Symmetry-preserving discrete schemes for some heat transfer equations

Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant difference equations and meshes, where the original continuous symmetries are preserved in discrete models. Conservation of symmetries in difference modeling helps to retain qualitative properties of the differential equations in their difference counterparts.Comment: 21 pages, 4 ps figure

Predictors of mortality in primary antiphospholipid syndrome. A single-centre cohort study.

The vascular mortality of antiphospholipid syndrome (APS) ranges from 1.4 % to 5.5 %, but its predictors are poorly known. It was the study objective to evaluate the impact of baseline lupus anticoagulant assays, IgG anticardiolipin (aCL), plasma fibrinogen (FNG) and von Willebrand factor (VWF), platelets (PLT) and of genetic polymorphisms of methylenetetrahydrofolate reductase C677T, of prothrombin G20210A and of paraoxonase-1 Q192R on mortality in primary APS (PAPS). Cohort study on 77 thrombotic PAPS and 33 asymptomatic carriers of aPL (PCaPL) seen from 1989 to 2015 and persistently positive for aPL as per annual review. At baseline all participants were tested twice for the ratios of kaolin clotting time (KCTr), activated partial thromboplastin time (aPTTr), dilute Russell viper venom time (DRVVTr), IgG aCL, FNG, VWF and once for PLT. All thrombotic PAPS were on warfarin with regular INR monitoring. During follow-up 11 PAPS deceased (D-PAPS) of recurrent thrombosis despite adequate anticoagulation yielding an overall vascular mortality of 10 %. D-PAPS had the strongest baseline aPTTr and DRVVTr and the highest mean baseline IgG aCL, FNG, VWF and PLT. Cox proportional hazards model identified baseline DRVVTr and FNG as main predictors of mortality with adjusted hazard ratios of 5.75 (95 % confidence interval [CI]: 1.5, 22.4) and of 1.03 (95 %CI: 1.01, 1.04), respectively. In conclusion, plasma DRVVTr and FNG are strong predictors of vascular mortality in PAPS; while FNG lowering agents exist further research should be directed at therapeutic strategies able to dampen aPL production

Group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations

A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new interesting nonlinear invariant models which have non-trivial invariance algebras are obtained. Furthermore, the possible additional equivalence transformations between equations from the class under consideration are investigated. Exact solutions of special forms of these equations are also constructed via classical Lie method and generalized conditional transformations. Local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations.Comment: 23 page

Conservation laws of semidiscrete canonical Hamiltonian equations

There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian equations. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for the semidiscretized nonlinear wave equation and Schrodinger equation.Comment: 19 pages, 2 table

First Penning-trap mass measurement in the millisecond half-life range: the exotic halo nucleus 11Li

In this letter, we report a new mass for $^{11}$Li using the trapping experiment TITAN at TRIUMF's ISAC facility. This is by far the shortest-lived nuclide, $t_{1/2} = 8.8 \rm{ms}$, for which a mass measurement has ever been performed with a Penning trap. Combined with our mass measurements of $^{8,9}$Li we derive a new two-neutron separation energy of 369.15(65) keV: a factor of seven more precise than the best previous value. This new value is a critical ingredient for the determination of the halo charge radius from isotope-shift measurements. We also report results from state-of-the-art atomic-physics calculations using the new mass and extract a new charge radius for $^{11}$Li. This result is a remarkable confluence of nuclear and atomic physics.Comment: Formatted for submission to PR

Isotropic Loop Quantum Cosmology

Isotropic models in loop quantum cosmology allow explicit calculations, thanks largely to a completely known volume spectrum, which is exploited in order to write down the evolution equation in a discrete internal time. Because of genuinely quantum geometrical effects the classical singularity is absent in those models in the sense that the evolution does not break down there, contrary to the classical situation where space-time is inextendible. This effect is generic and does not depend on matter violating energy conditions, but it does depend on the factor ordering of the Hamiltonian constraint. Furthermore, it is shown that loop quantum cosmology reproduces standard quantum cosmology and hence (e.g., via WKB approximation) to classical behavior in the large volume regime where the discreteness of space is insignificant. Finally, an explicit solution to the Euclidean vacuum constraint is discussed which is the unique solution with semiclassical behavior representing quantum Euclidean space.Comment: 30 page

New results on group classification of nonlinear diffusion-convection equations

Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient $(1+1)$-dimensional nonlinear diffusion-convection equations of the general form $f(x)u_t=(D(u)u_x)_x+K(u)u_x.$ We obtain new interesting cases of such equations with the density $f$ localized in space, which have large invariance algebra. Exact solutions of these equations are constructed. We also consider the problem of investigation of the possible local trasformations for an arbitrary pair of equations from the class under consideration, i.e. of describing all the possible partial equivalence transformations in this class.Comment: LaTeX2e, 19 page

From Lagrangian to Quantum Mechanics with Symmetries

We present an old and regretfully forgotten method by Jacobi which allows one to find many Lagrangians of simple classical models and also of nonconservative systems. We underline that the knowledge of Lie symmetries generates Jacobi last multipliers and each of the latter yields a Lagrangian. Then it is shown that Noether's theorem can identify among those Lagrangians the physical Lagrangian(s) that will successfully lead to quantization. The preservation of the Noether symmetries as Lie symmetries of the corresponding Schr\"odinger equation is the key that takes classical mechanics into quantum mechanics. Some examples are presented.Comment: To appear in: Proceedings of Symmetries in Science XV, Journal of Physics: Conference Series, (2012

Lie point symmetries of difference equations and lattices

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations