2,482 research outputs found
On Cayley graphs of virtually free groups
In 1985, Dunwoody showed that finitely presentable groups are accessible.
Dunwoody's result was used to show that context-free groups, groups
quasi-isometric to trees or finitely presentable groups of asymptotic dimension
1 are virtually free. Using another theorem of Dunwoody of 1979, we study when
a group is virtually free in terms of its Cayley graph and we obtain new proofs
of the mentioned results and other previously depending on them
Tits alternatives for graph products
We discuss various types of Tits Alternative for subgroups of graph products of groups, and prove that, under some natural conditions, a graph product of groups satisfies a given form of Tits Alternative if and only if each vertex group satisfies this alternative. As a corollary, we show that every finitely generated subgroup of a graph product of virtually solvable groups is either virtually solvable or large. As another corollary, we prove that every non-abelian subgroup of a right angled Artin group has an epimorphism onto the free group of rank 2. In the course of the paper we develop the theory of parabolic subgroups, which allows to describe the structure of subgroups of graph products that contain no non-abelian free subgroups. We also obtain a number of results regarding the stability of some group properties under taking graph products
Line-of-sight geometrical and instrumental resolution effects on intensity perturbations by sausage modes
Diagnostics of MHD waves in the solar atmosphere is a topic which often
encounters problems of interpretation, due partly to the high complexity of the
solar atmospheric medium. Forward modeling can significantly guide
interpretation, bridging the gap between numerical simulations and
observations, and increasing the reliability of mode identification for
application of MHD seismology. In this work we aim at determining the
characteristics of the fast MHD sausage mode in the corona on the modulation of
observable quantities such as line intensity and spectral line broadening.
Effects of line-of-sight angle, and spatial, temporal and spectral resolutions
are considered. We take a cylindrical tube simulating a loop in a low-{\beta}
coronal environment with an optically thin background, and let it oscillate
with the fast sausage mode. A parametric study is performed. Among other
results, we show that regardless of the ionisation state of the plasma, the
variation of spectral line broadening can be significant, even for low
intensity modulation. The nature of this broadening is not thermal but is
mostly turbulent. This places spectrometers in clear advantage over imaging
instruments for the detection of the sausage mode. The modulation of all
quantities is considerably affected by the line-of-sight angle, and especially
by the spatial and temporal resolution when these are on the order of the
mode's wavelength and period. This places high constraints on instrumentation.Comment: 16 pages, 20 figure
Commensurating endomorphisms of acylindrically hyperbolic groups and applications
We prove that the outer automorphism group is residually finite when
the group is virtually compact special (in the sense of Haglund and Wise)
or when is isomorphic to the fundamental group of some compact
-manifold.
To prove these results we characterize commensurating endomorphisms of
acylindrically hyperbolic groups. An endomorphism of a group is said
to be commensurating, if for every some non-zero power of
is conjugate to a non-zero power of . Given an acylindrically hyperbolic
group , we show that any commensurating endomorphism of is inner modulo
a small perturbation. This generalizes a theorem of Minasyan and Osin, which
provided a similar statement in the case when is relatively hyperbolic. We
then use this result to study pointwise inner and normal endomorphisms of
acylindrically hyperbolic groups.Comment: 47 pages. v4: final version, to appear in Groups, Geometry and
Dynamic
A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis
In this paper, we consider unilateral contact problem without friction
between a rigid body and deformable one in the framework of isogeometric
analysis. We present the theoretical analysis of the mixed problem using an
active-set strategy and for a primal space of NURBS of degree and for
a dual space of B-Spline. A inf-sup stability is proved to ensure a good
property of the method. An optimal a priori error estimate is demonstrated
without assumption on the unknown contact set. Several numerical examples in
two- and three-dimensional and in small and large deformation demonstrate the
accuracy of the proposed method
Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products
3D objects, modeled using Computer Aided Geometric Design tools, are
traditionally represented using a boundary representation (B-rep), and
typically use spline functions to parameterize these boundary surfaces.
However, recent development in physical analysis, in isogeometric analysis
(IGA) in specific, necessitates a volumetric parametrization of the interior of
the object. IGA is performed directly by integrating over the spline spaces of
the volumetric spline representation of the object. Typically, tensor-product
B-spline trivariates are used to parameterize the volumetric domain. A general
3D object, that can be modeled in contemporary B-rep CAD tools, is typically
represented using trimmed B-spline surfaces. In order to capture the generality
of the contemporary B-rep modeling space, while supporting IGA needs, Massarwi
and Elber (2016) proposed the use of trimmed trivariates volumetric elements.
However, the use of trimmed geometry makes the integration process more
difficult since integration over trimmed B-spline basis functions is a highly
challenging task. In this work, we propose an algorithm that precisely
decomposes a trimmed B-spline trivariate into a set of (singular only on the
boundary) tensor-product B-spline trivariates, that can be utilized to simplify
the integration process in IGA. The trimmed B-spline trivariate is first
subdivided into a set of trimmed B\'ezier trivariates, at all its internal
knots. Then, each trimmed B\'ezier trivariate, is decomposed into a set of
mutually exclusive tensor-product B-spline trivariates, that precisely cover
the entire trimmed domain. This process, denoted untrimming, can be performed
in either the Euclidean space or the parametric space of the trivariate. We
present examples on complex trimmed trivariates' based geometry, and we
demonstrate the effectiveness of the method by applying IGA over the
(untrimmed) results.Comment: 18 pages, 32 figures. Contribution accepted in International
Conference on Geometric Modeling and Processing (GMP 2019
Isogeometric Analysis on V-reps: first results
Inspired by the introduction of Volumetric Modeling via volumetric
representations (V-reps) by Massarwi and Elber in 2016, in this paper we
present a novel approach for the construction of isogeometric numerical methods
for elliptic PDEs on trimmed geometries, seen as a special class of more
general V-reps. We develop tools for approximation and local re-parametrization
of trimmed elements for three dimensional problems, and we provide a
theoretical framework that fully justify our algorithmic choices. We validate
our approach both on two and three dimensional problems, for diffusion and
linear elasticity.Comment: 36 pages, 44 figures. Reviewed versio
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