arXiv subjects

David Cohen

Publications and source records attributed to David Cohen.

48 records · Page 3Linked to original sources

arXiv2015

Multi-symplectic discretisation of wave map equations

We present a new multi-symplectic formulation of constrained Hamiltonian partial differential equations, and we study the associated local conservation laws. A multi-symplectic discretisation based on this new formulation is exemplified by means of the Euler box scheme. When applied to the wave map equation, this numerical scheme is explicit, preserves the constraint and can be seen as a generalisation of the Shake algorithm for constrained mechanical systems. Furthermore, numerical experiments show excellent conservation properties of the numerical solutions.

math.NA↗

arXiv2015

Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise

A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal approximation. This explicit time integrator allows for mean-square error bounds independent of the space discretisation and thus do not suffer from a step size restriction as in the often used Störmer-Verlet-leap-frog scheme. Furthermore, it satisfies an almost trace formula (i.e., a linear drift of the expected value of the energy of the problem). Numerical experiments are presented and confirm the theoretical results.

math.NA↗

arXiv2015

Confirming HD 23478 as a new magnetic B star hosting an H$α$-bright centrifugal magnetosphere

In this paper we report 23 magnetic field measurements of the B3IV star HD 23478: 12 obtained from high resolution Stokes $V$ spectra using the ESPaDOnS (CFHT) and Narval (TBL) spectropolarimeters, and 11 from medium resolution Stokes $V$ spectra obtained with the DimaPol spectropolarimeter (DAO). HD 23478 was one of two rapidly rotating stars identified as potential "centrifugal magnetosphere" hosts based on IR observations from the Apache Point Observatory Galactic Evolution Experiment survey. We derive basic physical properties of this star including its mass ($M=6.1^{+0.8}_{-0.7}\,M_\odot$), effective temperature ($T_{\rm eff}=20\pm2\,$kK), radius ($R=2.7^{+1.6}_{-0.9}\,R_\odot$), and age ($τ_{\rm age}=3^{+37}_{-1}\,$Myr). We repeatedly detect weakly-variable Zeeman signatures in metal, He and H lines in all our observations corresponding to a longitudinal magnetic field of $\langle B_z\rangle\approx-2.0\,$kG. The rotational period is inferred from Hipparcos photometry ($P_{\rm rot}=1.0498(4)\,$d). Under the assumption of the Oblique Rotator Model, our obsevations yield a surface dipole magnetic field of strength $B_d\geq9.5\,$kG that is approximately aligned with the stellar rotation axis. We confirm the presence of strong and broad H$α$ emission and gauge the volume of this star's centrifugal magnetosphere to be consistent with those of other H$α$ emitting centrifugal magnetosphere stars based on the large inferred Alfvén to Kepler radius ratio.

astro-ph.SR↗

arXiv2015

Dilations of matricies

We explore aspects of dilation theory in the finite dimensional case and show that for a commuting $n$-tuple of operators $T=(T_1,...,T_n) $ acting on some finite dimensional Hilbert space $H$ and a compact set $X\subset \mathbb{C}^n$ the following are equivalent: 1. $T$ has a normal $ X$-dilation. 2. For any $m\in \mathbb{N}$ there exists some finite dimensional Hilbert space $K$ containing $H$ and a tuple of commuting normal operators $N=(N_1,...,N_n)$ acting on $K$ such that $$ q(T)=P_Hq(N)|_H$$ for all polynomials $q$ of degree at most $m$ and such that the joint spectrum of $N$ is contained in $X$ (where $P_H$ is the projection from $K$ to $H$).

math.FA↗

arXiv2014

Conservative methods for stochastic differential equations with a conserved quantity

This paper proposes a novel conservative method for numerical computation of general stochastic differential equations in the Stratonovich sense with a conserved quantity. We show that the mean-square order of the method is $1$ if noises are commutative and that the weak order is also $1$. Since the proposed method may need the computation of a deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct conservative composition methods with similar orders as the above method. Finally, numerical experiments are presented to support our theoretical results.

math.NA↗

arXiv2014

Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions

For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time scales that cover arbitrary negative powers of the step size. This requires non-resonance conditions between the step size and the frequencies, but in contrast to previous results the results do not require any non-resonance conditions among the frequencies. The proof uses modulated Fourier expansions with appropriately modified frequencies.

math.NA↗

arXiv2014

Iterative Plan Construction for the Workflow Satisfiability Problem

The \emph{Workflow Satisfiability Problem (WSP)} is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there exists a \emph{plan} -- an assignment of tasks to authorized users -- such that all constraints are satisfied. Several bespoke algorithms have been constructed for solving the WSP, optimised to deal with constraints (business rules) of particular types. It is natural to see the WSP as a subclass of the {\em Constraint Satisfaction Problem (CSP)} in which the variables are tasks and the domain is the set of users. What makes the WSP distinctive as a CSP is that we can assume that the number of tasks is very small compared to the number of users. This is in sharp contrast with traditional CSP models where the domain is small and the number of variables is very large. As such, it is appropriate to ask for which constraint languages the WSP is fixed-parameter tractable (FPT), parameterized by the number of tasks. We have identified a new FPT constraint language, user-independent constraint, that includes many of the constraints of interest in business processing systems. We are also able to prove that the union of FPT languages remains FPT if they satisfy a simple compatibility condition. In this paper we present our generic algorithm, in which plans are grouped into equivalence classes, each class being associated with a \emph{pattern}. We demonstrate that our generic algorithm has running time $O^*(2^{k\log k})$, where $k$ is the number of tasks, for the language of user-independent constraints. We also show that there is no algorithm of running time $O^*(2^{o(k\log k)})$ for user-independent constraints unless the Exponential Time Hypothesis fails.

