42,559 research outputs found
A Solution Set-Based Entropy Principle for Constitutive Modeling in Mechanics
Entropy principles based on thermodynamic consistency requirements are widely
used for constitutive modeling in continuum mechanics, providing physical
constraints on a priori unknown constitutive functions. The well-known
M\"uller-Liu procedure is based on Liu's lemma for linear systems. While the
M\"uller-Liu algorithm works well for basic models with simple constitutive
dependencies, it cannot take into account nonlinear relationships that exist
between higher derivatives of the fields in the cases of more complex
constitutive dependencies.
The current contribution presents a general solution set-based procedure,
which, for a model system of differential equations, respects the geometry of
the solution manifold, and yields a set of constraint equations on the unknown
constitutive functions, which are necessary and sufficient conditions for the
entropy production to stay nonnegative for any solution. Similarly to the
M\"uller-Liu procedure, the solution set approach is algorithmic, its output
being a set of constraint equations and a residual entropy inequality. The
solution set method is applicable to virtually any physical model, allows for
arbitrary initially postulated forms of the constitutive dependencies, and does
not use artificial constructs like Lagrange multipliers. A Maple implementation
makes the solution set method computationally straightforward and useful for
the constitutive modeling of complex systems.
Several computational examples are considered, in particular, models of gas,
anisotropic fluid, and granular flow dynamics. The resulting constitutive
function forms are analyzed, and comparisons are provided. It is shown how the
solution set entropy principle can yield classification problems, leading to
several complementary sets of admissible constitutive functions; such problems
have not previously appeared in the constitutive modeling literature
Mixed Heavy-Light Matching in the Universal One-Loop Effective Action
Recently, a general result for evaluating the path integral at one loop was
obtained in the form of the Universal One-Loop Effective Action. It may be used
to derive effective field theory operators of dimensions up to six, by
evaluating the traces of matrices in this expression, with the mass-dependence
encapsulated in the universal coefficients. Here we show that it can account
for loops of mixed heavy-light particles in the matching procedure. Our
prescription for computing these mixed contributions to the Wilson coefficients
is conceptually simple. Moreover it has the advantage of maintaining the
universal structure of the effective action, which we illustrate using the
example of integrating out a heavy electroweak triplet scalar coupling to a
light Higgs doublet. Finally we also identify new structures that were
previously neglected in the universal results.Comment: 22 pages, 3 figures; v2: expanded discussion in Section 3, typos
correcte
Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
We develop a frame-covariant formulation of inflation in the slow-roll
approximation by generalizing the inflationary attractor solution for
scalar-curvature theories. Our formulation gives rise to new generalized forms
for the potential slow-roll parameters, which enable us to examine the effect
of conformal transformations and inflaton reparameterizations in
scalar-curvature theories. We find that cosmological observables, such as the
power spectrum, the spectral indices and their runnings, can be expressed in a
concise manner in terms of the generalized potential slow-roll parameters which
depend on the scalar-curvature coupling function, the inflaton wavefunction,
and the inflaton potential. We show how the cosmological observables of
inflation are frame-invariant in this generalized potential slow-roll
formalism, as long as the end-of-inflation condition is appropriately extended
to become frame-invariant as well. We then apply our formalism to specific
scenarios, such as the induced gravity inflation, Higgs inflation and
models of inflation, and obtain more accurate results, without making
additional approximations to the potential. Our results are shown to be
consistent to lowest order with those presented in the literature. Finally, we
outline how our frame-covariant formalism can be naturally extended beyond the
tree-level approximation, within the framework of the Vilkovisky--DeWitt
effective action.Comment: 40 pages, a couple of comments and reference to the 1962 paper by
R.H. Dicke were added, to appear in Nuclear Physics
Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory
The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived
from the (standard, second order) functional formalism. It is shown how these
identities form closed sets from which one can in principle fully determine the
Green's functions involving the temporal component of the gauge field without
approximation, given appropriate input.Comment: 20 pages, no figure
Bottom Up Quotients and Residuals for Tree Languages
In this paper, we extend the notion of tree language quotients to bottom-up
quotients. Instead of computing the residual of a tree language from top to
bottom and producing a list of tree languages, we show how to compute a set of
k-ary trees, where k is an arbitrary integer. We define the quotient formula
for different combinations of tree languages: union, symbol products,
compositions, iterated symbol products and iterated composition. These
computations lead to the definition of the bottom-up quotient tree automaton,
that turns out to be the minimal deterministic tree automaton associated with a
regular tree language in the case of the 0-ary trees
Counterterms in type I Supergravities
We compute the one-loop divergences of D=10, N=1 supergravity and of its
reduction to D=8. We study the tensor structure of the counterterms appearing
in D=8 and D=10 and compare these to expressions previously found in the low
energy expansion of string theory. The infinities have the primitive Yang-Mills
tree amplitude as a common factor.Comment: 26 pages, Latex, 4 eps figure
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