On the Spectrum of the Poincaré Variational Problem for Two Close-to-Touching Inclusions in 2D

We study the spectrum of the Poincaré variational problem for two close to touching inclusions in R ². We derive the asymptotics of its eigenvalues as the distance between the inclusions tends to zero.     

Sub-ODE method and soliton solutions for the variable-coefficient mKdV equation

In this work, an auxiliary equation is used for an analytic study on the time-variable coefficient modified Korteweg-de Vries (mKdV) equation. Five sets of new exact soliton-like solutions are obtained. The results show that the pulse parameters are time-dependent variable coefficients. Moreover, the basic conditions for the formation of derived solutions are presented.     

Solitons in nonlinear directional couplers with optical metamaterials

This paper obtains bright, dark, and singular optical solitons in nonlinear directional couplers with optical metamaterials. The mathematical principle of undetermined coefficients is applied to extract these soliton solutions, with phase-matching condition. The constraint conditions for the existence of soliton solutions naturally emerge from the solutions. Both twin-core couplers and multiple-core couplers are studied in this paper.

     

Optical solitons in nonlinear directional couplers with trial function scheme

Nonlinear Dynamics - This paper obtains bright, dark and singular soliton solutions to optical couplers that appear with four forms of nonlinearity. Twin-core couplers as well as multiple-core...     

Isotopes to assess sustainability of overexploited groundwater in the Souss–Massa system (Morocco)

Groundwater depletion and changes in isotopic and chemical contents constitute the main indicators of overexploitation, recharge, and flow paths in the Souss–Massa aquifer. These indicators highlight processes concerning sustainability of water resources in the aquifer (e.g. surface/groundwater interaction, recharge processes, and marine intrusion). The spatial variation of stable and radioactive isotopic contents indicates a mixing of modern and old water within the system. Recent recharge was observed mainly along the Souss River (the major surface-water drainage in the study area) and in the irrigated areas. Mapping of chemical and isotopic variation shows that the area is affected by abstraction, irrigation water return, and the evolution of modern recharge in time and space. The processes, distribution, and timing of groundwater flow are influenced by short- and long-term effects; long-term recharge is dependent on climatic conditions. This study can be used to make informed decisions about water-resource allocation and alternative management practices.     

Dynamic pricing of electricity in retail markets

This paper aims at defining a dynamic and flexible tariff structure for a distribution company that protects the retail consumers against the excessive fluctuations of the wholesales market prices. We propose a two-stage pricing scheme that sets in a first-stage a time-of-use tariff that is corrected later by a dynamic component once the real-time demand has been observed. A personalized tariff scheme may be offered by a distribution company to each dynamic customer by allowing him to choose the appropriate robustness level expressed in terms of variability between the first and the second-stage decisions. The arising limited recourse model has been tested on realistic test problems, by using a slight modification of a recently proposed interior point solution framework.      

ERROR ESTIMATES FOR THE RECURSIVE LINEARIZATION OF INVERSE MEDIUM PROBLEMS

This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.     

Cu(tn)]3[Cr(CN)6](2).3H2O: a unique two-dimensional Cu-Cr cyano-bridged ferromagnet (tn = 1,3-diaminopropane)

Reaction of the two-coordinate 'assembling complex-ligand' [Cu(tn)]2+ with the building block [Cr(CN)6]3- leads to a unique two-dimensional Cu-Cr cyano-bridged ferromagnet with unusual mu 3- and mu 4-bridging [Cu(tn)]2+ units.     

A branch-and-cut algorithm for the Steiner tree problem with delays

In this paper, we investigate the Steiner tree problem with delays, which is a generalized version of the Steiner tree problem applied to multicast routing. For this challenging combinatorial optimization problem, we present an enhanced directed cut-based MIP formulation and an exact solution method based on a branch-and-cut approach. Our computational study reveals that the proposed approach can optimally solve hard dense instances.     

On soliton solutions for the Fitzhugh–Nagumo equation with time-dependent coefficients

We consider a generalized Fitzhugh–Nagumo equation exhibiting time-varying coefficients and linear dispersion term. By means of specific solitary wave ansatz and the tanh method, a new variety of soliton solutions are derived. The physical parameters in the soliton solutions are obtained as function of the time-dependent model coefficients. The conditions of existence and uniqueness of solitons are presented. These solutions may be useful to explain the nonlinear dynamics of waves in an inhomogeneous media that is described by the variable coefficients Fitzhugh–Nagumo equation. Clearly, adaptive methods are straightforward and concise and their applications for the Fitzhugh–Nagumo equation with t-dependent coefficients enable one to construct soliton-like solutions.