Computer program to determine the irrotational nozzle admittance

Irrotational nozzle admittance is the boundary condition that must be satisfied by combustor flow oscillations at nozzle entrance. Defined as the ratio of axial velocity perturbation to the pressure perturbation at nozzle entrance, nozzle admittance can also be used to determine whether wave motion in nozzle under consideration adds or removes energy from combustor oscillations

Development of an analytical technique for the optimization of jet engine and duct acoustic liners

A special integral representation of the external solutions of the Helmholtz equation is described. The analytical technique developed for the generation of the optimum acoustic admittance for an arbitrary axisymmetric body is also presented along with some numerical procedures and some preliminary results for a straight duct

Development of an analytical technique for the optimization of jet engine and duct acoustic liners

A new method was developed for the calculation of optimum constant admittance solutions for the minimization of the sound radiated from an arbitrary axisymmetric body. This method utilizes both the integral equation technique used in the calculation of the optimum non-constant admittance liners and the independent solution generated as a by product of these calculations. The results generated by both these methods are presented for three duct geometries: (1) a straight duct; (2) the QCSEE inlet; and (3) the QCSEE inlet less its centerbody

Critical Dynamics in Glassy Systems

Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.Comment: 24 pages, accepted for publication on PRE. Discussion of the connection with MCT added in the Conclusion

Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion

Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both 1/N and loop expansions beyond leading order show remarkable improvement when compared to mean-field approximations. However, in truncations used so far, only the leading-order parts of the self energy responsible for memory loss, damping and equilibration are included, which makes it difficult to discuss convergence systematically. For that reason we derive the real and causal evolution equations for an O(N) model to next-to-next-to-leading order in the 2PI-1/N expansion. Due to the appearance of internal vertices the resulting equations appear intractable for a full-fledged 3+1 dimensional field theory. Instead, we solve the closely related three-loop approximation in the auxiliary-field formalism numerically in 0+1 dimensions (quantum mechanics) and compare to previous approximations and the exact numerical solution of the Schroedinger equation.Comment: 29 pages, minor changes, references added; to appear in PR

Symmetry Principle Preserving and Infinity Free Regularization and renormalization of quantum field theories and the mass gap

Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in non-Abelian gauge theories. Overlapping UV divergences are explicitly shown to be factorizable in the ILIs and be harmless via suitable subtractions. A new regularization and renormalization method is presented in the initial space-time dimension of the theory. The procedure respects unitarity and causality. Of interest, the method leads to an infinity free renormalization and meanwhile maintains the symmetry principles of the original theory except the intrinsic mass scale caused conformal scaling symmetry breaking and the anomaly induced symmetry breaking. Quantum field theories (QFTs) regularized through the new method are well defined and governed by a physically meaningful characteristic energy scale (CES) $M_c$ and a physically interesting sliding energy scale (SES) $\mu_s$ which can run from $\mu_s \sim M_c$ to a dynamically generated mass gap $\mu_s=\mu_c$ or to $\mu_s =0$ in the absence of mass gap and infrared (IR) problem. It is strongly indicated that the conformal scaling symmetry and its breaking mechanism play an important role for understanding the mass gap and quark confinement.Comment: 59 pages, Revtex, 4 figures, 1 table, Erratum added, published versio

Absence of vortex condensation in a two dimensional fermionic XY model

Motivated by a puzzle in the study of two dimensional lattice Quantum Electrodynamics with staggered fermions, we construct a two dimensional fermionic model with a global U(1) symmetry. Our model can be mapped into a model of closed packed dimers and plaquettes. Although the model has the same symmetries as the XY model, we show numerically that the model lacks the well known Kosterlitz-Thouless phase transition. The model is always in the gapless phase showing the absence of a phase with vortex condensation. In other words the low energy physics is described by a non-compact U(1) field theory. We show that by introducing an even number of layers one can introduce vortex condensation within the model and thus also induce a KT transition.Comment: 5 pages, 5 figure

Superfluidity and magnetism in multicomponent ultracold fermions

We study the interplay between superfluidity and magnetism in a multicomponent gas of ultracold fermions. Ward-Takahashi identities constrain possible mean-field states describing order parameters for both pairing and magnetization. The structure of global phase diagrams arises from competition among these states as functions of anisotropies in chemical potential, density, or interactions. They exhibit first and second order phase transition as well as multicritical points, metastability regions, and phase separation. We comment on experimental signatures in ultracold atoms.Comment: 4 pages, 3 figure

Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for Point-Link-Point-Interactions

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. This amounts to a generalization from 2-point to point-link-point interactions. We develop an associated graph theory with a generalized notion of connectivity and describe an algorithmic generation of the new multiple-line graphs. We indicate physical applications to spin glasses, partially annealed neural networks and SU(N) gauge Higgs systems. In particular the new expansion technique provides the possibility of avoiding the replica-trick in spin glasses. We consider variational estimates for the SU(2) Higgs model of the electroweak phase transition. The results for the transition line, obtained by dynamical linked cluster expansions, agree quite well with corresponding high precision Monte Carlo results.Comment: 41 pages, latex2e, 10 postscript figure