Split Boundary Research Articles

Meteorology and dust in the central Sahara: Observations from Fennec supersite‐1 during the June 2011 Intensive Observation Period

AbstractWe describe observations from the Fennec supersite at Bordj Badji Mokhtar (BBM) made during the June 2011 Fennec Intensive Observation Period. These are the first detailed in situ observations of meteorology and dust from the central Sahara, close to the center of the Saharan heat low and the summertime dust maximum. Historically, a shortage of such Saharan observations has created problems for evaluating processes, models, and remote sensing. There was a monsoon influence at BBM before 8 June and after 12 June, with dry Harmattan winds in between. A split boundary layer, generated by ventilation from the Atlantic, persisted during the drier phase. Extensive cold pools (haboobs) and microburst‐type events were regularly observed. Moisture reached BBM at night from the monsoon and the embedded haboobs. As well as the regularly occurring nocturnal low‐level jet (LLJ), a Saharan upper boundary layer (650 hPa) jet was observed, where winds feel drag from dry convection in the afternoon. This jet is linked to the diurnal cycles of moisture and cloud. Most dust was observed in the cloudier monsoon‐affected periods, and covarying dust and cloud amounts explain most of the variations in shortwave radiation that control the surface sensible flux. Dustiness is related to a standard parameterization of uplift using 10 m winds (“uplift potential”), and this is used to estimate uplift. Around 50% of uplift is nocturnal. Around 30% is from the LLJ, and 50% is from haboobs, which are mainly nocturnal. This demonstrates, for the first time from observations, the key role of haboobs, which are problematic for models.

The Research of a Fast and Effective Splitting Boundary Serarching Method for Power System

It is possible to prevent collapse of whole post-fault power system, which is in unstable condition, by determining the splitting boundary to calm down system oscillation. A fast splitting boundary-searching method for power system controlled islanding is presented in this paper. The aim of this method is that the generation load imbalance in each island is as small as possible. The method contains three phases: firstly, domain of each generator is formed according to power flow tracing algorithm; secondly, initial splitting boundary is determined based on generators’ grouping information; thirdly, the final splitting boundary is got based on initial splitting boundary. A program is developed based on the method. Simulations on IEEE 118-bus power system show the proposed method is effective and fast.

Split Local Artificial Boundary Conditions for the Two-Dimensional Sine-Gordon Equation on R2

AbstractIn this paper the numerical solution of the two-dimensional sine-Gordon equation is studied. Split local artificial boundary conditions are obtained by the operator splitting method. Then the original problem is reduced to an initial boundary value problem on a bounded computational domain, which can be solved by the finite difference method. Several numerical examples are provided to demonstrate the effectiveness and accuracy of the proposed method, and some interesting propagation and collision behaviors of the solitary wave solutions are observed.

A new approach to solve a set of nonlinear split boundary value problems

In this paper, we propose a new approach based on conjunction of the orthogonal collocation on finite elements method with decoupling and quasi-linearization technique to approximate solutions of a set of nonlinear split boundary value problems. The numerical stability, the convergence and the accuracy of the results are checked by this algorithm. The approach developed in this study is illustrated by some numerical examples. These examples are solved using a special software package which implements the proposed algorithms.

A Novel Real-Time Searching Method for Power System Splitting Boundary

It is possible to prevent collapse of the whole post-fault power system, which is in unstable condition, by determining the splitting boundary so as to calm down the system oscillation. A fast method of searching for the splitting boundary of power system controlled islanding is presented in this paper, the aim of which is to minimize the load-generation imbalance in each island. The method contains three phases, namely, defining the domain of each generator according to power flow tracing algorithm, determining an initial splitting boundary based on the grouping information of generators, and refining the initial one to get the final splitting boundary. A real-time searching program for power system splitting boundary was developed based on the method. Simulations on the IEEE 118-bus power system and a practical power system show that the proposed method is effective and fast.

Reverse osmosis modeling with the orthogonal collocation on finite element method

A mathematical model was used to predict the performance of hollow fiber reverse osmosis membrane. The model is based on the solution-diffusion mass transfer model and takes into account the effect of the flow pattern of the permeate in the membrane. According to the flow direction inside the membrane, two types of flow can be distinguished: the co-current and counter-current flow pattern. Several studies underlined the effectiveness of the counter-current flow pattern [1]. However, no study was carried out to demonstrate this assumption. This work aims to answer clearly the question of the choice of the flow type. The parameters used in this work are the overall recovery, the average concentration of the obtained product and the final concentration of the feed rate in the closed loop processes. The resolution of the mathematical model developed for the counter-current flow pattern is subjected to the split boundary value problem. To solve this problem, a robust and efficient procedure based on orthogonal collocation on finite element method was used. Experimental data were used to verify the proposed mathematical model and accomplish the comparative study between the two flow types. The results obtained show clearly the better efficiency of the counter-current flow pattern especially in the concentrating process.

