Groundwater waves in a coastal aquifer: A new governing equation including vertical effects and capillarity

Groundwater waves, that is, water table fluctuations, are a natural phenomenon in coastal aquifers. They represent an important part of the interaction between the ocean and aquifer and affect the mass exchange between them. This paper presents a new groundwater wave equation. Because it includes the effects of vertical flows and capillarity, the new equation is applicable to both intermediate-depth aquifers and high-frequency waves. Compared with the wave equation derived by Nielsen ed al. [1997], the present equation provides a closer representation of groundwater waves. In particular, it predicts high-frequency water table fluctuations as observed in the field. A validation of the new equation has been carried out by comparing the analytical solutions to it with predictions from direct simulations using the numerical model SUTRA. The effects of various physical parameters and their relative importance are also discussed.

A hybrid, inverse approach to the design of magnetic resonance imaging magnets

This paper describes a hybrid numerical method of an inverse approach to the design of compact magnetic resonance imaging magnets. The problem is formulated as a field synthesis and the desired current density on the surface of a cylinder is first calculated by solving a Fredholm equation of the first, kind. Nonlinear optimization methods are then invoked to fit practical magnet coils to the desired current density. The field calculations are performed using a semi-analytical method. The emphasis of this work is on the optimal design of short MRI magnets. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric MRI magnets as well as asymmetric magnets. The results highlight that the method can be used to obtain a compact MRI magnet structure and a very homogeneous magnetic field over the central imaging volume in clinical systems of approximately 1 m in length, significantly shorter than current designs. Viable asymmetric magnet designs, in which the edge of the homogeneous region is very close to one end of the magnet system are also presented. Unshielded designs are the focus of this work. This method is flexible and may be applied to magnets of other geometries. (C) 2000 American Association of Physicists in Medicine. [S0094-2405(00)00303-5].

Two-dimensional nonlinear dynamics of evanescent-wave guided atoms in a hollow fiber

We describe the classical and quantum two-dimensional nonlinear dynamics of large blue-detuned evanescent-wave guiding cold atoms in hollow fiber. We show that chaotic dynamics exists for classic dynamics, when the intensity of the beam is periodically modulated. The two-dimensional distributions of atoms in (x,y) plane are simulated. We show that the atoms will accumulate on several annular regions when the system enters a regime of global chaos. Our simulation shows that, when the atomic flux is very small, a similar distribution will be obtained if we detect the atomic distribution once each the modulation period and integrate the signals. For quantum dynamics, quantum collapses, and revivals appear. For periodically modulated optical potential, the variance of atomic position will be suppressed compared to the no modulation case. The atomic angular momentum will influence the evolution of wave function in two-dimensional quantum system of hollow fiber.

Decentralized control design for nonlinear plants: a v-metric approach

In this paper, a new v-metric based approach is proposed to design decentralized controllers for multi-unit nonlinear plants that admit a set of plant decompositions in an operating space. Similar to the gap metric approach in literature, it is shown that the operating space can also be divided into several subregions based on a v-metric indicator, and each of the subregions admits the same controller structure. A comparative case study is presented to display the advantages of proposed approach over the gap metric approach. (C) 2000 Elsevier Science Ltd. All rights reserved.

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature.

Similitude applied to centrifugal scaling of unsaturated flow

Centrifuge experiments modeling single-phase flow in prototype porous media typically use the same porous medium and permeant. Then, well-known scaling laws are used to transfer the results to the prototype. More general scaling laws that relax these restrictions are presented. For permeants that are immiscible with an accompanying gas phase, model-prototype (i.e., centrifuge model experiment-target system) scaling is demonstrated. Scaling is shown to be feasible for Miller-similar (or geometrically similar) media. Scalings are presented for a more, general class, Lisle-similar media, based on the equivalence mapping of Richards' equation onto itself. Whereas model-prototype scaling of Miller-similar media can be realized easily for arbitrary boundary conditions, Lisle-similarity in a finite length medium generally, but not always, involves a mapping to a moving boundary problem. An exception occurs for redistribution in Lisle-similar porous media, which is shown to map to spatially fixed boundary conditions. Complete model-prototype scalings for this example are derived.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) 'Aggregation model'. Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species. (C) 2004 Elsevier B.V All rights reserved.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

Global solutions for abstract neutral differential equations

We study the existence of global solutions for a class of abstract neutral differential equation defined on the whole real axis. Some concrete applications related to ordinary and partial differential equations are considered. (C) 2009 Elsevier Ltd. All rights reserved.

Existence results for a damped second order abstract functional differential equation with impulses

In this work we study the existence and regularity of mild solutions for a damped second order abstract functional differential equation with impulses. The results are obtained using the cosine function theory and fixed point criterions. (C) 2009 Elsevier Ltd. All rights reserved.

Existence of asymptotically almost automorphic solutions to some abstract partial neutral integro-differential equations

The paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro-differential equation with unbounded delay. An example is given to illustrate our results. (C) 2008 Elsevier Ltd. All rights reserved.

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 Elsevier Ltd. All rights reserved.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth a, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered. (C) 2011 Elsevier Ltd. All rights reserved.