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Two-variable asymptotic solution for three-dimensional solar powered low thrust trajectories in vicinity of ecliptic plane
Asymptotic integration method applied to problems of free vibrations in shells of positive curvature
Asymptotic formulas for elastic cylindrical shells and analysis of Kirchhoff-Love theory
Asymptotic expansion method for solving certain classes of singular perturbation problems with application in viscous flow
Matched asymptotic expansion method applied to ordinary and optimal trajectory problems in hypervelocity flight dynamics
Application of matched asymptotic expansions to hypervelocity flight mechanics
Optimal allocation in a pure capital working model with withdrawals, such as asymptotic properties, and algorithms
HF gaseous squeeze film bearing asymptotically analyzed by considering internal and edge regions separately
Asymptotic kinetic equation for inhomogeneous plasma compared to results for initial value problem and Bogoliubov method
Stability and asymptotic behavior of dynamical systems defined by autonomous functional or partial differential equation and conditions for applying Liapunov theorem
Matched asymptotic expansion method applied to hypervelocity flight trajectories, obtaining solutions to flight dynamic equations
Constant thickness elastic conical shells subject to lateral loads, deriving asymptotic solution
A simplified chemical-kinetic cool-flame mechanism for n-alkanes developed recently is applied to premixed laminar cool-flame deflagrations. The present contribution derives the structure of the associated freely propagating cool premixed flame controlled by the low-temperature chemistry and develops formulas for calculating the corresponding laminar burning velocity. Application of activation-energy asymptotics reveals finite-rate chemistry without heat release occurring throughout the preheat zone and leakage of both fuel and oxygen through the thin heat-release zone, there being zones of consumption of an intermediate species on each side of the heat-release zone, thicker than that zone but still thin compared with the preheat-zone thickness. Predicted laminar burning velocities are compared with recently reported measurements for n-dodecane, performed in a newly deigned high-pressure ignition apparatus, resulting in reasonable agreement.
A simplified chemical-kinetic cool-flame mechanism for n-alkanes developed recently is applied to premixed laminar cool-flame deflagrations. The present contribution derives the structure of the associated freely propagating cool premixed flame controlled by the low-temperature chemistry and develops formulas for calculating the corresponding laminar burning velocity. Application of activation-energy asymptotics reveals finite-rate chemistry without heat release occurring throughout the preheat zone and leakage of both fuel and oxygen through the thin heat-release zone, there being zones of consumption of an intermediate species on each side of the heat-release zone, thicker than that zone but still thin compared with the preheat-zone thickness. Predicted laminar burning velocities are compared with recently reported measurements for n-dodecane, performed in a newly deigned high-pressure ignition apparatus, resulting in reasonable agreement.
We propose a new AdS 3 /CFT 2 duality, in which the bulk string theory has a target spacetime AdS 3 times a squashed three-sphere $S$$^{3}_{b}$, and the dual CFT 2 is a symmetric product of sigma models on R Φ × $S$$^{3}_{b}$, deformed by a Φ-dependent Z 2 twist operator. The duality maps the asymptotic region of AdS 3 to the region Φ → ∞, where the twist interaction in the CFT 2 turns off. The AdS 3 backgrounds in question have R AdS < ℓ s , and so lie on the string side of the string/black hole correspondence transition. As a consequence, the high energy density of states consists of a string gas in AdS 3 rather than an ensemble of BTZ black holes. Furthermore, this property allows us to derive the dual CFT 2 by a systematic analysis of the worldsheet string theory on AdS 3 .
We consider asymptotic observables in quantum field theories in which the S-matrix makes sense. We argue that in addition to scattering amplitudes, a whole compendium of inclusive observables exists where the time-ordering is relaxed. These include expectation values of electromagnetic or gravitational radiation fields as well as out-of-time-order amplitudes. We explain how to calculate them in two ways: by relating them to amplitudes and products of amplitudes, and by using a generalization of the LSZ reduction formula. As an application, we discuss one-loop master integrals contributing to gravitational radiation in the post-Minkowski expansion, emphasizing the role of classical cut contributions and highlighting the different infrared physics of in-in observables.
The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.
Abstract A fundamental understanding of the interaction between microstructure and underlying physical mechanisms is essential, especially for developing more accurate multi-physics models for heterogeneous materials. Effects of microstructure on the material response at the macroscale are modeled by using the generalized thermomechanics. In this study, strain gradient theory is employed as a higher-order theory on the macroscale with thermodynamics modeled as a first-order theory on the microscale. Hence, energy depends only on the temperature such that we circumvent an extension of Fourier’s law and analyze the “simplest” thermo-mechanical model in strain gradient elasticity. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this “simplest” model in generalized thermomechanics creates dozens of parameters to be determined. We develop a thermo-mechanical framework, in which microstructure is modeled as a periodic structure and through asymptotic homogenization approach, higher-order parameters at macroscopic scale are calculated. To illustrate the importance of higher-order parameters in overall thermo-mechanical response of a heterogeneous materials, finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Verification example of a bulk system and several case studies of porous structures demonstrate how such numerical framework can be beneficial in the design of materials with tailored microstructures.