Elasticity of semiflexible polymers in two dimensions

We study theoretically the entropic elasticity of a semi-flexible polymer, such as DNA, confined to two dimensions. Using the worm-like-chain model we obtain an exact analytical expression for the partition function of the polymer pulled at one end with a constant force. The force-extension relation for the polymer is computed in the long chain limit in terms of Mathieu characteristic functions. We also present applications to the interaction between a semi-flexible polymer and a nematic field, and derive the nematic order parameter and average extension of the polymer in a strong field.Comment: 16 pages, 3 figure

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

Classical and quantum three-dimensional integrable systems with axial symmetry

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of a kinetic part plus a potential dependent on the position only, the $z$-component of the angular momentum, $L$, and a Hamiltonian-like constant, $\widetilde H$, for which the kinetic part is quadratic in the momenta. We find the explicit form of these potentials compatible with complete integrability. The classical equations of motion, written in terms of two arbitrary potential functions, is separated in oblate spheroidal coordinates. The quantization of such systems leads to a set of two differential equations that can be presented in the form of spheroidal wave equations.Comment: 17 pages, 3 figure

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

Realizations of the Lie superalgebra q(2) and applications

The Lie superalgebra q(2) and its class of irreducible representations V_p of dimension 2p (p being a positive integer) are considered. The action of the q(2) generators on a basis of V_p is given explicitly, and from here two realizations of q(2) are determined. The q(2) generators are realized as differential operators in one variable x, and the basis vectors of V_p as 2-arrays of polynomials in x. Following such realizations, it is observed that the Hamiltonian of certain physical models can be written in terms of the q(2) generators. In particular, the models given here as an example are the sphaleron model, the Moszkowski model and the Jaynes-Cummings model. For each of these, it is shown how the q(2) realization of the Hamiltonian is helpful in determining the spectrum.Comment: LaTeX file, 15 pages. (further references added, minor changes in section 5

Fifth-year medical students’ perspectives on rural training in Botswana: A qualitative approach

Background. The curriculum of the Faculty of Medicine at the University of Botswana includes rural community exposure for students throughout their 5 years of training. In addition to community exposure during the first 2 years, students complete 16 weeks of family medicine and 8 weeks of public health medicine. However, as a new faculty, students’ experiences and perceptions regarding rural clinical training are not yet known.Objective. To describe the experiences and perceptions of the 5th-year medical students during their rural training and solicit their recommendations for improvement.Methods. This qualitative study used face-to-face interviews with 5th-year undergraduate medical students (N=36) at the end of their family medicine rotation in Mahalapye and Maun villages. We used a phenomenological paradigm to underpin the study. Voice-recorded interviews were transcribed and analysed using Atlas TI version 7 software (USA).Results. Three main themes were identified: (i) experiences and perceptions of the rural training environment; (ii) perceptions of the staff at rural sites; and (iii) perceptions of clinical benefits and relevance during rural training. While the majority of students perceived rural training as beneficial and valuable, a few felt that learning was compromised by limited resources and processes, such as medical equipment, internet connectivity and inadequate supervision.Conclusion. While the majority of students perceived rural training as beneficial, students identified limitations in both resources and supervision that need to be improved. Understanding students’ rural training experiences and perceptions can help the Faculty of Medicine, stakeholders and site facilitators to guide future rural training implementation

Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page

New Algebraic Quantum Many-body Problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page