A High-Order Method for Stiff Boundary Value Problems with Turning Points

This paper describes some high-order collocation-like methods for the numerical solution of stiff boundary-value problems with turning points. The presentation concentrates on the implementation of these methods in conjunction with the implementation of the a priori mesh construction algorithm introduced by Kreiss, Nichols and Brown [SIAM J. Numer. Anal., 23 (1986), pp. 325–368] for such problems. Numerical examples are given showing the high accuracy which can be obtained in solving the boundary value problem for singularly perturbed ordinary differential equations with turning points

Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation

Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of the local environment (i.e., a thermal bath). In the case of classical systems, strong system-bath interaction has been successfully modelled by the Generalised Langevin Equation (GLE) formalism. Here we show that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014) can be extended to include some crucial aspects of the quantum fluctuations. In particular, the expected isotopic effect is observed along with the convergence of the quantum and classical transition rates in the strong coupling limit. Saturation of the transition rates at low temperature is also retrieved, in qualitative, yet not quantitative, agreement with the analytic predictions. The discrepancies in the tunnelling regime are due to an incorrect sampling close to the barrier top. The domain of applicability of the quasiclassical GLE is also discussed.Comment: 21 pages, 5 figures. Presented at the NESC16 conference: Advances in theory and simulation of non-equilibrium system

Applications of the Generalised Langevin Equation: towards a realistic description of the baths

The Generalised Langevin Equation (GLE) method, as developed in Ref. [Phys. Rev. B 89, 134303 (2014)], is used to calculate the dissipative dynamics of systems described at the atomic level. The GLE scheme goes beyond the commonly used bilinear coupling between the central system and the bath, and permits us to have a realistic description of both the dissipative central system and its surrounding bath. We show how to obtain the vibrational properties of a realistic bath and how to convey such properties into an extended Langevin dynamics by the use of the mapping of the bath vibrational properties onto a set of auxiliary variables. Our calculations for a model of a Lennard-Jones solid show that our GLE scheme provides a stable dynamics, with the dissipative/relaxation processes properly described. The total kinetic energy of the central system always thermalises toward the expected bath temperature, with appropriate fluctuation around the mean value. More importantly, we obtain a velocity distribution for the individual atoms in the central system which follows the expected canonical distribution at the corresponding temperature. This confirms that both our GLE scheme and our mapping procedure onto an extended Langevin dynamics provide the correct thermostat. We also examined the velocity autocorrelation functions and compare our results with more conventional Langevin dynamics.Comment: accepted for publication in PR

A Close and Supportive Interparental Bond During Pregnancy Predicts Greater Decline in Sexual Activity From Pregnancy to Postpartum: Applying an Evolutionary Perspective

A common topic for advice given to parents after childbirth – both from relationship experts and popular media – is how to “bounce back” to one’s pre-pregnancy sexuality, with warnings that postpartum declines in sexual frequency will take a serious toll on one’s relationship. However, these admonishments may not accurately reflect the ways in which the unique reproductive context of pregnancy and the postpartum transition alter associations between sexual frequency and relationship quality. Evolutionary perspectives on reproductive strategies would suggest that in the postpartum context, decreased sexual activity would help target parental investment in the current offspring (rather than creating new offspring); however, if the parental relationship is lacking in intimacy and support, continued sexual activity may help seal the cracks in the bond. We tested this theory in a longitudinal dyadic study of changes in relationship quality and sexual frequency from pregnancy to 6 months postpartum among 159 heterosexual couples. We found that across three different measures of relationship quality taken from interviews and behavioral observation of couple interactions, higher relationship quality (i.e., greater support, intimacy, and responsiveness) predicted greater decline in sexual frequency whereas sexual frequency remained relatively stable in lower quality relationships. These findings suggest that, during the postpartum transition, decreased sexual frequency may not be a reliable signal of poor relationship quality

