25,183 research outputs found
Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows
In this work, we consider the discretization of nonlinear hyperbolic systems
in nonconservative form with the high-order discontinuous Galerkin spectral
element method (DGSEM) based on collocation of quadrature and interpolation
points (Kopriva and Gassner, J. Sci. Comput., 44 (2010), pp.136--155; Carpenter
et al., SIAM J. Sci. Comput., 36 (2014), pp.~B835-B867). We present a general
framework for the design of such schemes that satisfy a semi-discrete entropy
inequality for a given convex entropy function at any approximation order. The
framework is closely related to the one introduced for conservation laws by
Chen and Shu (J. Comput. Phys., 345 (2017), pp.~427--461) and relies on the
modification of the integral over discretization elements where we replace the
physical fluxes by entropy conservative numerical fluxes from Castro et al.
(SIAM J. Numer. Anal., 51 (2013), pp.~1371--1391), while entropy stable
numerical fluxes are used at element interfaces. Time discretization is
performed with strong-stability preserving Runge-Kutta schemes. We use this
framework for the discretization of two systems in one space-dimension: a
system with a nonconservative product associated to a
linearly-degenerate field for which the DGSEM fails to capture the physically
relevant solution, and the isentropic Baer-Nunziato model. For the latter, we
derive conditions on the numerical parameters of the discrete scheme to further
keep positivity of the partial densities and a maximum principle on the void
fractions. Numerical experiments support the conclusions of the present
analysis and highlight stability and robustness of the present schemes
The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
We use the effective field theory (EFT) framework to calculate the tail
effect in gravitational radiation reaction, which enters at 4PN order in the
dynamics of a binary system. The computation entails a subtle interplay between
the near (or potential) and far (or radiation) zones. In particular, we find
that the tail contribution to the effective action is non-local in time, and
features both a dissipative and a `conservative' term. The latter includes a
logarithmic ultraviolet (UV) divergence, which we show cancels against an
infrared (IR) singularity found in the (conservative) near zone. The origin of
this behavior in the long-distance EFT is due to the point-particle limit
-shrinking the binary to a point- which transforms a would-be infrared
singularity into an ultraviolet divergence. This is a common occurrence in an
EFT approach, which furthermore allows us to use renormalization group (RG)
techniques to resum the resulting logarithmic contributions. We then derive the
RG evolution for the binding potential and total mass/energy, and find
agreement with the results obtained imposing the conservation of the (pseudo)
stress-energy tensor in the radiation theory. While the calculation of the
leading tail contribution to the effective action involves only one diagram,
five are needed for the one-point function. This suggests logarithmic
corrections may be easier to incorporate in this fashion. We conclude with a
few remarks on the nature of these IR/UV singularities, the (lack of)
ambiguities recently discussed in the literature, and the completeness of the
analytic Post-Newtonian framework.Comment: 24 pages. 3 figures. v2: Extended discussion on the nature of IR/UV
singularities. Published versio
The Fate of SUSY Flat Directions and their Role in Reheating
We consider the role of supersymmetric flat directions in reheating the
Universe after inflation. One or more flat directions can develop large vevs
during inflation, which can potentially affect reheating by slowing down
scattering processes among inflaton decay products or by coming to dominate the
energy density of the Universe. Both effects occur only if flat directions are
sufficiently long-lived. The computation of their perturbative decay rate, and
a simple estimate of their nonperturbative decay have led to the conclusion
that this is indeed the case. In contrast, we show that flat directions can
decay quickly through nonperturbative channels in realistic models. The mass
matrix for MSSM excitations around flat directions has nondiagonal entries,
which vary with the phase of the (complex) flat directions. The quasi-periodic
motion of the flat directions results in a strong parametric resonance, leading
to the rapid depletion of the flat direction within its first few rotations.
