5,409 research outputs found
Implicit and Implicit-Explicit Strong Stability Preserving Runge-Kutta Methods with High Linear Order
When evolving in time the solution of a hyperbolic partial differential
equation, it is often desirable to use high order strong stability preserving
(SSP) time discretizations. These time discretizations preserve the
monotonicity properties satisfied by the spatial discretization when coupled
with the first order forward Euler, under a certain time-step restriction.
While the allowable time-step depends on both the spatial and temporal
discretizations, the contribution of the temporal discretization can be
isolated by taking the ratio of the allowable time-step of the high order
method to the forward Euler time-step. This ratio is called the strong
stability coefficient. The search for high order strong stability time-stepping
methods with high order and large allowable time-step had been an active area
of research. It is known that implicit SSP Runge-Kutta methods exist only up to
sixth order. However, if we restrict ourselves to solving only linear
autonomous problems, the order conditions simplify and we can find implicit SSP
Runge-Kutta methods of any linear order. In the current work we aim to find
very high linear order implicit SSP Runge-Kutta methods that are optimal in
terms of allowable time-step. Next, we formulate an optimization problem for
implicit-explicit (IMEX) SSP Runge-Kutta methods and find implicit methods with
large linear stability regions that pair with known explicit SSP Runge-Kutta
methods of orders plin=3,4,6 as well as optimized IMEX SSP Runge-Kutta pairs
that have high linear order and nonlinear orders p=2,3,4. These methods are
then tested on sample problems to verify order of convergence and to
demonstrate the sharpness of the SSP coefficient and the typical behavior of
these methods on test problems
PO and PN in the wind of the oxygen-rich AGB star IK Tau
Phosphorus-bearing compounds have only been studied in the circumstellar
environments (CSEs) of the asymptotic giant branch (AGB) star IRC +10216 and
the protoplanetary nebula CRL 2688, both C-rich objects, and the O-rich red
supergiant VY CMa. The current chemical models cannot reproduce the high
abundances of PO and PN derived from observations of VY CMa. No observations
have been reported of phosphorus in the CSEs of O-rich AGB stars. We aim to set
observational constraints on the phosphorous chemistry in the CSEs of O-rich
AGB stars, by focussing on the Mira-type variable star IK Tau. Using the IRAM
30m telescope and the Submillimeter Array (SMA), we observed four rotational
transitions of PN (J=2-1,3-2,6-5,7-6) and four of PO
(J=5/2-3/2,7/2-5/2,13/2-11/2,15/2-13/2). The IRAM 30m observations were
dedicated line observations, while the SMA data come from an unbiased spectral
survey in the frequency range 279-355 GHz.
We present the first detections of PN and PO in an O-rich AGB star and
estimate abundances X(PN/H2) of about 3x10^-7 and X(PO/H2) in the range
0.5-6.0x10^-7. This is several orders of magnitude higher than what is found
for the C-rich AGB star IRC +10216. The diameter (<=0.7") of the PN and PO
emission distributions measured in the interferometric data corresponds to a
maximum radial extent of about 40 stellar radii. The abundances and the spatial
occurrence of the molecules are in very good agreement with the results
reported for VY CMa. We did not detect PS or PH3 in the survey. We suggest that
PN and PO are the main carriers of phosphorus in the gas phase, with abundances
possibly up to several 10^-7. The current chemical models cannot account for
this, underlining the strong need for updated chemical models that include
phosphorous compounds.Comment: Accepted for publication in Astronomy & Astrophysics, 10 pages, 8
figure
Precise Determination of |V{us}| from Lattice Calculations of Pseudoscalar Decay Constants
Combining the ratio of experimental kaon and pion decay widths, Gamma(K to mu
antineutrino{mu} (gamma)) / Gamma(pi to mu \antineutrino (gamma)), with a
recent lattice gauge theory calculation of f{K}/f{pi} provides a precise value
for the CKM quark mixing matrix element |V{us}|=0.2236(30) or if 3 generation
unitarity is assumed |V{us}|=0.2238(30). Comparison with other determinations
of that fundamental parameter, implications, and an outlook for future
improvements are given
Pressure and non-linear susceptibilities in QCD at finite chemical potentials
When the free energy density of QCD is expanded in a series in the chemical
potential, mu, the Taylor coefficients are the non-linear quark number
susceptibilities. We show that these depend on the prescription for putting
chemical potential on the lattice, making all extrapolations in chemical
potential prescription dependent at finite lattice spacing. To put bounds on
the prescription dependence, we investigate the magnitude of the non-linear
susceptibilities over a range of temperature, T, in QCD with two degenerate
flavours of light dynamical quarks at lattice spacing 1/4T. The prescription
dependence is removed in quenched QCD through a continuum extrapolation, and
the dependence of the pressure, P, on mu is obtained.Comment: 15 pages, 2 figures. Data on chi_uuuu added, discussion enhance
Wigner formula of rotation matrices and quantum walks
Quantization of a random-walk model is performed by giving a qudit (a
multi-component wave function) to a walker at site and by introducing a quantum
coin, which is a matrix representation of a unitary transformation. In quantum
walks, the qudit of walker is mixed according to the quantum coin at each time
step, when the walker hops to other sites. As special cases of the quantum
walks driven by high-dimensional quantum coins generally studied by Brun,
Carteret, and Ambainis, we study the models obtained by choosing rotation as
the unitary transformation, whose matrix representations determine quantum
coins. We show that Wigner's -dimensional unitary representations of
rotations with half-integers 's are useful to analyze the probability laws
of quantum walks. For any value of half-integer , convergence of all moments
of walker's pseudovelocity in the long-time limit is proved. It is generally
shown for the present models that, if is even, the probability measure
of limit distribution is given by a superposition of terms of scaled
Konno's density functions, and if is odd, it is a superposition of
terms of scaled Konno's density functions and a Dirac's delta function at the
origin. For the two-, three-, and four-component models, the probability
densities of limit distributions are explicitly calculated and their dependence
on the parameters of quantum coins and on the initial qudit of walker is
completely determined. Comparison with computer simulation results is also
shown.Comment: v2: REVTeX4, 15 pages, 4 figure
Continuous-time quantum walk on integer lattices and homogeneous trees
This paper is concerned with the continuous-time quantum walk on Z, Z^d, and
infinite homogeneous trees. By using the generating function method, we compute
the limit of the average probability distribution for the general isotropic
walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous
trees. In addition, we compute the asymptotic approximation for the probability
of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page
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