law. In this work, we will investigate numerically the non-Darcy effect on incompressible flows through disordered porous media. Numerical simulations at pore-scale level are carried out with the Reynolds number varying from 0.02 to 30, which covers the Darcy and non-Darcy flow regimes. Three regimes are identified for flow through porous media, i.e., a linear Darcy regime at vanishing Reynolds number, a cubic transitional or weak inertial regime at low but finite Reynolds number, and a quadratic Forchheimer or strong inertial regime at larger Reynolds numbers. Finally, a general correlation is proposed to include the non-Darcy effect, as an extension to the common empirical expressions.     

A generalized macroscopic model for sound-absorbing poroelastic media using the homogenization method

This paper proposes a new macroscopic model for sound-absorbing poroelastic media which is derived by using the homogenization theory based on the method of asymptotic expansions. The derivation of the macroscopic properties and governing equations takes into account the multiphysics occurring in poroelastic media for sound absorption, including elastic motions of the solid phase, compressible viscous fluid flow, and the distributions of pressure and temperature in the fluid phase. The coupled effects between the elastic solid and the fluid pressure, and the temperature and the fluid pressure are also considered. In contrast to the conventional Biot’s model, which includes heuristic formulae, the proposed method yields a rigorous model that is consistent with the principal governing equations on the microscopic scale. Utilizing several models that have simple microscopic geometry and comparing the numerical solutions obtained using the proposed method with corresponding analytical solutions, we demonstrate that the derived macroscopic governing equations can provide accurate and effective predictions.     

An iterative learning approach to compensation for the servo track writing error in high track density disk drives

The servo tracks of hard disk drives are written at the time of manufacture with the equipment of servo track writer. The disk vibrations or head fluctuations during servo track writing process give rise to servo track writing error. The servo track writing error may cause some critical errors during data writing operation. In this paper, we propose a new correction algorithm for the servo track writing error based on the iterative learning control technique. The estimate of the servo track writing error is constructed from the position error signal and updated iteratively at each disk rotation. Then, the estimate of servo track writing error is used to correct the position error signal in a feed-forward manner. Our correction algorithm is robust to system model uncertainties, computationally quite simple, and has fast convergence rate. Furthermore, we give a rigorous analysis for the convergence of our correction algorithm. In order to demonstrate the practical use of our work, we present some experimental results using a commercially available hard disk drive.     

A security flow control algorithm and its denotational semantics correctness proof

We derive a security flow control algorithm for message-based, modular systems and prove the algorithm correct. The development is noteworthy because it is completely rigorous: the flow control algorithm is derived as an abstract interpretation of the denotational semantics of the programming language for the modular system, and the correctness proof is a proof by logical relations of the congruence between the denotational semantics and its abstract interpretation. Effectiveness is also addressed: we give conditions under which an abstract interpretation can be computed as a traditional iterative data flow analysis, and we prove that our security flow control algorithm satisfies the conditions. We also show that symbolic expressions (that is, data flow values that contain unknowns) can be used in a convergent, iterative analysis. An important consequence of the latter result is that the security flow control algorithm can analyse individual modules in a system for well formedness and later can link the analyses to obtain an analysis of the entire system.     

A note on the existence conditions for fault detection and isolation observers

This paper proves that the necessary and sufficient conditions for the existence of FDI observers given by Hou and Muller (Theorem 3) are incorrect. A necessary correction to their theorem is presented and proved. A simple and useful condition is also proposed for the existence of the FDI observers with a rigorous proof. Examples illustrate the effectiveness of the proposed existence condition.     

Some Bulk-Viscous Solutions in a First-Order Theory

We first motivate the study of viscosity in cosmology. Whilst most studies assume that the universe is filled with a perfect fluid, viscosity is expected to play a role, at least during some stages of the evolution of the Universe. There are several theories of viscosity. Eckart’s first-order theory was found to permit superluminal signals, and equilibrium states were found to be unstable. To solve these problems, the Israel-Stewart second-order theory was proposed. More recently, a relatively new first-order theory has appeared, which is claimed to also solve these problems.We briefly reviewthis first-order theory and present the basic field equations. Then we attempt to find homogeneous and isotropic solutions in the theory. It is noted that there do not exist stiff matter (pressure = energy density) solutions in the theory, in contrast to other theories. We then find power-law solutions without a cosmological term. Surprisingly, there do not exist simple exponential solutions, again in contrast to other theories. Finally, we present a solution with a cosmological term and make some concluding remarks.     

