Two-layer Problem Research Articles

An Evaluation of Methods and Available Software for Seismic Refraction Tomography Analysis

Seismic refraction tomography is an alternative to conventional seismic refraction analysis methods. While the limitations and potential pitfalls of conventional refraction methods are well-known the same is not true for refraction tomography. As refraction tomography becomes more widely used, the need to know and understand its capabilities as well as its limitations becomes more critical. In this study we created eight representative models for use in evaluating three commercially available codes as well as refraction tomography in general. These models range from simple two-layer or dipping-layer problems to more complicated models designed to represent features of karst terrains. We demonstrate quantitatively and qualitatively that all three codes perform at a similar level, although each has strengths and weaknesses. Refraction tomography performs well in many situations where conventional methods fail, e.g., where lateral or vertical gradients compose a significant component of the velocity structure.

An Efficient Neural Algorithm for Two-layer Planarization Problem in Graph Drawing

A neural algorithm for the two-layer planarization problem using a gradient ascent learning of the Hopfield network is presented. This algorithm which is designed to embed a two-layer graph on a plane, uses the Hopfield network to get a near-maximal two-layer planar subgraph, and increases the energy by modifying the weights and the thresholds in gradient ascent direction to help the network escape from the state of near-maximal two-layer planar subgraph to the state of the maximal two-layer planar subgraph. The experimental results show that the proposed algorithm generates much better solutions than traditional Hopfield network and simulated annealing.

NONCOOPERATIVE GAME ON SCHEDULING: THE SINGLE MACHINE CASE

Considering the diversified requirements of modern manufacturing, the paper studies a group of scheduling problems where jobs and machine have independent performance objectives. Based on noncooperative game, it is modeled as a two-layer optimization problem. In job-layer, the jobs' strategies resulted from competition for machine resource achieve Nash Equilibrium (NE), while in machine-layer, machine induces the NE to some global optimum by indirectly influencing jobs' selfish behaviors. Referring to Lagrangian relaxation, an iterative algorithm is developed to solve the problem. Numerical example is also given for illustration.

Surface-tension-driven instabilities of a pure liquid layer evaporating into an inert gas

A theoretical model of the evaporation of a pure liquid layer is developed. We focus on the influence of an inert gaseous component, in addition to vapor, on surface-tension-driven Bénard instabilities. It is assumed that the gas phase is perfectly mixed at some distance from the liquid–gas interface (given composition, pressure, and temperature). If this distance is not much larger than the liquid layer thickness, it is shown that a reduction of the full two-layer problem to a one-layer problem is possible, provided the evaporation rate is not too large. An analytical expression is given for the corresponding dimensionless heat transfer coefficient (a generalized, wavenumber-dependent Biot number) at the evaporating interface. The approach is validated through a comparison with a direct numerical resolution of the full two-layer problem.

Weakly nonlinear study of Marangoni instabilities in an evaporating liquid layer

We propose a theoretical study of Marangoni driven convection in an evaporating liquid layer surmounted by an inert gas–vapor mixture. After reduction of the full two-layer problem to a one-sided model we use a Galerkin–Eckhaus method leading to a finite set of amplitude equations for the weakly nonlinear analysis of the problem. We analyze the stability of the roll, square, and hexagonal patterns emerging above the linear stability threshold for a water–air and for an ethanol–air system.

Network design with grooming constraints

Abstract Networks are physically and logically decomposed into layers with different technological features. Often, the routing of a demand through a non-multiplexing layer is made by grooming several demands at another, multiplexing-capable layer, thus using less capacity on the former but more on the latter. The problem of designing such a multi-layer network so as to route a set of traffic demands can be solved by embedding multiplexing into a well-suited model. We restrict to a two-layer problem as this is most common in today's network world, then we represent grooming through a model based on paths and semi-paths, and propose a row-column generation approach to solve a set of problems on real-world large networks.

On transient heat conduction in a one-dimensional composite slab

A theoretical solution is presented of a problem of transient heat conduction in a one-dimensional three-layer composite slab. A full series solution for impulsive heating is found by employing a ‘natural’ orthogonal relationship between the eigenfunctions. The eigenfunction expansion solution is compared with a finite difference numerical solution. Based on a previous analysis of the two-layer problem, and the present three-layer problem, a conjectured partial solution for an n-layer composite slab is given.

Mathematical Model of Electrodiffusion Transfer through a Diffusion Layer–Heterogeneous Ion-Exchange Membrane System

The kinetics of the charge and ion transport in a two-layer system which comprises a diffusion layer and an ion-exchange membrane in a salt solution and involves hydrogen and hydroxyl ions formed from water is modeled mathematically, making it possible to apply mathematical modeling to solving kinetic problems in complex electrodialysis systems where a two-layer problem is just a fragment.

