Effective field theory approach to Casimir interactions on soft matter surfaces

We utilize an effective field theory approach to calculate Casimir interactions between objects bound to thermally fluctuating fluid surfaces or interfaces. This approach circumvents the complicated constraints imposed by such objects on the functional integration measure by reverting to a point particle representation. To capture the finite size effects, we perturb the Hamiltonian by DH that encapsulates the particles' response to external fields. DH is systematically expanded in a series of terms, each of which scales homogeneously in the two power counting parameters: \lambda \equiv R/r, the ratio of the typical object size (R) to the typical distance between them (r), and delta=kB T/k, where k is the modulus characterizing the surface energy. The coefficients of the terms in DH correspond to generalized polarizabilities and thus the formalism applies to rigid as well as deformable objects. Singularities induced by the point particle description can be dealt with using standard renormalization techniques. We first illustrate and verify our approach by re-deriving known pair forces between circular objects bound to films or membranes. To demonstrate its efficiency and versatility, we then derive a number of new results: The triplet interactions present in these systems, a higher order correction to the film interaction, and general scaling laws for the leading order interaction valid for objects of arbitrary shape and internal flexibility.Comment: 4 pages, 1 figur

Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The covariance of the construction with respect to the change of the constraint basis is provided by introducing a connection in the ``constraint bundle'', which becomes a key ingredient of the conversion procedure for the non-scalar constraints. Unlike in the case of scalar second-class constraints, no Abelian conversion is possible in general. Within the BRST framework, a systematic procedure is worked out for converting non-scalar second-class constraints into non-Abelian first-class ones. The BRST-extended system is quantized, yielding an explicitly covariant quantization of the original system. An important feature of second-class systems with non-scalar constraints is that the appropriately generalized Dirac bracket satisfies the Jacobi identity only on the constraint surface. At the quantum level, this results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page

Design of a Multiply Nested Primitive Equation Ocean Model

A new multiply nested primitive equation ocean model is presented. The model employs a two-way interactive nesting technique successfully applied for many years in the Geophysical Fluid Dynamics Laboratory–NOAA hurricane prediction model. The formulation of the mesh nesting algorithm allows flexibility in deciding the number of meshes and the ratio of grid resolutions between adjacent meshes. Other advanced features include realistic coastline geometry and spatially variable grid spacing. The results of various idealized experiments indicate good performance of the nesting technique. The most important feature of the model is the ability to combine large-scale and regional-scale predictions. The model is tested as a general circulation model (GCM) in a 3-yr spinup experiment of the large-scale circulation in the tropical Pacific Ocean. It demonstrates skill comparable to that of other recently developed GCMs. The resulting large-scale fields are then used in the nested configuration as initial conditions for simulations of the ocean response to a westerly wind burst and a tropical cyclone. Significant improvements over a coarse, single-mesh model have been achieved in resolving finescale features of the wind-induced current and temperature fields. These results highlight the importance of model resolution for realistic simulations of mesoscale ocean variability

A Numerical Investigation of the Local Ocean Response to Westerly Wind Burst Forcing in the Western Equatorial Pacific

Numerical simulations of the local equatorial ocean response to idealized westerly wind burst (WWB) forcing are described. In particular, the authors examine the development and evolution of the subsurface westward jet (SSWJ) that has been observed to accompany these wind events. This westward current is interpreted as the signature of equatorial waves that accompany the downwelling and upwelling that occurs along the edges of the wind forcing region. Some important features of the SSWJ include maximum intensity toward the eastern edge of the forcing region, a time lag between the wind forcing and peak SSWJ development, and an eastward spreading of the SSWJ with time. The effect of wind burst zonal profile, magnitude, duration, and fetch on the SSWJ are explored. The response of an initially resting ocean to WWB forcing is compared with that for model oceans that are spun up with annual-mean surface fluxes and monthly varying fluxes. It is demonstrated that the gross features of the response for the spun up simulations can be well approximated by adding the background zonal current structure prior to the introduction of the wind burst to the initially resting ocean current response to the WWB. This result suggests that the zonal current structure that is present prior to the commencement of WWB forcing plays a key role in determining whether or not a SSWJ will develop

Does Low Frequency X-ray QPO Behavior in GRS 1915+105 Influence Subsequent X-ray and Infrared Evolution?