Generic Optimal Temperature Profiles for a Class of Jacketed Tubular Reactors

This paper deals with the optimal and safe operation of jacketed tubular reactors. Despite the existence of advanced distributed controllers, optimal steady-state reference profiles to be tracked are often unknown. In Logist et al. [2008], a procedure which combines analytical and numerical optimal control techniques, has been proposed for deriving optimal analytical (and thus generic) references, and it has been illustrated for plug flow reactors. The aim of this paper is to illustrate the general applicability of this procedure by allowing dispersion. As dispersion significantly complicates a possible solution process (due to second-order derivatives and split boundary conditions), hardly any generic results are known. Nevertheless, the dispersive plug flow reactor model is important for practice, since varying the dispersion level allows to mimic an entire reactor range, i.e., from plug flow to perfectly mixed reactors. As an example a jacketed tubular reactor in which an exothermic irreversible first-order reaction takes place is adopted. It is shown that the procedure yields generic reference solutions for (i) three different cost criteria, and (ii) different dispersion levels.

Acoustic scattering by a sphere with a hemispherically split boundary condition

A general analytical model is developed for the scattering of sound by a sphere with a nonuniform impedance boundary condition that is divided into two uniformly distributed hemispheres. In addition to the overall solution for the time harmonic pressure, the analytical result gives insight into the modal contributions and coupling for different cases of source incidence and boundary impedance. Modal cross coupling is shown to exist between incoming and scattered wave modes of equi-order and nonequal degree when the degrees are opposite in parity (odd-even or even-odd coupling). This cross coupling is strongest between modes of adjacent degree, and decreases as the degrees become dissimilar. The overall magnitude of the cross coupling is dependent on the extent of the impedance mismatch between the two surface hemispheres. Simulation and discussion are given for several specific cases of source incidence and impedance (each hemisphere is given a different constant impedance value). These results are consistent with expectations from the scattering of sound by a sphere with a uniformly distributed surface boundary. The broad scattering characteristics of the hemispherically divided sphere are shown to be analogous to connecting the appropriate sectors from the corresponding uniformly distributed spheres.

Basic properties of free stratified flows

Results of analytical studies of the governing equations of stratified rotating fluids based on the unification of theories of continuous and discrete groups, perturbations and modern numerical visualizations are described. Symmetries of basic systems and their simplified versions, different approximations and constitutive turbulent models are compared. A new method to calculate discrete groups analytically, which does not need a preliminary search for continuous groups, is developed. As an example of the practical use of the developed algorithm, a complete classification of cellular and roll structures of Benard convection is presented. A complete classification of 3D periodic motions in compressible viscous stratified and rotating fluids, including regular (wave) and singular elements, is performed by perturbation methods. In all cases, in a viscous fluid, besides waves there are two different periodic boundary layers. In a homogeneous fluid the split boundary layers are merged, thus forming a joint doubly-degenerate structure. Stratification and rotation reduce the degeneration of the 3D periodic boundary layers. Calculations of a 3D periodic wave beam emitted by an oscillating part of a sloping plane are visualized by a computer-graphics method. The existence of thin extended components on the edges of the 3D wave cone is demonstrated.

On the Diffusion of Fluids Through Solids Undergoing Large Deformations

In this paper, we investigate the problem of diffusion of a Newtonian fluid through a non-linearly elastic solid undergoing large deformations, within the framework of mixture theory. Our aim is to delineate the effect of various boundary conditions on the diffusion process. We find that the results are quite insensitive to the boundary conditions in that the predictions agree exceedingly well with the experiments (whether it is the saturation boundary condition used by Rajagopal, Wineman and Gandhi, the traction splitting boundary condition used by Rajagopal and Tao, the natural boundary condition used by Baek and Srinivasa, or the fact that the chemical potential is continuous across the boundary), provided that an appropriate choice is made for the drag.

On the convergence rate and optimization of a numerical method with splitting of boundary conditions for the stokes system in a spherical layer in the axisymmetric case: Modification for thick layers

The convergence rate of a fast-converging second-order accurate iterative method with splitting of boundary conditions constructed by the authors for solving an axisymmetric Dirichlet boundary value problem for the Stokes system in a spherical gap is studied numerically. For R/r exceeding about 30, where r and R are the radii of the inner and outer boundary spheres, it is established that the convergence rate of the method is lower (and considerably lower for large R/r) than the convergence rate of its differential version. For this reason, a really simpler, more slowly converging modification of the original method is constructed on the differential level and a finite-element implementation of this modification is built. Numerical experiments have revealed that this modification has the same convergence rate as its differential counterpart for R/r of up to 5 × 103. When the multigrid method is used to solve the split and auxiliary boundary value problems arising at iterations, the modification is more efficient than the original method starting from R/r ∼ 30 and is considerably more efficient for large values of R/r. It is also established that the convergence rates of both methods depend little on the stretching coefficient η of circularly rectangular mesh cells in a range of η that is well sufficient for effective use of the multigrid method for arbitrary values of R/r smaller than ∼ 5 × 103.

Solving Optimal Continuous Thrust Rendezvous Problems with Generating Functions

The optimal control of a spacecraft as it transitions between specified states using continuous thrust in a fixed amount of time is studied using a recently developed technique based on Hamilton-Jacobi theory. Started from the first-order necessary conditions for optimality, a Hamiltonian system is derived for the state and adjoints with split boundary conditions. Then, with recognition of the two-point boundary-value problem as a canonical transformation, generating functions are employed to find the optimal feedback control, as well as the optimal trajectory. Although the optimal control problem is formulated in the context of the necessary conditions for optimality, our closed-loop solution also formally satisfies the sufficient conditions for optimality via the fundamental connection between the optimal cost function and generating functions. A solution procedure for these generating functions is posed and numerically tested on a nonlinear optimal rendezvous problem in the vicinity of a circular orbit. Generating functions are developed as series expansions, and the optimal trajectories obtained from them are compared favorably with those of a numerical solution to the two-point boundary-value problem using a forward-shooting method.

Association of ecotones with relative elevation and fire in an upland Florida landscape

Abstract Question: What are the importance of elevation and fire in maintaining ecotones of Florida scrub assemblages along a gradual topographic gradient? Location: Archbold Biological Station (ABS), 12 km south of Lake Placid, Florida, USA. Methods: Vegetation cover of upland Florida shrublands was quantified using the line-intercept method along 20 transects traversing similar elevation gradients, stratified by time since fire (TSF). We objectively identified shrubland ecotones using a split moving windows boundary analysis (SMW) with three different window widths. Non-metric multidimensional scaling ordination was used to determine relationships among plant assemblages defined by SMW. Results: We located up to four ecotones per transect, the majority of which were wide, highly heterogeneous zones. Relative elevation controlled the distribution of plant assemblages in upland Florida shrublands. Ecotones in shrublands > 30 years TSF had relatively low dissimilarity values in SMW, indicating that previou...

Fine-scale pattern of the boundary zones in alkaline grassland communities

We investigated the pattern of boundary types in alkaline grassland communities in Hungary. We used moving split window boundary analysis with dissimilarity functions, usually applied to detect ecotones and landscape boundaries at a coarse scale. The results were compared with those of correspondence analysis and clustering methods for the same data set, as well as with the local frequency distributions of populations along the studied transects. The MSW technique, usually applied in boundary and transition zone detection, was effective at a fine scale as well. The visible boundaries and transition zones were detectable with this method in most cases, but only sharp and narrow boundaries were verified with ordination and classification. If the changes are gradual in microtopography, then it is possible to detect transition zones between the vegetation patches. These types of transition zones can be considered as ecoclines. Despite the gentle microtopographical gradient, a marked border was detected betwee...

Automated visual inspection for microdrills in printed circuit board production

The rapid growth in printed circuit board production has led to the growing importance of microdrilling. Owing to the trend for high-density circuits on printed circuit boards, the diameter of a microdrill has to be much finer than ever before. The inspection for microdrills becomes more difficult and the detection of defects is harder. An automated visual inspection scheme for detecting the major defects of microdrills is proposed. The colour images of microdrills are first derived, and the boundary of the lip relief plane is extracted. A robust K-curvature corner detection algorithm is then used to detect the corners on the blade boundaries and to split boundaries into segments. The least-squares linear regression method is used to fit the segments into linear equations. With the fitted equations, the intersections on the boundaries of two facets are located and their distances (gap or overlap) are measured. In addition, the defects of taper and flare are identified by comparing the angle measurements with predefined specifications. Two types of microdrills are used to verify the proposed inspection process. Experimental results show that the proposed scheme reliably achieves precise inspection.

