92 research outputs found
Noncommutative elliptic theory. Examples
We study differential operators, whose coefficients define noncommutative
algebras. As algebra of coefficients, we consider crossed products,
corresponding to action of a discrete group on a smooth manifold. We give index
formulas for Euler, signature and Dirac operators twisted by projections over
the crossed product. Index of Connes operators on the noncommutative torus is
computed.Comment: 23 pages, 1 figur
Simulation of a GOx-GCH4 Rocket Combustor and the Effect of the GEKO Turbulence Model Coefficients
In this study, a single injector methane-oxygen rocket combustor is numerically studied. The simulations included in this study are based on the hardware and experimental data from the Technical University of Munich. The focus is on the recently developed generalized kâw turbulence model (GEKO) and the effect of its adjustable coefficients on the pressure and on wall heat flux profiles, which are compared with the experimental data. It was found that the coefficients of âjetâ,
ânear-wallâ, and âmixingâ have a major impact, whereas the opposite can be deduced about the âseparationâ parameter Csep, which highly influences the pressure and wall heat flux distributions due to the changes in the eddy-viscosity field. The simulation results are compared with the standard kâ# model, displaying a qualitatively and quantitatively similar behavior to the GEKO model at a
Csep equal to unity. The default GEKO model shows a stable performance for three oxidizer-to-fuel ratios, enhancing the reliability of its use. The simulations are conducted using two chemical kinetic
mechanisms: Zhukov and Kong and the more detailed RAMEC. The influence of the combustion model is of the same order as the influence of the turbulence model. In general, the numerical results
present a good or satisfactory agreement with the experiment, and both GEKO at Csep = 1 or the standard kâ# model can be recommended for usage in the CFD simulations of rocket combustion
chambers, as well as the ZhukovâKong mechanism in conjunction with the flamelet approach
Topological Expansion and Exponential Asymptotics in 1D Quantum Mechanics
Borel summable semiclassical expansions in 1D quantum mechanics are
considered. These are the Borel summable expansions of fundamental solutions
and of quantities constructed with their help. An expansion, called
topological,is constructed for the corresponding Borel functions. Its main
property is to order the singularity structure of the Borel plane in a
hierarchical way by an increasing complexity of this structure starting from
the analytic one. This allows us to study the Borel plane singularity structure
in a systematic way. Examples of such structures are considered for linear,
harmonic and anharmonic potentials. Together with the best approximation
provided by the semiclassical series the exponentially small contribution
completing the approximation are considered. A natural method of constructing
such an exponential asymptotics relied on the Borel plane singularity
structures provided by the topological expansion is developed. The method is
used to form the semiclassical series including exponential contributions for
the energy levels of the anharmonic oscillator.Comment: 46 pages, 22 EPS figure
Asymptotic Improvement of Resummation and Perturbative Predictions in Quantum Field Theory
The improvement of resummation algorithms for divergent perturbative
expansions in quantum field theory by asymptotic information about perturbative
coefficients is investigated. Various asymptotically optimized resummation
prescriptions are considered. The improvement of perturbative predictions
beyond the reexpansion of rational approximants is discussed.Comment: 21 pages, LaTeX, 3 tables; title shortened; typographical errors
corrected; minor changes of style; 2 references adde
Poincare isomorphism in K-theory on manifolds with edges
The aim of this paper is to construct the Poincare isomorphism in K-theory on
manifolds with edges. We show that the Poincare isomorphism can naturally be
constructed in the framework of noncommutative geometry. More precisely, to a
manifold with edges we assign a noncommutative algebra and construct an
isomorphism between the K-group of this algebra and the K-homology group of the
manifold with edges viewed as a compact topological space.Comment: 15 pages, no figure
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
We study the dynamics of four dimensional gauge theories with adjoint
fermions for all gauge groups, both in perturbation theory and
non-perturbatively, by using circle compactification with periodic boundary
conditions for the fermions. There are new gauge phenomena. We show that, to
all orders in perturbation theory, many gauge groups are Higgsed by the gauge
holonomy around the circle to a product of both abelian and nonabelian gauge
group factors. Non-perturbatively there are monopole-instantons with fermion
zero modes and two types of monopole-anti-monopole molecules, called bions. One
type are "magnetic bions" which carry net magnetic charge and induce a mass gap
for gauge fluctuations. Another type are "neutral bions" which are magnetically
neutral, and their understanding requires a generalization of multi-instanton
techniques in quantum mechanics - which we refer to as the
Bogomolny-Zinn-Justin (BZJ) prescription - to compactified field theory. The
BZJ prescription applied to bion-anti-bion topological molecules predicts a
singularity on the positive real axis of the Borel plane (i.e., a divergence
from summing large orders in peturbation theory) which is of order N times
closer to the origin than the leading 4-d BPST instanton-anti-instanton
singularity, where N is the rank of the gauge group. The position of the
bion--anti-bion singularity is thus qualitatively similar to that of the 4-d IR
renormalon singularity, and we conjecture that they are continuously related as
the compactification radius is changed. By making use of transseries and
Ecalle's resurgence theory we argue that a non-perturbative continuum
definition of a class of field theories which admit semi-classical expansions
may be possible.Comment: 112 pages, 7 figures; v2: typos corrected, discussion of
supersymmetric models added at the end of section 8.1, reference adde
Key Role of Polyphosphoinositides in Dynamics of Fusogenic Nuclear Membrane Vesicles
The role of phosphoinositides has been thoroughly described in many signalling and membrane trafficking events but their function as modulators of membrane structure and dynamics in membrane fusion has not been investigated. We have reconstructed models that mimic the composition of nuclear envelope precursor membranes with naturally elevated amounts of phosphoinositides. These fusogenic membranes (membrane vesicle 1(MV1) and nuclear envelope remnants (NER) are critical for the assembly of the nuclear envelope. Phospholipids, cholesterol, and polyphosphoinositides, with polyunsaturated fatty acid chains that were identified in the natural nuclear membranes by lipid mass spectrometry, have been used to reconstruct complex model membranes mimicking nuclear envelope precursor membranes. Structural and dynamic events occurring in the membrane core and at the membrane surface were monitored by solid-state deuterium and phosphorus NMR. âMV1-likeâ (PCâ¶PIâ¶PIPâ¶PIP2, 30â¶20â¶18â¶12, mol%) membranes that exhibited high levels of PtdIns, PtdInsP and PtdInsP2 had an unusually fluid membrane core (up to 20% increase, compared to membranes with low amounts of phosphoinositides to mimic the endoplasmic reticulum). âNER-likeâ (PCâ¶CHâ¶PIâ¶PIPâ¶PIP2, 28â¶42â¶16â¶7â¶7, mol%) membranes containing high amounts of both cholesterol and phosphoinositides exhibited liquid-ordered phase properties, but with markedly lower rigidity (10â15% decrease). Phosphoinositides are the first lipids reported to counterbalance the ordering effect of cholesterol. At the membrane surface, phosphoinositides control the orientation dynamics of other lipids in the model membranes, while remaining unchanged themselves. This is an important finding as it provides unprecedented mechanistic insight into the role of phosphoinositides in membrane dynamics. Biological implications of our findings and a model describing the roles of fusogenic membrane vesicles are proposed
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