We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential. 1 ar X iv :1 70 3. 10 48 2v 1 [ qu an tph ] 3 0 M ar 2 01 7

Maximum likelihood (ML) is a popular method for inferring a phylogenetic tree of the evolutionary relationship of a set of taxa, from observed homologous aligned genetic sequences of the taxa. Generally, the computation of the ML tree is based on numerical methods, which in a few cases, are known to converge to a local maximum on a tree, which is suboptimal. The extent of this problem is unknow...

The high precision attained by cosmological data in the last few years has increased the interest in exact solutions. Analytic expressions for solutions in the Standard Model are presented here for all combinations of Λ = 0 , Λ 6= 0, κ = 0 and κ 6= 0, in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the ΛγCDM Model) has Λ 6= 0, κ 6= 0, and...

It now becomes apparent that condensed DNA toroid which emerges in a poor solvent condition can be realised in the framework of the non-linear sigma model on a line segment. In fact, the classical solutions of the model, i.e., of the bending potential exhibit toroidal forms, and fit well with the delta-function term of the attractive interaction. The proposed theory is in good agreement with ex...

Because of its technical difficulties the existence of analytic solutions to the iterative differential equation x′(z) = x(az + bx(z) + cx′(z)) is a source of open problems. In this article we obtain analytic solutions, using Schauder’s fixed point theorem. Also we present a unique solution which is a nonconstant polynomial in the complex field.

We analyze the controllability and observability (C/O) of the liquid water distribution in the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell (PEMFC) using a one-dimensional channel-to-channel unit fuel cell model. This modeling domain is sufficient to illustrate the control objectives and analysis techniques but requires further development for stack level modeling. A co...

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree–Fock) of Coulomb systems. We prove the following: Let {φ1, . . . , φM} be any solution to the rank–M multiconfiguration equations for a molecule with L fixed nuclei at R1, . . . , RL ∈ R. Then, for any j ∈ {1, . . . , M}, k ∈ {1, . . . , L}, there exi...

In this paper we make use of the the sn-ns method to obtain new exact solutions to so called repulsive or de-focusing nonlinear Schrödinger equation. These solutions are given in terms of Jacobi elliptic functions sn and ns.

Under the perturbative picture of planetary microlensing, planet is considered to act as a uniform-shear Chang-Refsdal lens on one two images produced by host star that comes close angular Einstein radius planet, leaving other image unaffected. However, this approximation only valid for isolated caustics and breaks down in resonant regime. Recently, planetary-caustic degeneracy arising from abo...

An efficient adaptive moving mesh method for investigation of the semi-classical limit of the focusing nonlinear Schrödinger equation is presented. The method employs a dynamic mesh to resolve the sea of solitons observed for small dispersion parameters. A second order semi-implicit discretization is used in conjunction with a dynamic mesh generator to achieve a cost-efficient, accurate, and st...