307 research outputs found
Analysis of orthogonal metal cutting processes
The orthogonal metal cutting process for a controlled contact tool is simulated using a limit analysis theorem. The basic principles are stated in the form of a primal optimization problem with an objective function subjected to constraints of the equilibrium equation, its static boundary conditions and a constitutive inequality. An Eulerian reference co-ordinate is used to describe the steady state motion of the workpiece relative to the tool. Based on a duality theorem, a dual functional bounds the objective functional of the primal problem from above by a sharp inequality. The dual formulation seeks the least upper bound and thus recovers the maximum of the primal functional theoretically. A finite element approximation of the continuous variables in the dual problem reduces it to a convex programming. Since the original dual problem admits discontinuous solutions in the form of bounded variation functions, care must be taken in the finite element approximation to account for such a possibility. This is accomplished by a combined smoothing and successive approximation algorithm. Convergence is robust from any initial iterate. Results are obtained for a wide range of control parameters including cutting depth, rake angle, rake length and friction. The converged solutions provide information on cutting force, chip thickness, chip stream angle and shear angle which agree well both in values and trend with the published data. But the available data represent only a small subset in the range of parameters exhaustively investigated in this paper.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50099/1/1620340122_ftp.pd
Mass gap without vacuum energy
We consider soft nonlocal deformations of massless theories that introduce a
mass gap. By use of a renormalization scheme that preserves the ultraviolet
softness of the deformation, renormalized quantities of low mass dimension,
such as normal mass terms, vanish via finite counterterms. The same applies to
the renormalized cosmological constant. We connect this discussion to gauge
theories, since they are also subject to a soft nonlocal deformation due to the
effects of Gribov copies. These effects are softer than usually portrayed.Comment: 7 page
Glueball Spectroscopy on S^3
For SU(2) gauge theory on the three-sphere we implement the influence of the
boundary of the fundamental domain, and in particular the -dependence,
on a subspace of low-energy modes of the gauge field. We construct a basis of
functions that respect these boundary conditions and use these in a variational
approximation of the spectrum of the lowest order effective hamiltonian.Comment: 8p. latex, 3 uuencoded PostScript figures appende
Maximal Non-Abelian Gauges and Topology of Gauge Orbit Space
We introduce two maximal non-abelian gauge fixing conditions on the space of
gauge orbits M for gauge theories over spaces with dimensions d < 3. The gauge
fixings are complete in the sense that describe an open dense set M_0 of the
space of gauge orbits M and select one and only one gauge field per gauge orbit
in M_0. There are not Gribov copies or ambiguities in these gauges. M_0 is a
contractible manifold with trivial topology. The set of gauge orbits which are
not described by the gauge conditions M \ M_0 is the boundary of M_0 and
encodes all non-trivial topological properties of the space of gauge orbits.
The gauge fields configurations of this boundary M \ M_0 can be explicitly
identified with non-abelian monopoles and they are shown to play a very
relevant role in the non-perturbative behaviour of gauge theories in one, two
and three space dimensions. It is conjectured that their role is also crucial
for quark confinement in 3+1 dimensional gauge theories.Comment: 31 pages, harvmac, 1 figur
The ice-limit of Coulomb gauge Yang-Mills theory
In this paper we describe gauge invariant multi-quark states generalising the
path integral framework developed by Parrinello, Jona-Lasinio and Zwanziger to
amend the Faddeev-Popov approach. This allows us to produce states such that,
in a limit which we call the ice-limit, fermions are dressed with glue
exclusively from the fundamental modular region associated with Coulomb gauge.
The limit can be taken analytically without difficulties, avoiding the Gribov
problem. This is llustrated by an unambiguous construction of gauge invariant
mesonic states for which we simulate the static quark--antiquark potential.Comment: 25 pages, 4 figure
Glueballs on the three-sphere
We study the non-perturbative effects of the global features of the
configuration space for SU(2) gauge theory on the three-sphere. The strategy is
to reduce the full problem to an effective theory for the dynamics of the
low-energy modes. By explicitly integrating out the high-energy modes, the
one-loop correction to the effective hamiltonian is obtained. Imposing the
dependence through boundary conditions in configuration space
incorporates the non-perturbative effects of the non-contractable loops in the
full configuration space. After this we obtain the glueball spectrum of the
effective theory with a variational method.Comment: 48 p LaTeX, 13 Postscript figures appende
"Confinement Mechanism in Various Abelian Projections of Lattice Gluodynamics"
We show that the monopole confinement mechanism in lattice gluodynamics is a
particular feature of the maximal abelian projection. We give an explicit
example of the projection (the minimal abelian
projection), in which the confinement is due to topological objects other than
monopoles. We perform analytical and numerical study of the loop expansion of
the Faddeev--Popov determinant for the maximal and the minimal abelian
projections, and discuss the fundamental modular region for these projections.Comment: 16 pages (LaTeX) and 3 figures, report ITEP-94-6
One-loop effective action for SU(2) gauge theory on S^3
We consider the effective theory for the low-energy modes of SU(2) gauge
theory on the three-sphere. By explicitely integrating out the high-energy
modes, the one-loop correction to the hamiltonian for this problem is obtained.
We calculate the influence of this correction on the glueball spectrum.Comment: 12p. latex, 3 PostScript figures included (epsf
Instantons and Gribov Copies in the Maximally Abelian Gauge
We calculate the Faddeev-Popov operator corresponding to the maximally
Abelian gauge for gauge group SU(N). Specializing to SU(2) we look for explicit
zero modes of this operator. Within an illuminating toy model (Yang-Mills
mechanics) the problem can be completely solved and understood. In the field
theory case we are able to find an analytic expression for a normalizable zero
mode in the background of a single `t Hooft instanton. Accordingly, such an
instanton corresponds to a horizon configuration in the maximally Abelian
gauge. Possible physical implications are discussed.Comment: 31 pages, 8 figures, v3: references adde
Dynamical gluon mass generation from <A^2> in linear covariant gauges
We construct the multiplicatively renormalizable effective potential for the
mass dimension two local composite operator A^2 in linear covariant gauges. We
show that the formation of is energetically favoured and that the gluons
acquire a dynamical mass due to this gluon condensate. We also discuss the
gauge parameter independence of the resultant vacuum energy.Comment: 21 pages. 14 .eps figures. v2: minor modifications. v3: version
accepted for publication in JHE
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