cs.DS↗

arXiv2014

X-rays from Magnetically Confined Wind Shocks: Effect of Cooling-Regulated Shock Retreat

We use 2D MHD simulations to examine the effects of radiative cooling and inverse Compton (IC) cooling on X-ray emission from magnetically confined wind shocks (MCWS) in magnetic massive stars with radiatively driven stellar winds. For the standard dependence of mass loss rate on luminosity $\Mdot \sim L^{1.7} $, the scaling of IC cooling with $L$ and radiative cooling with $\Mdot$ means that IC cooling become formally more important for lower luminosity stars. However, because the sense of the trends is similar, we find the overall effect of including IC cooling is quite modest. More significantly, for stars with high enough mass loss to keep the shocks radiative, the MHD simulations indicate a linear scaling of X-ray luminosity with mass loss rate; but for lower luminosity stars with weak winds, X-ray emission is reduced and softened by a {\em shock retreat} resulting from the larger post-shock cooling length, which within the fixed length of a closed magnetic loop forces the shock back to lower pre-shock wind speeds. A semi-analytic scaling analysis that accounts both for the wind magnetic confinement and this shock retreat yields X-ray luminosities that have a similar scaling trend, but a factor few higher values, compared to time-averages computed from the MHD simulations. The simulation and scaling results here thus provide a good basis for interpreting available X-ray observations from the growing list of massive stars with confirmed large-scale magnetic fields.

astro-ph.SR↗

arXiv2011

The Physical Basis of the Lx-Lbol Empirical Law for O-star X-rays

X-ray satellites since Einstein have empirically established that the X-ray luminosity from single O-stars scales linearly with bolometric luminosity, Lx ~ 10^-7 Lbol. But straightforward forms of the most favored model, in which X-rays arise from instability-generated shocks embedded in the stellar wind, predict a steeper scaling, either with mass loss rate Lx ~ Mdot ~ Lbol^1.7 if the shocks are radiative, or with Lx ~ Lx ~ Mdot^2 ~ Lbol^3.4 if they are adiabatic. We present here a generalized formalism that bridges these radiative vs. adiabatic limits in terms of the ratio of the shock cooling length to the local radius. Noting that the thin-shell instability of radiative shocks should lead to extensive mixing of hot and cool material, we then propose that the associated softening and weakening of the X-ray emission can be parametrized by the cooling length ratio raised to a power m, the "mixing exponent." For physically reasonable values m ~= 0.4, this leads to an X-ray luminosity Lx ~ Mdot^0.6 ~ Lbol that matches the empirical scaling. We conclude by noting that such thin-shell mixing may also be important for X-rays from colliding wind binaries, and that future numerical simulation studies will be needed to test this thin-shell mixing ansatz for X-ray emission.

astro-ph.SR↗

arXiv2011

Convergent Numerical Schemes for the Compressible Hyperelastic Rod Wave Equation

We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this equation. By using a time splitting integrator which preserves the invariants of the problem, we can also show that the scheme preserves the positivity of the energy density.

math.NA↗

arXiv2001

Mass Loss and Magnetospheres: X-rays from Hot Stars and Young Stellar Objects

High-resolution X-ray spectra of high-mass stars and low-mass T-Tauri stars obtained during the first year of the Chandra mission are providing important clues about the mechanisms which produce X-rays on very young stars. For zeta Puppis (O4 If) and zeta Ori (O9.5 I), the broad, blue-shifted line profiles, line ratios, and derived temperature distribution suggest that the X-rays are produced throughout the wind via instability-driven wind shocks. For some less luminous OB stars, like theta^1 Ori C (O7 V) and tau Sco (B0 V), the line profiles are symmetric and narrower. The presence of time-variable emission and very high-temperature lines in theta^1 Ori C and tau Sco suggest that magnetically confined wind shocks may be at work. The grating spectrum of the classical T-Tauri star TW Hya is remarkable because the forbidden-line emission of He-like Ne IX and O VII is very weak, implying that the X-ray emitting region is very dense, n = 6E+12 cgs, or that the X-rays are produced very close to the ultraviolet hotspot at the base of an accretion funnel. ACIS light curves and spectra of flares and low-mass and high-mass young stellar objects in Orion and rho Ophiuchus further suggest that extreme magnetic activity is a general property of many very young stars.

astro-ph↗

arXiv1998

Role of Interfaces in the Proximity Effect in Anisotropic Superconductors

We report measurements of the critical temperature of YBCO-Co doped YBCO Superconductor-Normal bilayer films. Depending on the morphology of the S-N interface, the coupling between S and N layers can be turned on to depress the critical temperature of S by tens of degrees, or turned down so the layers appear almost totally decoupled. This novel effect can be explained by the mechanism of quasiparticle transmission into an anisotropic superconductor.

cond-mat.supr-con↗