Symplectic algorithm for constant-pressure molecular dynamics using a Nose-Poincare thermostat

We present a new algorithm for isothermal-isobaric molecular-dynamics simulation. The method uses an extended Hamiltonian with an Andersen piston combined with the Nos'e-Poincar'e thermostat, recently developed by Bond, Leimkuhler and Laird [J. Comp. Phys., 151, (1999)]. This Nos'e-Poincar'e-Andersen (NPA) formulation has advantages over the Nos'e-Hoover-Andersen approach in that the NPA is Hamiltonian and can take advantage of symplectic integration schemes, which lead to enhanced stability for long-time simulations. The equations of motion are integrated using a Generalized Leapfrog Algorithm and the method is easy to implement, symplectic, explicit and time reversible. To demonstrate the stability of the method we show results for test simulations using a model for aluminum.Comment: 7 page

Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials

We introduce a spectral transform for the finite relativistic Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a non-symmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L,M) to define the spectral transform for the RTL. The inverse spectral transform is described in terms of a terminating T-fraction. The generalized eigenvalues are constants of motion and the auxiliary spectral data have explicit time evolution. Using the connection with the theory of Laurent orthogonal polynomials, we study the long-time behaviour of the RTL. As in the case of the Toda lattice the matrix entries have asymptotic limits. We show that L tends to an upper Hessenberg matrix with the generalized eigenvalues sorted on the diagonal, while M tends to the identity matrix.Comment: 24 pages, 9 figure

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order "conservation laws". In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction

Inverse moment problem for elementary co-adjoint orbits

We give a solution to the inverse moment problem for a certain class of Hessenberg and symmetric matrices related to integrable lattices of Toda type.Comment: 13 page

Additional Constants of Motion for a Discretization of the Calogero--Moser Model

The maximal super-integrability of a discretization of the Calogero--Moser model introduced by Nijhoff and Pang is presented. An explicit formula for the additional constants of motion is given.Comment: 7 pages, no figure

Does regretting first vaginal intercourse have an effect on young adults' sexual behaviour?

Background The aims of this research were to determine personal differences depending on the reason for regretting or not first vaginal intercourse and its effects on sexual behaviour later on among young adults, and to assess the association between reasons for engaging in first vaginal intercourse and regretting it. Data were drawn from the 2017 Swiss national survey on youth sexual behaviours among young adults (mean age 26 years) living in Switzerland. Out of the 7142 participants, 4793 (51% females) answered the question 'Looking back now to the first time you had vaginal intercourse, do you think that…' with five possible answers: (1) I should not have done it (6.7%); (2) I should have waited longer (7.7%); (3) I should have done it earlier (7.4%); (4) It was about the right time (67.9%); and (5) I don't know (10.3%). The five groups were compared on sociodemographic and sex behaviour-related variables, analysed separately by gender. One-third of participants regretted their first experience. In the multivariate analysis, compared with the 'right time' group, all other groups were more likely to find their first experience unpleasant and to have done it with a casual partner. Those in the 'I should not have done it' and 'I should have waited longer' groups were also more likely to have done it because of external pressure, especially among females. The study results underline the significance to choose the right time and the right partner for first vaginal intercourse and the importance of including partner respect and avoiding external pressure as part of sexual education

Discretization of hyperbolic type Darboux integrable equations preserving integrability

A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.Comment: 16 page

Statistical properties of charged interfaces

We consider the equilibrium statistical properties of interfaces submitted to competing interactions; a long-range repulsive Coulomb interaction inherent to the charged interface and a short-range, anisotropic, attractive one due to either elasticity or confinement. We focus on one-dimensional interfaces such as strings. Model systems considered for applications are mainly aggregates of solitons in polyacetylene and other charge density wave systems, domain lines in uniaxial ferroelectrics and the stripe phase of oxides. At zero temperature, we find a shape instability which lead, via phase transitions, to tilted phases. Depending on the regime, elastic or confinement, the order of the zero-temperature transition changes. Thermal fluctuations lead to a pure Coulomb roughening of the string, in addition to the usual one, and to the presence of angular kinks. We suggest that such instabilities might explain the tilting of stripes in cuprate oxides. The 3D problem of the charged wall is also analyzed. The latter experiences instabilities towards various tilted phases separated by a tricritical point in the elastic regime. In the confinement regime, the increase of dimensionality favors either the melting of the wall into a Wigner crystal of its constituent charges or a strongly inclined wall which might have been observed in nickelate oxides.Comment: 17 pages, 11 figure

Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy

Adler and van Moerbeke \cite{AVM} described a reduction of 2D-Toda hierarchy called Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik \cite{AL} using semidiscrete zero-curvature equations. In this paper we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization lead us to the semidiscrete zero-curvature equations for the non-abelian (or multicomponent) version of Ablowitz-Ladik equations \cite{GI}. In this way we extend the link between biorthogonal polynomials on the unit circle and Ablowitz-Ladik hierarchy to the matrix case.Comment: 23 pages, accepted on publication on J. Phys. A., electronic link: http://stacks.iop.org/1751-8121/42/36521

Deformations of Calogero-Moser Systems

Recent results are surveyed pertaining to the complete integrability of some novel n-particle models in dimension one. These models generalize the Calogero-Moser systems related to classical root systems. Quantization leads to difference operators instead of differential operators.Comment: 4 pages, Latex (version 2.09), talk given at NEEDS '93, Gallipoli, Ital