This may preclude any significant role for the flat directions in reheating the
Universe after inflation in models in which the inflaton decays perturbatively.Comment: 30 pages, 6 .ps figures. Final published versio
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A linear algebraic method for pricing temporary life annuities and insurance policies
We recast the valuation of annuities and life insurance contracts under mortality and interest rates, both of which are stochastic, as a problem of solving a system of linear equations with random perturbations. A sequence of uniform approximations is developed which allows for fast and accurate computation of expected values. Our reformulation of the valuation problem provides a general framework which can be employed to find insurance premiums and annuity values covering a wide class of stochastic models for mortality and interest rate processes. The proposed approach provides a computationally efficient alternative to Monte Carlo based valuation in pricing mortality-linked contingent claims
High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows
In this article we present the first better than second order accurate
unstructured Lagrangian-type one-step WENO finite volume scheme for the
solution of hyperbolic partial differential equations with non-conservative
products. The method achieves high order of accuracy in space together with
essentially non-oscillatory behavior using a nonlinear WENO reconstruction
operator on unstructured triangular meshes. High order accuracy in time is
obtained via a local Lagrangian space-time Galerkin predictor method that
evolves the spatial reconstruction polynomials in time within each element. The
final one-step finite volume scheme is derived by integration over a moving
space-time control volume, where the non-conservative products are treated by a
path-conservative approach that defines the jump terms on the element
boundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian
(ALE) method, where the mesh velocity can be chosen independently of the fluid
velocity.
The new scheme is applied to the full seven-equation Baer-Nunziato model of
compressible multi-phase flows in two space dimensions. The use of a Lagrangian
approach allows an excellent resolution of the solid contact and the resolution
of jumps in the volume fraction. The high order of accuracy of the scheme in
space and time is confirmed via a numerical convergence study. Finally, the
proposed method is also applied to a reduced version of the compressible
Baer-Nunziato model for the simulation of free surface water waves in moving
domains. In particular, the phenomenon of sloshing is studied in a moving water
tank and comparisons with experimental data are provided
B-tests: Low Variance Kernel Two-Sample Tests
A family of maximum mean discrepancy (MMD) kernel two-sample tests is
introduced. Members of the test family are called Block-tests or B-tests, since
the test statistic is an average over MMDs computed on subsets of the samples.
The choice of block size allows control over the tradeoff between test power
and computation time. In this respect, the -test family combines favorable
properties of previously proposed MMD two-sample tests: B-tests are more
powerful than a linear time test where blocks are just pairs of samples, yet
they are more computationally efficient than a quadratic time test where a
single large block incorporating all the samples is used to compute a
U-statistic. A further important advantage of the B-tests is their
asymptotically Normal null distribution: this is by contrast with the
U-statistic, which is degenerate under the null hypothesis, and for which
estimates of the null distribution are computationally demanding. Recent
results on kernel selection for hypothesis testing transfer seamlessly to the
B-tests, yielding a means to optimize test power via kernel choice.Comment: Neural Information Processing Systems (2013
Delta M_K and epsilon_K in SUSY at the Next-to-Leading order
We perform a Next-to-Leading order analysis of Delta S=2 processes beyond the
Standard Model. Combining the recently computed NLO anomalous dimensions and
the B parameters of the most general Delta S=2 effective Hamiltonian, we give
an analytic formula for Delta M_K and epsilon_K in terms of the Wilson
coefficients at the high energy scale. This expression can be used for any
extension of the Standard Model with new heavy particles. Using this result, we
consider gluino-mediated contributions to Delta S=2 transitions in general SUSY
models and provide an improved analysis of the constraints on off-diagonal mass
terms between the first two generations of down-type squarks. Finally, we
improve the constraints on R-violating couplings from Delta M_K and epsilon_K.Comment: 20 pages, 1 figure, uses JHEP.cls; the magic numbers in eq. (2.7),
previously given in the basis (13) of hep-ph/9711402, are now given in the
basis (2.3) of this work. All numerical results are unchange
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