16,462 research outputs found
Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate
We consider the axial compression of a thin sheet wrapped around a rigid
cylindrical substrate. In contrast to the wrinkling-to-fold transitions
exhibited in similar systems, we find that the sheet always buckles into a
single symmetric fold, while periodic solutions are unstable. Upon further
compression, the solution breaks symmetry and stabilizes into a recumbent fold.
Using linear analysis and numerics, we theoretically predict the buckling force
and energy as a function of the compressive displacement. We compare our theory
to experiments employing cylindrical neoprene sheets and find remarkably good
agreement.Comment: 20 pages, 5 figure
Some Remarks on {}-invariant Fedosov Star Products and Quantum Momentum Mappings
In these notes we consider the usual Fedosov star product on a symplectic
manifold emanating from the fibrewise Weyl product , a
symplectic torsion free connection on M, a formal series of closed two-forms on M and a certain formal
series s of symmetric contravariant tensor fields on M. For a given symplectic
vector field X on M we derive necessary and sufficient conditions for the
triple determining the star product * on which the Lie
derivative \Lie_X with respect to X is a derivation of *. Moreover, we also
give additional conditions on which \Lie_X is even a quasi-inner derivation.
Using these results we find necessary and sufficient criteria for a Fedosov
star product to be -invariant and to admit a quantum Hamiltonian.
Finally, supposing the existence of a quantum Hamiltonian, we present a
cohomological condition on that is equivalent to the existence of a
quantum momentum mapping. In particular, our results show that the existence of
a classical momentum mapping in general does not imply the existence of a
quantum momentum mapping.Comment: 15 pages, one corollary and one definition added to Section 4, typos
remove
Polymake and Lattice Polytopes
The polymake software system deals with convex polytopes and related objects
from geometric combinatorics. This note reports on a new implementation of a
subclass for lattice polytopes. The features displayed are enabled by recent
changes to the polymake core, which will be discussed briefly.Comment: 12 pages, 1 figur
Dyson-Schwinger study of chiral density waves in QCD
The formation of inhomogeneous chiral condensates in QCD matter at nonzero
density and temperature is investigated for the first time with Dyson-Schwinger
equations. We consider two massless quark flavors in a so-called chiral density
wave, where scalar and pseudoscalar quark condensates vary sinusoidally along
one spatial dimension. We find that the inhomogeneous region covers the major
part of the spinodal region of the first-order phase transition which is
present when the analysis is restricted to homogeneous phases. The triple point
where the inhomogeneous phase meets the homogeneous phases with broken and
restored chiral symmetry, respectively, coincides, within numerical accuracy,
with the critical point of the homogeneous calculation. At zero temperature,
the inhomogeneous phase seems to extend to arbitrarily high chemical
potentials, as long as pairing effects are not taken into account.Comment: 5 pages, 4 figures; v2: few minor modifications, matches published
versio
The parameterized space complexity of model-checking bounded variable first-order logic
The parameterized model-checking problem for a class of first-order sentences
(queries) asks to decide whether a given sentence from the class holds true in
a given relational structure (database); the parameter is the length of the
sentence. We study the parameterized space complexity of the model-checking
problem for queries with a bounded number of variables. For each bound on the
quantifier alternation rank the problem becomes complete for the corresponding
level of what we call the tree hierarchy, a hierarchy of parameterized
complexity classes defined via space bounded alternating machines between
parameterized logarithmic space and fixed-parameter tractable time. We observe
that a parameterized logarithmic space model-checker for existential bounded
variable queries would allow to improve Savitch's classical simulation of
nondeterministic logarithmic space in deterministic space .
Further, we define a highly space efficient model-checker for queries with a
bounded number of variables and bounded quantifier alternation rank. We study
its optimality under the assumption that Savitch's Theorem is optimal
Dirac particles in Rindler space
We show that a uniformly accelerated observer experiences a "thermal" flux of Dirac particles in the ordinary Minkowski vacuum
Data driven problems in elasticity
We consider a new class of problems in elasticity, referred to as Data-Driven
problems, defined on the space of strain-stress field pairs, or phase space.
The problem consists of minimizing the distance between a given material data
set and the subspace of compatible strain fields and stress fields in
equilibrium. We find that the classical solutions are recovered in the case of
linear elasticity. We identify conditions for convergence of Data-Driven
solutions corresponding to sequences of ap- proximating material data sets.
Specialization to constant material data set sequences in turn establishes an
appropriate notion of relaxation. We find that relaxation within this
Data-Driven framework is fundamentally different from the classical relaxation
of energy functions. For instance, we show that in the Data-Driven framework
the relaxation of a bistable material leads to material data sets that are not
graphs.Comment: Result now covers the two well problem in full generality. Proof
simplified. New Figure 9 illustrates geometry of separatio
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