Solution of a Two-Layer Flow Problem with Inhomogeneous Evaporation at the Thermocapillary Interface

The Ostroumov–Birikh type exact solution of thermodiffusion convection equations is constructed in the frame of mathematical model considering evaporation through the liquid–gas interface and the influence of direct and inverse thermodiffusion effects. It is interpreted as a solution describing steady flow of evaporating liquid driven by co-current gas-vapor flux on a working section of a plane horizontal channel. Functional form of required functions is presented. An algorithm for finding all the constants and parameters contained in the solution is outlined, and their explicit expressions are written. The solution is derived for the case of vapor absorption on the upper wall of the channel which is set with the help of the first kind boundary condition for the function of vapor concentration. Applicability field of the solution is briefly discussed

Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid Monte Carlo diffusion model

The general two-layer inverse problem in biomedical photon migration is to estimate the absorption and scattering coefficients of each layer as well as the top-layer thickness. We attempted to solve this problem, using experimental and simulated spatially resolved frequency-domain (FD) reflectance for optical properties typical of skin overlying muscle or skin overlying fat in the near infrared. Two forward models of light propagation were used: a two-layer diffusion solution [Appl. Opt. 37, 779 (1998)] and a hybrid Monte Carlo (MC) diffusion model [Appl. Opt. 37, 7401 (1998)]. MC-simulated FD reflectance data were fitted as relative measurements to the hybrid and the pure diffusion models. It was found that the hybrid model could determine all the optical properties of the two-layer media studied to ~5%. Also, the same accuracy could be achieved by means of fitting MC-simulated cw reflectance data as absolute measurements, but fitting them as relative ones is an ill-posed problem. In contrast, two-layer diffusion could not retrieve the top-layer optical properties as accurately for FD data and was ill-posed for both relative and absolute cw data. The hybrid and the pure diffusion models were also fitted to experimental FD reflectance measurements from two-layer tissue-simulating phantoms representative of skin-on-fat and skin-on-muscle baseline optical properties. Both the hybrid and the diffusion models could determine the optical properties of the lower layer. The hybrid model demonstrated its potential to retrieve quantitatively the transport scattering coefficient of skin (the upper layer), which was not possible with the pure diffusion model. Systematic discrepancies between model and experiment may compromise the accuracy of the deduced top-layer optical properties. Identifying and eliminating such discrepancies is critical to practical application of the method.

A novel sinc solution of the boundary integral form fortwo-dimensional bi-material elasticity problems

In this paper we illustrate a procedure for obtaining an approximate solution of the integral equation form of the two-dimensional Lamé equation for a two-layer problem, based on collocation via use of Sinc approximation. The Sinc approach automatically concentrates points near corners of the boundary where the solution has singularities and yields exponential convergence. A model two-layer bi-material elasticity problem is numerically investigated here as an illustration of this novel approach.

Benard-Marangoni convection in two-layered liquids

We describe experiments on Benard-Marangoni convection in horizontal layers of two immiscible liquids. Unlike previous experiments, which used gases as the upper fluid, we find a square planform close to onset which undergoes a secondary bifurcation to rolls at higher temperature differences. The scale of the convection pattern is that of the thinner lower fluid layer for which buoyancy and surface tension forces are comparable. The wave number of the pattern near onset agrees with the linear stability prediction for the full two-layer problem. The square planform is in qualitative agreement with recent two-layer weakly nonlinear theories, which fail however to predict the transition to rolls.

Two-layer assignment method for online Chinese character recognition

A method of stroke order and number-free online recognition of Chinese characters is proposed. Both input characters and model characters are represented with complete relational graphs (CRGs). Classification of an input character can be implemented by matching its CRG against every CRG of the model base. However, efficient algorithms for graph matching are not available. Therefore, the graph-matching problem is transformed into a two-layer assignment problem and is solved with the Hungarian method. Two complexity reduction schemes are presented to save computational time. Tests demonstrate the efficiency of the proposed method.

Bubble-sort approach to channel routing

An efficient bubble-sort technique for solving the two-layer non-Manhattan channel-routing problem is presented. The time and space complexities of our algorithm are O(kn) and O(n), respectively, where k is the number of sorting passes required and n is the total number of two-terminal nets in a routing channel. The algorithm is easily extended to handle the cases with multiterminal nets distributed in a channel. Various tests verify the efficiency of the bubble-sort based router. Experimental results indicate that the router is time-efficient for routing. A three-layer algorithm having O(kn) time based on an identical problem formulation is proposed for solving the non-Manhattan channel routing.

