Role of Landau quantization on the neutron-drip transition in magnetar crusts

The role of a strong magnetic field on the neutron-drip transition in the crust of a magnetar is studied. The composition of the crust and the neutron-drip threshold are determined numerically for different magnetic field strengths using the experimental atomic mass measurements from the 2012 Atomic Mass Evaluation complemented with theoretical masses calculated from the Brussels-Montreal Hartree-Fock-Bogoliubov nuclear mass model HFB-24. The equilibrium nucleus at the neutron-drip point is found to be independent of the magnetic field strength. As demonstrated analytically, the neutron-drip density and pressure increase almost linearly with the magnetic field strength in the strongly quantizing regime for which electrons lie in the lowest Landau level. For weaker magnetic fields, the neutron-drip density exhibits typical quantum oscillations. In this case, the neutron-drip density can be either increased by about 14% or decreased by 25% depending on the magnetic field strength. These variations are shown to be almost universal, independently of the nuclear mass model employed. These results may have important implications for the physical interpretation of timing irregularities and quasiperiodic oscillations detected in soft gamma-ray repeaters and anomalous x-ray pulsars, as well as for the cooling of strongly magnetized neutron stars.

An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

On the coupling of Navier–Stokes and linearised Euler equations for aeroacoustic simulation

Aerodynamic generation of sound is governed by the Navier–Stokes equations while acoustic propagation in a non-uniform medium is effectively described by the linearised Euler equations. Different numerical schemes are required for the efficient solution of these two sets of equations, and therefore, coupling techniques become an essential issue. Two types of one-way coupling between the flow solver and the acoustic solver are discussed: (a) for aerodynamic sound generated at solid surfaces, and (b) in the free stream. Test results indicate how the coupling achieves the necessary accuracy so that Computational Fluid Dynamics codes can be used in aeroacoustic simulations.

An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

On a flexible elimination algorithm with applications to panel element equations

A flexible elimination algorithm is presented and is applied to the solution of dense systems of linear equations. Properties of the algorithm are exploited in relation to panel element methods for potential flow and subsonic compressible flow. Further properties in relation to distributed computing are also discussed.

Thickness-induced stabilization of ferroelectricity in SrRuO3/Ba0.5Sr0.5TiO3/Au thin film capacitors

Pulsed-laser deposition has been used to fabricate Au/Ba0.5Sr0.5TiO3/SrRuO3/MgO thin film capacitor structures. Crystallographic and microstructural investigations indicated that the Ba0.5Sr0.5TiO3 (BST) had grown epitaxially onto the SrRuO3 lower electrode, inducing in-plane compressive and out- of-plane tensile strain in the BST. The magnitude of strain developed increased systematically as film thickness decreased. At room temperature this composition of BST is paraelectric in bulk. However, polarization measurements suggested that strain had stabilized the ferroelectric state, and that the decrease in film thickness caused an increase in remanent polarization. An increase in the paraelectric-ferroelectric transition temperature upon a decrease in thickness was confirmed by dielectric measurements. Polarization loops were fitted to Landau-Ginzburg-Devonshire (LGD) polynomial expansion, from which a second order paraelectric-ferroelectric transition in the films was suggested at a thickness of similar to500 nm. Further, the LGD analysis showed that the observed changes in room temperature polarization were entirely consistent with strain coupling in the system. (C) 2002 American Institute of Physics.

An isothermal-isobaric Langevin thermostat for simulating nanoparticles under pressure: Application to Au clusters

We present a method for simulating clusters or, molecules subjected to an external pressure, which is exerted by a pressure-transmitting medium. It is based on the canoninical Langevin thermostat, but extended in such a way that the Brownian forces are allowed to operate only from the region exterior to the cluster. We show that the frictional force of the Langevin thermostat is linked to the pressure of the reservoir in a unique way, and that this property manifests itself when the particle it acts upon is not pointlike but has finite dimensions. By choosing appropriately the strength of the random forces and the friction coefficient, both temperature and pressure can be controlled independently. We illustrate the capabilities of this new method by calculating the compressibility of small gold clusters under pressure.

The practical implications of using standardized estimation equations in calculating the prevalence of chronic kidney disease

Background. Kidney Disease Outcomes Quality Initiative (KDOQI) chronic kidney disease (CKD) guidelines have focused on the utility of using the modified four-variable MDRD equation (now traceable by isotope dilution mass spectrometry IDMS) in calculating estimated glomerular filtration rates (eGFRs). This study assesses the practical implications of eGFR correction equations on the range of creatinine assays currently used in the UK and further investigates the effect of these equations on the calculated prevalence of CKD in one UK region Methods. Using simulation, a range of creatinine data (30–300 µmol/l) was generated for male and female patients aged 20–100 years. The maximum differences between the IDMS and MDRD equations for all 14 UK laboratory techniques for serum creatinine measurement were explored with an average of individual eGFRs calculated according to MDRD and IDMS 30 ml/min/1.73 m2. Observed data for 93,870 patients yielded a first MDRD eGFR 3 months later of which 47 093 (71%) continued to have an eGFR

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Sequentially continuous non-linear fundamental systems of solutions of affine equations in locally convex spaces

According to the Mickael's selection theorem any surjective continuous linear operator from one Fr\'echet space onto another has a continuous (not necessarily linear) right inverse. Using this theorem Herzog and Lemmert proved that if $E$ is a Fr\'echet space and $T:E\to E$ is a continuous linear operator such that the Cauchy problem $\dot x=Tx$, $x(0)=x_0$ is solvable in $[0,1]$ for any $x_0\in E$, then for any $f\in C([0,1],E)$, there exists a continuos map $S:[0,1]\times E\to E$, $(t,x)\mapsto S_tx$ such that for any $x_0\in E$, the function $x(t)=S_tx_0$ is a solution of the Cauchy problem $\dot x(t)=Tx(t)+f(t)$, $x(0)=x_0$ (they call $S$ a fundamental system of solutions of the equation $\dot x=Tx+f$). We prove the same theorem, replacing "continuous" by "sequentially continuous" for locally convex spaces from a class which contains strict inductive limits of Fr\'echet spaces and strong duals of Fr\'echet--Schwarz spaces and is closed with respect to finite products and sequentially closed subspaces. The key-point of the proof is an extension of the theorem on existence of a sequentially continuous right inverse of any surjective sequentially continuous linear operator to some class of non-metrizable locally convex spaces.

On the solvability of Hamilton's equations in Hilbert spaces

We construct a bounded function $H : l_2\times l_2 \to R$ with continuous Frechet derivative such that for any $q_0\in l_2$ the Cauchy problem $\dot p= - {\partial H\over\partial q}$, $\dot q={\partial H\over\partial p}$, $p(0) = 0$, q(0) = q_0$ has no solutions in any neighborhood of zero in R.