Using observations with the Rossi X-ray Timing Explorer, we examine the behavior of 2-10 Hz quasi-periodic oscillations (QPOs) during spectrally-hard dips in the x-ray light curve of GRS 1915+105 that are accompanied by infrared flares. Of the twelve light-curves examined, nine are beta-class and three are alpha-class following the scheme of Belloni et al. (2000). In most cases, the QPO frequency is most strongly correlated to the power law flux, which partially contradicts some earlier claims that the strongest correlation is between QPO frequency and blackbody flux. Seven beta-class curves are highly correlated to blackbody features. In several cases, the QPO evolution appears to decouple from the spectral evolution. We find that beta-class light-curves with strong correlations can be distinguished from those without by their ``trigger spike'' morphology. We also show that the origin and strength of the subsequent infrared flare may be causally linked to the variations in QPO frequency evolution and not solely tied to the onset of soft x-ray flaring behavior. We divide the twelve alpha- and beta-class light-curves into three groups based on the evolution of the QPO, the morphology of the trigger spike, and the infrared flare strength. An apparent crossover case leads us to conclude that these groups are not unique modes but represent part of a continuum of accretion behaviors. We believe the QPO behavior at the initiation of the hard dip can ultimately be used to determine the terminating x-ray behavior, and the following infrared flaring behavior.Comment: 29 pages, 9 figures, to be published in Ap

Non-Relativistic Gravitation: From Newton to Einstein and Back

We present an improvement to the Classical Effective Theory approach to the non-relativistic or Post-Newtonian approximation of General Relativity. The "potential metric field" is decomposed through a temporal Kaluza-Klein ansatz into three NRG-fields: a scalar identified with the Newtonian potential, a 3-vector corresponding to the gravito-magnetic vector potential and a 3-tensor. The derivation of the Einstein-Infeld-Hoffmann Lagrangian simplifies such that each term corresponds to a single Feynman diagram providing a clear physical interpretation. Spin interactions are dominated by the exchange of the gravito-magnetic field. Leading correction diagrams corresponding to the 3PN correction to the spin-spin interaction and the 2.5PN correction to the spin-orbit interaction are presented.Comment: 10 pages, 3 figures. v2: published version. v3: Added a computation of Einstein-Infeld-Hoffmann in higher dimensions within our improved ClEFT which partially confirms and partially corrects a previous computation. See notes added at end of introductio

Next to leading order spin-orbit effects in the motion of inspiralling compact binaries

Using effective field theory (EFT) techniques we calculate the next-to-leading order (NLO) spin-orbit contributions to the gravitational potential of inspiralling compact binaries. We use the covariant spin supplementarity condition (SSC), and explicitly prove the equivalence with previous results by Faye et al. in arXiv:gr-qc/0605139. We also show that the direct application of the Newton-Wigner SSC at the level of the action leads to the correct dynamics using a canonical (Dirac) algebra. This paper then completes the calculation of the necessary spin dynamics within the EFT formalism that will be used in a separate paper to compute the spin contributions to the energy flux and phase evolution to NLO.Comment: 25 pages, 4 figures, revtex4. v2: minor changes, refs. added. To appear in Class. Quant. Gra

Spectral Difference Equations Satisfied by KP Soliton Wavefunctions

The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these translational operators converge to the differential operators in the spectral parameter previously discussed as part of the theory of "bispectrality". Consequently, these translational operators can be seen as demonstrating a form of bispectrality for the non-rational solitons as well.Comment: to appear in "Inverse Problems

A nonlinear scalar model of extreme mass ratio inspirals in effective field theory I. Self force through third order

The motion of a small compact object in a background spacetime is investigated in the context of a model nonlinear scalar field theory. This model is constructed to have a perturbative structure analogous to the General Relativistic description of extreme mass ratio inspirals (EMRIs). We apply the effective field theory approach to this model and calculate the finite part of the self force on the small compact object through third order in the ratio of the size of the compact object to the curvature scale of the background (e.g., black hole) spacetime. We use well-known renormalization methods and demonstrate the consistency of the formalism in rendering the self force finite at higher orders within a point particle prescription for the small compact object. This nonlinear scalar model should be useful for studying various aspects of higher-order self force effects in EMRIs but within a comparatively simpler context than the full gravitational case. These aspects include developing practical schemes for higher order self force numerical computations, quantifying the effects of transient resonances on EMRI waveforms and accurately modeling the small compact object's motion for precise determinations of the parameters of detected EMRI sources.Comment: 30 pages, 8 figure