Efficient algorithms for single- and two-layer linear placement of parallel graphs

This paper outlines an algorithm for optimum linear ordering (OLO) of a weighted parallel graph with O( n log k) worst-case time complexity, and O(n + k log( n k ) log k) expected-case time complexity, where n is the total number of nodes and k is the number of chains in the parallel graph. Next, the two-layer OLO problem is considered, where the goal is to place the nodes linearly in two routing layers minimizing the total wire length. The two-layer problem is shown to subsume the maxcut problem and a befitting heuristic algorithm is proposed. Experimental results on randomly generated samples show that the heuristic algorithm runs very fast and outputs optimum solutions in more than 90% instances.

The DC field components of horizontal and vertical electric dipole sources immersed in three-layered stratified media

Abstract. Formulas for computing the Cartesian components of the static (DC) fields of horizontal electric dipoles ( HEDs) and vertical electric dipoles ( VEDs) located in the central zone of a three-layer horizontally stratified medium are derived and presented in a summary form suitable for immediate computation. Formulas are given for the electric and magnetic field components in the upper and central regions. In the general case the computation involves the summation of a convergent infinite series. For the particular case of an infinitely thick central region (corresponding to the two-layer problem), the analysis produces relatively simple closed-form equations for the field components which are suitable for a 'hand calculation'. Specimen calculations for dipoles in seawaters are included and the derived results are compared with computations made using an ac model.

The DC field components of horizontal and vertical electric dipole sources immersed in three-layered stratified media

Formulas for computing the Cartesian components of the static (DC) fields of horizontal electric dipoles ( HEDs) and vertical electric dipoles ( VEDs) located in the central zone of a three-layer horizontally stratified medium are derived and presented in a summary form suitable for immediate computation. Formulas are given for the electric and magnetic field components in the upper and central regions. In the general case the computation involves the summation of a convergent infinite series. For the particular case of an infinitely thick central region (corresponding to the two-layer problem), the analysis produces relatively simple closed-form equations for the field components which are suitable for a 'hand calculation'. Specimen calculations for dipoles in seawaters are included and the derived results are compared with computations made using an ac model.

Falling weight deflectometer data interpretation using dynamic impedance

This paper deals with the characterization of pavements and their supporting subgrade by comparing the measured dynamic impedance of a site, based on falling weight deflectometer data, with that of a two-layer, elastodynamic model. The pavement is modelled as a Kirchhoff plate and the subgrade as an incompressible, semi-infinite, elastic half space. The impedance of the two-layer problem is developed in graphical form as a function of a dimensionless angular frequency that depends on the pavement and subgrade properties. The characterization methodology outlined is applied to both simulated and actual field data. The effects of bedrock location and increasing subgrade stiffness with depth on dynamic impedance are addressed, and some limitations associated with the back calculation of system parameters are discussed. Key words: pavements, layer moduli, impedance, dynamic, back calculation.

Numerical modelling of the Black Sea eigen-oscillations on a curvilinear boundary fitted coordinate system

The paper presents a numerical solution of barotropic and two-layer eigen-oscillation problems for the Black Sea on a boundary fitted coordinate system. This solution is compared with model and empirical data obtained by other workers. Frequencies of the eigen-oscillations found by the numerical solution of spectral problem are compared with the data obtained by spectral analysis of the sea-level oscillations measured near the town of Achtopol and Cape Irakli in stormy sea on 17–21 February 1979. Extreme oscillations of the sea-level result from resonant amplifications of three eigenmodes of the Black Sea of 68.3 −1, 36.6 −1 and 27.3 −1 cycles h −1 frequency.

Optimal algorithms for bubble sort based non-Manhattan channel routing

It has been pointed out that, in many cases, results generated by non-Manhattan channel routers will be better than those generated by Manhattan routers. Non-optimal bubble sort based algorithms for non-Manhattan channel routing have been proposed in the literature by also allowing connections in the +45/spl deg/ and /spl minus/45/spl deg/ directions. In this paper, optimal algorithms are proposed for the two-layer and three-layer non-Manhattan channel routing problems based on an identical problem formulation. The time complexities of our algorithms and the existing algorithm (which produces the best results so far) are O(K/sup 2/ * N) and O(K * N/sup 2/), respectively, where N is the number of terminals (i.e., the length) of the channel and N is the number of routing tracks (i.e., the height) in the channel. K is always less than N, and in most cases is much smaller than N. Clearly, a significant improvement in time complexity over the existing algorithm (which produces the best results so far) is achieved, while ensuring optimality. >