Towards More Complete Models of TCP Latency and Throughput

Recently, several researchers have developed equations for modeling TCP behaviors, such as the expected throughput or latency, based on Markov chains derived from TCP with additional simplifying assumptions. In this paper, we suggest new directions for Markov chain analyses of TCP. Our first contribution is to closely examine not just the expectation but the entire cumulative distribution function of transfer times under various models. Particularly for short or medium transfers, the distribution is likely to be more useful than the expectation in terms of measuring end-user satisfaction. We find that the shapes of TCP cumulative distribution functions are remarkably robust to small changes in the model. Our results suggest that simplifying Markov analyses can be extended to yield approximations for the entire distribution as well as for the expectation.Our second contribution is to consider correction procedures to enhance these models. A correction procedure is a rule of thumb that allows equations from one model to be used in other situations. As an example, several analyses use a Drop-Tail loss model. We determine correction procedures for the deviation between this model and other natural loss models based on simulations. The existence of a simple correction procedure in this instance suggests that the high-level behavior of TCP is robust against changes in the loss model.     

Numerical investigation of dynamics of elliptical magnetic microparticles in shear flows

We study the rotational dynamics of magnetic prolate elliptical particles in a simple shear flow subjected to a uniform magnetic field, using direct numerical simulations based on the finite element method. Focusing on paramagnetic and ferromagnetic particles, we investigate the effects of the magnetic field strength and direction on their rotational dynamics. In the weak field regime (below a critical field strength), the particles are able to perform complete rotations, and the symmetry property of particle rotational speed is influenced by the direction and strength of the magnetic field. In the strong field regime (above a critical strength), the particles are pinned at steady angles. The steady angle depends on both the direction and strength of the magnetic field. Our results show that paramagnetic and ferromagnetic particles exhibit markedly different rotational dynamics in a uniform magnetic field. The numerical findings are in good agreement with theoretical prediction. Our numerical investigation further reveals drastically different lateral migration behaviors of paramagnetic and ferromagnetic particles in a wall-bounded simple shear flow under a uniform magnetic field. These two kinds of particles can thus be separated by combining a shear flow and a uniform magnetic field. We also study the lateral migration of paramagnetic and ferromagnetic particles in a pressure-driven flow (a more practical flow configuration in microfluidics), and observe similar lateral migration behaviors. These findings demonstrate a simple but useful way to manipulate non-spherical microparticles in microfluidic devices.     

一种基于流量控制技术的分布式DDOS攻击检测框架研究

DDOS攻击是当前网络安全的最大威胁之一。将分布式检测技术与流量控制技术相结合提出了一种D＆SFC（Distributed and Simple Flow Control）DDOS攻击检测框架,即具有简单流量控制功能的分布式DDOS检测框架。其特点是利用多层次的结构,结合包过滤及带宽控制技术,在网络拓扑的不同节点上实现网络流量的简单控制,在进行DDOS攻击检测的同时降低了攻击数据包对网络性能的影响。     

Dynamics of citation distribution

We study the citation dynamics of scientific publications over the years. We propose a simple cellular automaton model featuring a combination of two distinct mechanisms, i.e. the random assignment and the preferential attachment, to investigate the dynamics of journal citation. Different from most previous studies focusing on highly cited papers, we analyze the time evolution of the entire citation distribution. Empirical data can be well reproduced by numerical simulations. Within the linear regime of the Cited Half-Life, a steady accumulation of citations can be expected. Moreover, within this linear regime, the ratio between the above two mechanisms is a constant. Besides the average citation represented by the Impact Factor, such a constant ratio can also be a characteristic of the journal.     

Large-scale analytical water quality model coupled with GIS for simulation of point sourced pollutant discharges

Mathematical modeling is an important tool for water quality studies, and the integration of water quality models with geographic information systems (GIS) is very useful for information extraction and for results interpretation. In this context, this work presents the development of a water quality model coupled with GIS (MapWindow GIS) for representing impacts of point-sourced pollutants released with distinct durations under different flow scenarios, allowing a systemic view of the entire basin, and capable of being used with low data availability. The model is called SIAQUA-IPH and uses a pollutograph convolution scheme to represent multiple discharges and confluences in the basin, based on analytical solutions of the longitudinal advection-dispersion equation. Operational tests presented a full operational performance from all technical solutions adopted, and a representation of plumes considered satisfactory in comparison to observations. Additionally, a simple sensitivity analysis is presented, that gives useful insights about the model application.     

