3,531 research outputs found
On averaged exponential integrators for semilinear wave equations with solutions of low-regularity
In this paper we introduce a class of second-order exponential schemes for the time integration of semilinear wave equations. They are constructed such that the established error bounds only depend on quantities obtained from a well-posedness result of a classical solution. To compensate missing regularity of the solution the proofs become considerably more involved compared to a standard error analysis. Key tools are appropriate filter functions as well as the integration-by-parts and summation-by-parts formulas. We include numerical examples to illustrate the advantage of the proposed methods
Moored acoustic travel time (ATT) current meters : evolution, performance, and future designs
New laboratory measurements and numeric model studies show
the present folded-path ATT current meters are stable and
sensitive, but are not well suited for mean flow observations
in surface gravity waves. Alternate designs which reduce
unwanted wake effects are proposed. ATT flowmeter history,
principles of acoustic flow sensors, mean flow near cylinders,
and the need for linear flow sensors are reviewed.Prepared for the Office of Naval Research under
Contract Number N00014-76-C-0197; NR083-400 to
the Woods Hole Oceanographic Institution
Multigrid method for nearly singular and slightly indefinite problems
This paper deals with nearly singular, possibly indefinite problems for which the usual multigrid solvers converge very slowly or even diverge. The main difficulty is related to some badly approximated smooth functions which correspond to eigenfunctions with nearly zero eigenvalues. A correction to the usual coarse-grid equations is derived, both in the correction scheme and in the full approximation scheme. The performance of the new algorithm using this correction is essentially as that of usual multigrid for definite problems
Metric preheating and limitations of linearized gravity
Recently it has become clear that the resonant amplification of quantum field
fluctuations at preheating must be accompanied by resonant amplification of
scalar metric perturbations, since the two are united by Einstein's equations.
Furthermore, this "metric preheating" enhances particle production and leads to
gravitational rescattering effects even at linear order. In multi-field models
with strong preheating (q \gg 1), metric perturbations are driven nonlinear,
with the strongest amplification typically on super-Hubble scales (k \to 0).
This amplification is causal, being due to the super- Hubble coherence of the
inflaton condensate, and is accompanied by resonant growth of entropy
perturbations. The amplification invalidates the use of the linearized Einstein
field equations, irrespective of the amount of fine-tuning of the initial
conditions. This has serious implications at all scales - from the large-angle
cosmic microwave background (CMB) anisotropies to primordial black holes. We
investigate the (q,k) parameter space in a two-field model, and introduce the
time to nonlinearity, t_{nl}, as the timescale for the breakdown of the
linearized Einstein equations. Backreaction effects are expected to shut down
the linear resonances, but cannot remove the existing amplification, which
threatens the viability of strong preheating when confronted with the CMB. We
discuss ways to escape the above conclusions, including secondary phases of
inflation and preheating solely to fermions. Finally we rank known classes of
inflation from strongest (chaotic and strongly coupled hybrid inflation) to
weakest (hidden sector, warm inflation) in terms of the distortion of the
primordial spectrum due to these resonances in preheating.Comment: 31 pages, 16 figures, Revtex. Final version. Nuclear Physics B (in
press
Branes And Supergroups
Extending previous work that involved D3-branes ending on a fivebrane with
, we consider a similar two-sided problem. This
construction, in case the fivebrane is of NS type, is associated to the
three-dimensional Chern-Simons theory of a supergroup U or OSp
rather than an ordinary Lie group as in the one-sided case. By -duality, we
deduce a dual magnetic description of the supergroup Chern-Simons theory; a
slightly different duality, in the orthosymplectic case, leads to a strong-weak
coupling duality between certain supergroup Chern-Simons theories on
; and a further -duality leads to a version of Khovanov
homology for supergroups. Some cases of these statements are known in the
literature. We analyze how these dualities act on line and surface operators.Comment: 143 page
Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics
We consider the Cauchy-problem for a class of scalar linear dispersive
equations with rapidly oscillating initial data. The problem of high-frequency
asymptotics of such models is reviewed,in particular we highlight the
difficulties in crossing caustics when using (time-dependent) WKB-methods.
Using Wigner measures we present an alternative approach to such asymptotic
problems. We first discuss the connection of the naive WKB solutions to
transport equations of Liouville type (with mono-kinetic solutions) in the
prebreaking regime. Further we show that the Wigner measure approach can be
used to analyze high-frequency limits in the post-breaking regime, in
comparison with the traditional Fourier integral operator method. Finally we
present some illustrating examples.Comment: 38 page
Operator’s whole body vibrations dependent of agrotechnical surface, speed of movement and seat upholstery
The paper presents the recorded vibrations that affect the operator’s body when an agricultural tractor moves along three types of agrotechnical surfaces, i.e. asphalt, an alfalfa field, and a field path, and when seven different tractor seat upholsteries are used. The research was performed in accordance with the HRN ISO 2631-1 and HRN ISO 2631-4 standards. The tractor used in the research was an IMT 560 and the duration of the measurement was 30 minutes, which was repeated three times for every tractor seat upholstery type. The research was exploitative. The measurements were performed using an MMF VM30 meter. The paper reveals a different level of vibrations in dependence with different surfaces and seat upholsteries. The fewest vibrations were produced by asphalt, and the best upholsteries are memory foam and sponge
Thermodynamics of the dissipative two-state system: a Bethe Ansatz study
The thermodynamics of the dissipative two-state system is calculated exactly
for all temperatures and level asymmetries for the case of Ohmic dissipation.
We exploit the equivalence of the two-state system to the anisotropic Kondo
model and extract the thermodynamics of the former by solving the thermodynamic
Bethe Ansatz equations of the latter. The universal scaling functions for the
specific heat and static dielectric susceptibility
are extracted for all dissipation strengths for
both symmetric and asymmetric two-state systems. The logarithmic corrections to
these quantities at high temperatures are found in the Kondo limit , whereas for we find the expected power law temperature
dependences with the powers being functions of the dissipative coupling
. The low temperature behaviour is always that of a Fermi liquid.Comment: 24 pages, 32 PS figures. Typos corrected, final versio
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