10,910 research outputs found
Analysis of a Darcy-Cahn-Hilliard Diffuse Interface Model for the Hele-Shaw Flow and its Fully Discrete Finite Element Approximation
In this paper we present PDE and finite element analyses for a system of
partial differential equations (PDEs) consisting of the Darcy equation and the
Cahn-Hilliard equation, which arises as a diffuse interface model for the two
phase Hele-Shaw flow. We propose a fully discrete implicit finite element
method for approximating the PDE system, which consists of the implicit Euler
method combined with a convex splitting energy strategy for the temporal
discretization, the standard finite element discretization for the pressure and
a split (or mixed) finite element discretization for the fourth order
Cahn-Hilliard equation. It is shown that the proposed numerical method
satisfies a mass conservation law in addition to a discrete energy law that
mimics the basic energy law for the Darcy-Cahn-Hilliard phase field model and
holds uniformly in the phase field parameter . With help of the
discrete energy law, we first prove that the fully discrete finite method is
unconditionally energy stable and uniquely solvable at each time step. We then
show that, using the compactness method, the finite element solution has an
accumulation point that is a weak solution of the PDE system. As a result, the
convergence result also provides a constructive proof of the existence of
global-in-time weak solutions to the Darcy-Cahn-Hilliard phase field model in
both two and three dimensions. Finally, we propose a nonlinear multigrid
iterative algorithm to solve the finite element equations at each time step.
Numerical experiments based on the overall solution method of combining the
proposed finite element discretization and the nonlinear multigrid solver are
presented to validate the theoretical results and to show the effectiveness of
the proposed fully discrete finite element method for approximating the
Darcy-Cahn-Hilliard phase field model.Comment: 30 pages, 4 tables, 2 figure
Finiteness properties of cubulated groups
We give a generalized and self-contained account of Haglund-Paulin's
wallspaces and Sageev's construction of the CAT(0) cube complex dual to a
wallspace. We examine criteria on a wallspace leading to finiteness properties
of its dual cube complex. Our discussion is aimed at readers wishing to apply
these methods to produce actions of groups on cube complexes and understand
their nature. We develop the wallspace ideas in a level of generality that
facilitates their application.
Our main result describes the structure of dual cube complexes arising from
relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex
codimension-1 subgroups of a group G that is hyperbolic relative to
P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual
CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact
when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual
CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved
results in Sections 7 and 8. Several theorem numbers have changed from the
previous versio
Emergency burr holes:" How to do it"
This paper describes a simple approach to emergency burr hole evacuation of extra-axial intracranial haematoma that can be used in the uncommon situation when life saving specialist neurosurgical intervention is not available
\u3ci\u3eDeath in Supernatural: Critical Essays\u3c/i\u3e, edited by Amanda Taylor and Susan Nylander
A review of the collection of critical essays, Death in Supernatural: Critical Essay
Alien Registration- Wise, Lillian G. (Houlton, Aroostook County)
https://digitalmaine.com/alien_docs/35090/thumbnail.jp
Packing subgroups in relatively hyperbolic groups
We introduce the bounded packing property for a subgroup of a countable
discrete group G. This property gives a finite upper bound on the number of
left cosets of the subgroup that are pairwise close in G. We establish basic
properties of bounded packing, and give many examples; for instance, every
subgroup of a countable, virtually nilpotent group has bounded packing. We
explain several natural connections between bounded packing and group actions
on CAT(0) cube complexes.
Our main result establishes the bounded packing of relatively quasiconvex
subgroups of a relatively hyperbolic group, under mild hypotheses. As an
application, we prove that relatively quasiconvex subgroups have finite height
and width, properties that strongly restrict the way families of distinct
conjugates of the subgroup can intersect. We prove that an infinite,
nonparabolic relatively quasiconvex subgroup of a relatively hyperbolic group
has finite index in its commensurator. We also prove a virtual malnormality
theorem for separable, relatively quasiconvex subgroups, which is new even in
the word hyperbolic case.Comment: 45 pages, 2 figures. To appear in Geom. Topol. v2: Updated to address
concerns of the referee. Added theorem that an infinite, nonparabolic
relatively quasiconvex subgroup H of a relatively hyperbolic group has finite
index in its commensurator. Added several new geometric results to Section 7.
Theorem 8.9 on packing relative to peripheral subgroups is ne
The control of global brain dynamics: opposing actions of frontoparietal control and default mode networks on attention
Understanding how dynamic changes in brain activity control behavior is a major challenge of cognitive neuroscience. Here, we consider the brain as a complex dynamic system and define two measures of brain dynamics: the synchrony of brain activity, measured by the spatial coherence of the BOLD signal across regions of the brain; and metastability, which we define as the extent to which synchrony varies over time. We investigate the relationship among brain network activity, metastability, and cognitive state in humans, testing the hypothesis that global metastability is “tuned” by network interactions. We study the following two conditions: (1) an attentionally demanding choice reaction time task (CRT); and (2) an unconstrained “rest” state. Functional MRI demonstrated increased synchrony, and decreased metastability was associated with increased activity within the frontoparietal control/dorsal attention network (FPCN/DAN) activity and decreased default mode network (DMN) activity during the CRT compared with rest. Using a computational model of neural dynamics that is constrained by white matter structure to test whether simulated changes in FPCN/DAN and DMN activity produce similar effects, we demonstate that activation of the FPCN/DAN increases global synchrony and decreases metastability. DMN activation had the opposite effects. These results suggest that the balance of activity in the FPCN/DAN and DMN might control global metastability, providing a mechanistic explanation of how attentional state is shifted between an unfocused/exploratory mode characterized by high metastability, and a focused/constrained mode characterized by low metastability
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