The Dirac Equation in the Kerr-de Sitter Metric

We consider a Fermion in the presence of a rotating BH immersed in a universe with a positive cosmological constant. After presenting a rigorous classification of the number and type of the horizons, we adopt the Carter tetrad to separate the aforementioned equation into radial and angular equations. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that in the limit of a vanishing cosmological constant reproduces the square root of the squared total angular momentum operator for a Dirac particle in the Kerr metric. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues, and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.     

Manifold splines with a single extraordinary point

This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result, manifold splines can unify planar spline representations as their special cases. Despite its earlier success, the existing manifold spline framework is plagued by the topology-dependent, large number of singular points (i.e., |2g−2| for any genus-g surface), where the analysis of surface behaviors such as continuity remains extremely difficult. The unique theoretical contribution of this paper is that we devise new mathematical tools so that manifold splines can now be constructed with only one singular point, reaching their theoretic lower bound of singularity for real-world applications. Our new algorithm is founded upon the concept of discrete Ricci flow and associated techniques. First, Ricci flow is employed to compute a special metric of any manifold domain (serving as a parametric domain for manifold splines), such that the metric becomes flat everywhere except at one point. Then, the metric naturally induces an affine atlas covering the entire manifold except this singular point. Finally, manifold splines are defined over this affine atlas. The Ricci flow method is theoretically sound, and practically simple and efficient. We conduct various shape experiments and our new theoretical and algorithmic results alleviate the modeling difficulty of manifold splines, and hence, promote the widespread use of manifold splines in surface and solid modeling, geometric design, and reverse engineering.     

An Efficient Correction Method to Obtain a Formally Third-Order Accurate Flow Solver for Node-Centered Unstructured Grids

A new method of obtaining third-order accuracy on unstructured grid flow solvers is presented. The method involves a simple correction to a traditional linear Galerkin scheme on tetrahedra and can be conveniently added to existing second-order accurate node-centered flow solvers. The correction involves gradients of the flux computed with a quadratic least squares approximation. However, once the gradients are computed, no second derivative information or high-order quadrature is necessary to achieve third-order accuracy. The scheme is analyzed both analytically using truncation error, and numerically using solution error for an exact solution to the Euler equations. Two demonstration cases for steady, inviscid flow reveal increased accuracy and excellent shock capturing with no loss in steady-state convergence rate. Computational timing results are presented which show the additional expense from the correction is modest compared to the increase in accuracy.     

A hybrid nonlinear state observer for concentration profiles reconstruction in nonlinear simulated moving bed

In this paper, a state observer is proposed for the reconstruction of the concentration profiles in a simulated moving bed. The approach is based on a simple Luenberger-like correction term. The observer is used under the assumption that the flow rates are constant during each switching period. The matrix gain of the correction term may then be re-computed at the beginning of each switching period corresponding to flow rates being changed by the controller. Validating simulations are proposed to assess the efficiency of the proposed profile reconstruction and its robustness against uncertainties on modelling parameters. Comparisons are also done with open-loop simulation based-observer in order to strengthen the relevance of the correction term.     

Canonization for disjoint unions of theories

If there exist efficient procedures (canonizers) for reducing terms of two first-order theories to canonical form, can one use them to construct such a procedure for terms of the disjoint union of the two theories? We prove this is possible whenever the original theories are convex. As an application, we prove that algorithms for solving equations in the two theories (solvers) can not be combined in a similar fashion. These results are relevant to the widely used Shostak’s method for combining decision procedures for theories. They provide the first rigorous answers to the questions about the possibility of directly combining canonizers and solvers.     

Error analysis of solutions of second-order boundary value problems obtained with residual correction method

Based on the maximum principle of differential equations and with the aid of asymptotic iteration technique, this paper tries to establish monotonic relation of second-order obstacle boundary value problems with their approximate solutions to eventually obtain the upper and lower approximate solutions of the exact solution. To obtain numerical solutions, the cubic spline approximation method is applied to discretize equations, and then according to the ‘residual correction method’ proposed in this paper, residual correction values are added into discretized grid points to translate once complex inequalities’ constraint mathematical programming problems into simple equational iteration problems. The numerical results also show that such method has the characteristic of correcting residual values to symmetrical values for such problems, as a result, the mean approximate solutions obtained even with a considerably small quantity of grid points still quite approximate the exact solution. Furthermore, the error range of approximate solutions can be identified very easily by using the obtained upper and lower approximate solutions, even if the exact solution is unknown.