Flow and reactive transport in porous media induced by well injection: Similarity solution

The authors study concentration profiles of solutes undergoingequilibrium absorption in the vicinity of a water well. Forthe case of a contamination event, the limit problem of vanishingwell radius, which is of self-similar nature, is analysed indetail. Existence, uniqueness, and qualitative properties ofsolutions of the corresponding ordinary differential equationsare shown. Some numerical examples are also presented.     

百万大气压下的压强校准及5.5 Mbar静压强的获得

进行了百万大气压下,静水压和非静水压条件下的压力校准,同时观察到金刚石砧容器中红宝石R线红移至830nm处,由校准公式算得对应的压强为5.5Mbar。 关键词：     

Solution Branches for Non-linear Equilibrium Problems--Bifurcation and Domain Perturbations

Consider the following simple, but typical, example of a non-linearequilibrium (differential equation) problem: u = –f(u) for (x, y) D, u = 0 for (x, y) D. Usually the eigenvalues of the (small u) linearized problemare simple, and each simple eigen value generates two solutionbranches for the full problem. However, the full problem nearlyalways has many other solution branches, and this paper describeshow to find these other branches and why they arise.     

LAND USE OPTIMIZATION USING SELF-ORGANIZING ALGORITHMS

ABSTRACT. In many spatial systems the interaction between various regions decreases dramatically with distance. This suggests that local trade-offs may be more important than global ones in land use planning and that a decentralized, parallel optimization of the individual regions may be an attractive supplement to more centralized optimization approaches. In this paper, we solve a forest planning problem using a series of decentralized approaches. The approaches can be characterized as self-organizing algorithms and are modeled in the framework of a cellular automaton. We compare our results with those obtained by more centralized approaches, viz. a large sample approach, simulated annealing, and a genetic algorithm. We find that the self-organizing algorithms generally converge much faster to solutions which are at least as good as those obtained by simulated annealing and the genetic algorithm.     

Short-cut distillation columns based on orthogonal polynomials of a discrete variable

Increasing competition in the process industries enforces theapplication of mathematical simulation techniques both in thedesign phase and in the operating phase of a plant. A basicapparatus for separation processes is the distillation column.Its rigorous (tray by tray) mathematical modelling results ina system of simultaneous nonlinear equations (algebraic in thesteady-state case, differential-algebraic in the dynamic case).For high (and realistic) numbers of trays and components, thesesystems may become rather large (thousands of equations). Inaddition, realistic plant models often include several distillationcolumns. As a consequence, the numerical solution of these modelsmay become difficult and time-consuming. This has led to attemptsto model the distillation columns less rigorously with the aimof achieving a considerable reduction in the number of equations.The name shortcut distillation columns is common for modelsof this type. The present paper uses a discrete weighted residualmethod for the development of short-cut models. It suggestsa Galerkin method based on orthogonal polynomials in a discretevariable: the tray number. It is a remarkable advantage of thistechnique that even very coarse models satisfy all global balancesexactly.     

Dual Decomposition Schemes for Multicriteria Decision Making

This paper presents two interactive procedures for decisionproblems with multiple criteria and decentralized information.One is a resource-directive procedure and the other is a price-directiveprocedure. The procedures are completely general and make nopresumptions about linearity or convexity. Nevertheless, successivelyimproved upper and lower bounds on the optimal value are determinedin each iterative step. Consequently, the communication is progressive.The procedures are illustrated in an example from integer programming.     

Uniform Asymptotic Representation of Solutions of the Basic Semiconductor-Device Equations

In this paper we analyse the basic semiconductor-device equationsmodelling a symmetric one-dimensional voltage-controlled diodeunder the assumptions of zero recombination-generation and constantmobilities. Employing the singular-perturbation formulationwith the normed Debye length as perturbation parameter we derivethe zeroth-order terms of the matched asymptotic expansion ofthe solutions, which are sums of uniformly smooth outer terms(reduced solutions) and exponentially varying inner terms (layersolutions). The main result of the paper is that, if the perturbationparameter is sufficiently small, then there exists a solutionof the semiconductor-device problem which is approximated uniformlyby the zeroth-order term of the expansion, even for large appliedvoltages. This result shows the validity of the asymptotic expansionsof the solutions of the semiconductor-device problem in physicallyrelevant high-injection situations.     

Pair approximation for polarization interaction and adiabatic nuclear and electronic sampling method for fluids with dipole polarizability

The adiabatic nuclear and electronic sampling method (ANES), originally formulated as an efficient Monte Carlo algorithm for systems with fluctuating charges, is applied to the simulation of a polarizable water model with induced dipole moments. Structural, thermodynamic and dipolar properties obtained by ANES and a newer algorithm, the pair approximation for polarization interaction (PAPI), are compared with full iteration. With the best parameters, the inaccuracy of both approximate methods was found to be comparable with the uncertainty of the full iteration. The PAPI method with iteration radius equal to the second minimum of the oxygen—oxygen correlation function is, depending on the convergence tolerance, 10–15 times faster than the full iteration for 256 molecules, and yields very accurate structure and thermodynamics with deviation about 0.3%. When the iteration radius is increased to the cutoff distance, exact results are recovered at the cost of decreased efficiency. The ANES method with small nuclear displacements proved to inefficiently sample the configurational space. Simulations at low electronic temperatures with large nuclear displacements are inaccurate for up to 100 electronic moves, and increasing this number would make the simulations as slow as the full iteration. The most accurate and efficient adiabatic ANES simulations are those with infinite electronic temperature, large nuclear displacements and 1–10 electronic moves. The extra freedom of induced dipoles in the ANES method at high electronic temperatures modifies the observed dipolar properties; however, the question of whether the dielectric constant is also modified needs further consideration.     

Theoretical determination of the vibrational levels of NH+ 3 and its isotopomers

The vibrational levels associated with the electronic ground state X²A₂″ of NH⁺ ₃ have been determined up to 5000 cm^?1 by perturbation and variational calculations with full dimensionality of the molecule. For the variational part a new version of MULTIMODE was used which uses the ab initio electronic energy and its first derivative to define the potential energy function. These quantities were generated by the B97-1 density functional and RCCSD(T) approaches. For ND⁺ ₃, ND₂H⁺ and NDH⁺ ₂ the vibrational levels were calculated only by perturbation theory. The rotational constants for all the isotopomers were determined and the first transition dipole moments for NH⁺ ₃ and ND⁺ ₃ were plotted. A critical comparison of the perturbation and variational techniques suggests a possible further modification to the MULTIMODE algorithm for large systems.