Relaxational approach to solving the Schrödinger equation

A relaxational approach to solving the Schr\"odinger equation is developed that utilizes split boundary conditions. The method solves the wave equation for the eigenvalues and eigenfunctions simultaneously. Advantages over numerical integration offered with the technique include simplification of the selection of boundary conditions and initial eigensystem estimates. The power of this technique is demonstrated by numerical solution of the radial Schr\"odinger equation for several important or problematic potentials, including the Saxon-Wood potential, the laser-dressed Coulombic potential, the regulated Coulombic potential, the Morse potential, and the Lennard-Jones potential. In order to demonstrate this method's applicability to even highly nonlinear systems, the ground-state energy levels of the helium and lithium atomic systems are solved utilizing a self-consistent-field approximation. The application of the method to two- and three-dimensional systems is then briefly discussed.

Optimization of the fuel input to an industrial heating plant

The paper describes the calculation of the minimum amount of fuel required to warm a simple model of a batch heating plant that has an active temperature constraint on the furnace gas. The method of calculation combines optimal control theory and a direct search with a downhill simplex to place the temperatures of the multiple nodes of the load inside a target envelope. The split boundary value problem is solved by shooting. Shooting is facilitated by omitting from the plant model the thermal storage of the gas enclosed within the plant. The purpose of the calculation is to illustrate that minimizing a linear integral of fuel flow does not lead to bang-bang control and that the constraint on the gas temperature is easily handled by treating it as a control constraint.

The trivial connection contribution to Witten’s invariant and finite type invariants of rational homology spheres

We derive an analog of the Melvin-Morton bound on the power series expansion of the colored Jones polynomial of algebraically split links and boundary links. This allows us to produce a simple formula for the trivial connection contribution to Witten’s invariant of rational homology spheres. We show that thenth term in the 1/K expansion of the logarithm of this contribution is a finite type invariant of Ohtsuki order 3n and of at most Garoufalidis ordern.

Feedback-based flow control of B-ISDN/ATM networks

We consider a system comprising of a single bottleneck switch/node that is fed by N independent Markov-modulated fluid sources. There is a fixed propagation delay incurred by the traffic between these sources and the switch. We assume that the switch sends periodic feedback in the form of a single congestion indicator bit. This feedback also incurs a fixed propagation delay in reaching the sources. Upon reaching the sources (or the access controllers associated with the sources), this congestion indicator bit is used to choose between two rates for the excess traffic, high or low, possibly depending on the state of that source. The switch employs a threshold mechanism based on its buffer level to discard excess traffic. We show that the stationary distribution of this system satisfies a set of first-order linear differential equations along with a set of split boundary conditions. We obtain an explicit solution to these using spectral decomposition. To this end we investigate the related eigenvalue problem. Based on these results we investigate the role of delayed feedback vis-a-vis various time-constants and traffic parameters associated with the system. In particular, we identify conditions under which the feedback scheme offers significant improvement over the open-loop scheme.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Continuous cocurrent processes in the nonsteady state

Although continuous heat- and mass-transfer processes are usually conducted in countercurrent flow, there are certain cases in which the cocurrent flow can be used to some advantages from an operation point of view. For example, in the packed adsorption column, flooding due to high vapor or gas flow rate can be eliminated if cocurrent flow is employed. Use of cocurrent flow can also reduce the pressure drop requirement in the packed column. Reiss (1967) discussed several instances in which cocurrent mode operation may be favored over countercurrent flow. In the case of heat transfer, cocurrent flow is also suitable for some special situations. For instance, if it is necessary to limit the maximum temperature of cooler fluid or if it is important to change the temperature of at least one fluid rapidly (McCabe et al., 1985). The transient behaviors of both cocurrent and countercurrent processes are important in the startup and control of mass- and heat-transfer operations. Previously, numerical solutions based on a method of characteristics was used to study the transients of countercurrent processes (Tan and Spinner, 1984). Owing to the split boundary conditions, analytic solutions are difficult to obtain even for the linear system. For cocurrent flow, compact analytic solutions in terms of well-known tabulated function can be derived. The purpose of this note is to present the nonsteadystate behavior of continuous cocurrent flow of two contacting phases. The transient responses to the inlet disturbances are derived based on a simple mathematical model. This simplified model is equally applicable to either mass- or heat-transfer processes. Laplace transformation method is used to obtain compact analytic solutions. These solutions can be easily evaluated with the aid of the known tabulated mathematical functions or charts. Both the derivation and the final form of solutions are easier to apply in comparison to the work of Li (1986).