Anisotropy study of multiferroicity in the pyroxene NaFeGe2_2O6_6

We present a study of the anisotropy of the dielectric, magnetic and magnetoelastic properties of the multiferroic clinopyroxene NaFeGe$_2$O$_6$. Pyroelectric currents, dielectric constants and magnetic susceptibilities as well as the thermal expansion and the magnetostriction were examined on large synthetic single crystals of NaFeGe$_2$O$_6$. The spontaneous electric polarization detected below $T_{\rm C}\simeq 11.6$ K in an antiferromagnetically ordered state ($T_{\rm N}\simeq 13$ K) is mainly lying within the $ac$ plane with a small component along $b$, indicating a triclinic symmetry of the multiferroic phase of NaFeGe$_2$O$_6$. The electric polarization can be strongly modified by applying magnetic fields along different directions. We derive detailed magnetic-field versus temperature phase diagrams and identify three multiferroic low-temperature phases, which are separated by a non-ferroelectric, antiferromagnetically ordered state from the paramagnetic high-temperature phase.Comment: 14 pages, 8 figures. (minor modifications and corrections of the text

Nonequilibrium processes from Generalised Langevin Equations: realistic nanoscale systems connected to two thermal baths

We extend the Generalised Langevin Equation (GLE) method [Phys. Rev. B 89, 134303 (2014)] to model a central classical region connected to two realistic thermal baths at two different temperatures. In such nonequilibrium conditions a heat flow is established, via the central system, in between the two baths. The GLE-2B (GLE two baths) scheme permits us to have a realistic description of both the dissipative central system and its surrounding baths. Following the original GLE approach, the extended Langevin dynamics scheme is modified to take into account two sets of auxiliary degrees of freedom corresponding to the mapping of the vibrational properties of each bath. These auxiliary variables are then used to solve the non-Markovian dissipative dynamics of the central region. The resulting algorithm is used to study a model of a short Al nanowire connected to two baths. The results of the simulations using the GLE-2B approach are compared to the results of other simulations that were carried out using standard thermostatting approaches (based on Markovian Langevin and Nose-Hoover thermostats). We concentrate on the steady state regime and study the establishment of a local temperature profile within the system. The conditions for obtaining a flat profile or a temperature gradient are examined in detail, in agreement with earlier studies. The results show that the GLE-2B approach is able to treat, within a single scheme, two widely different thermal transport regimes, i.e. ballistic systems, with no temperature gradient, and diffusive systems with a temperature gradient.Comment: present version accepted for publication in Phys. Rev. B (Apr 2016

Magnetoelectric properties of A2A_2[FeCl5_5(H2_2O)] with A=A = K, Rb, Cs

The compounds $A_2$[FeCl$_5$(H$_2$O)] with $A=$ K, Rb, Cs are identified as new linear magnetoelectric materials. We present a detailed investigation of their linear magnetoelectric properties by measurements of pyroelectric currents, dielectric constants and magnetization. The anisotropy of the linear magnetoelectric effect of the K-based and Rb-based compound is consistent with the magnetic point group $m'm'm'$, already reported in literature. A symmetry analysis of the magnetoelectric effect of the Cs-based compound allows to determine the magnetic point group $mmm'$ and to develop a model for its magnetic structure. In addition, magnetic-field versus temperature phase diagrams are derived and compared to the closely related multiferroic (NH$_4$)$_2$[FeCl$_5$(H$_2$O)].Comment: 17 pages, 10 figures (updated to the weakly revised version that has been accepted for publication

Purification of Curcumin from Ternary Extract-Similar Mixtures of Curcuminoids in a Single Crystallization Step

Crystallization-based separation of curcumin from ternary mixtures of curcuminoids having compositions comparable to commercial extracts was studied experimentally. Based on solubility and supersolubility data of both, pure curcumin and curcumin in presence of the two major impurities demethoxycurcumin (DMC) and bis(demethoxy)curcumin (BDMC), seeded cooling crystallization procedures were derived using acetone, acetonitrile and 50/50 (wt/wt) mixtures of acetone/2-propanol and acetone/acetonitrile as solvents. Starting from initial curcumin contents of 67–75% in the curcuminoid mixtures single step crystallization processes provided crystalline curcumin free of BDMC at residual DMC contents of 0.6–9.9%. Curcumin at highest purity of 99.4% was obtained from a 50/50 (wt/wt) acetone/2-propanol solution in a single crystallization step. It is demonstrated that the total product yield can be significantly enhanced via addition of water, 2-propanol and acetonitrile as anti-solvents at the end of a cooling crystallization process