654 research outputs found
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
We examine the effect of accuracy of high-order spectral element methods,
with or without adaptive mesh refinement (AMR), in the context of a classical
configuration of magnetic reconnection in two space dimensions, the so-called
Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point
of the velocity. A recently developed spectral-element adaptive refinement
incompressible magnetohydrodynamic (MHD) code is applied to simulate this
problem. The MHD solver is explicit, and uses the Elsasser formulation on
high-order elements. It automatically takes advantage of the adaptive grid
mechanics that have been described elsewhere in the fluid context [Rosenberg,
Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows
both statically refined and dynamically refined grids. Tests of the algorithm
using analytic solutions are described, and comparisons of the Orszag-Tang
solutions with pseudo-spectral computations are performed. We demonstrate for
moderate Reynolds numbers that the algorithms using both static and refined
grids reproduce the pseudo--spectral solutions quite well. We show that
low-order truncation--even with a comparable number of global degrees of
freedom--fails to correctly model some strong (sup--norm) quantities in this
problem, even though it satisfies adequately the weak (integrated) balance
diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic
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TEAMwork: Testing Emotional Attunement and Mutuality During Parent-Adolescent fMRI.
The parent-child relationship and family context influence the development of emotion regulation (ER) brain circuitry and related skills in children and adolescents. Although both parents' and children's ER neurocircuitry simultaneously affect how they interact with one another, neuroimaging studies of parent-child relationships typically include only one member of the dyad in brain imaging procedures. The current study examined brain activation related to parenting and ER in parent-adolescent dyads during concurrent fMRI scanning with a novel task - the Testing Emotional Attunement and Mutuality (TEAM) task. The TEAM task includes feedback trials indicating the other dyad member made an error, resulting in a monetary loss for both participants. Results indicate that positive parenting practices as reported by the adolescent were positively correlated with parents' hemodynamic activation of the ventromedial prefrontal cortex, a region related to empathy, during these error trials. Additionally, during feedback conditions both parents and adolescents exhibited fMRI activation in ER-related regions, including the dorsolateral prefrontal cortex, anterior insula, fusiform gyrus, thalamus, caudate, precuneus, and superior parietal lobule. Adolescents had higher left amygdala activation than parents during the feedback condition. These findings demonstrate the utility of dyadic fMRI scanning for investigating relational processes, particularly in the parent-child relationship
From limit cycles to strange attractors
We define a quantitative notion of shear for limit cycles of flows. We prove
that strange attractors and SRB measures emerge when systems exhibiting limit
cycles with sufficient shear are subjected to periodic pulsatile drives. The
strange attractors possess a number of precisely-defined dynamical properties
that together imply chaos that is both sustained in time and physically
observable.Comment: 27 page
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Always on my mind: Cross-brain associations of mental health symptoms during simultaneous parent-child scanning.
How parents manifest symptoms of anxiety or depression may affect how children learn to modulate their own distress, thereby influencing the children's risk for developing an anxiety or mood disorder. Conversely, children's mental health symptoms may impact parents' experiences of negative emotions. Therefore, mental health symptoms can have bidirectional effects in parent-child relationships, particularly during moments of distress or frustration (e.g., when a parent or child makes a costly mistake). The present study used simultaneous functional magnetic resonance imaging (fMRI) of parent-adolescent dyads to examine how brain activity when responding to each other's costly errors (i.e., dyadic error processing) may be associated with symptoms of anxiety and depression. While undergoing simultaneous fMRI scans, healthy dyads completed a task involving feigned errors that indicated their family member made a costly mistake. Inter-brain, random-effects multivariate modeling revealed that parents who exhibited decreased medial prefrontal cortex and posterior cingulate cortex activation when viewing their child's costly error response had children with more symptoms of depression and anxiety. Adolescents with increased anterior insula activation when viewing a costly error made by their parent had more anxious parents. These results reveal cross-brain associations between mental health symptomatology and brain activity during parent-child dyadic error processing
On completeness of logic programs
Program correctness (in imperative and functional programming) splits in
logic programming into correctness and completeness. Completeness means that a
program produces all the answers required by its specification. Little work has
been devoted to reasoning about completeness. This paper presents a few
sufficient conditions for completeness of definite programs. We also study
preserving completeness under some cases of pruning of SLD-trees (e.g. due to
using the cut).
We treat logic programming as a declarative paradigm, abstracting from any
operational semantics as far as possible. We argue that the proposed methods
are simple enough to be applied, possibly at an informal level, in practical
Prolog programming. We point out importance of approximate specifications.Comment: 20 page
An efficient iterative solution method for the Chebyshev collocation of advection-dominated transport problems
A new Chebyshev collocation algorithm is proposed for the iterative solution of advection-diffusion problems. The main features of the method lie in the original way in which a finite-difference preconditioner is built and in the fact that the solution is collocated on a set of nodes matching the standard Gauss-Lobatto-Chebyshev set only in the case of pure diffusion problems. The key point of the algorithm is the capability of the preconditioner to represent the high-frequency modes when dealing with advection-dominated problems. The basic idea is developed for a one-dimensional case and is extended to two-dimensional problems. A series of numerical experiments is carried out to demonstrate the efficiency of the algorithm. The proposed algorithm can also be used in the context of the incompressible Navier-Stokes equations
Quantitative Stability of Linear Infinite Inequality Systems under Block Perturbations with Applications to Convex Systems
The original motivation for this paper was to provide an efficient
quantitative analysis of convex infinite (or semi-infinite) inequality systems
whose decision variables run over general infinite-dimensional (resp.
finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed
set . Parameter perturbations on the right-hand side of the inequalities are
required to be merely bounded, and thus the natural parameter space is
. Our basic strategy consists of linearizing the parameterized
convex system via splitting convex inequalities into linear ones by using the
Fenchel-Legendre conjugate. This approach yields that arbitrary bounded
right-hand side perturbations of the convex system turn on constant-by-blocks
perturbations in the linearized system. Based on advanced variational analysis,
we derive a precise formula for computing the exact Lipschitzian bound of the
feasible solution map of block-perturbed linear systems, which involves only
the system's data, and then show that this exact bound agrees with the
coderivative norm of the aforementioned mapping. In this way we extend to the
convex setting the results of [3] developed for arbitrary perturbations with no
block structure in the linear framework under the boundedness assumption on the
system's coefficients. The latter boundedness assumption is removed in this
paper when the decision space is reflexive. The last section provides the aimed
application to the convex case
Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles
We study the global dynamics of integrate and fire neural networks composed
of an arbitrary number of identical neurons interacting by inhibition and
excitation. We prove that if the interactions are strong enough, then the
support of the stable asymptotic dynamics consists of limit cycles. We also
find sufficient conditions for the synchronization of networks containing
excitatory neurons. The proofs are based on the analysis of the equivalent
dynamics of a piecewise continuous Poincar\'e map associated to the system. We
show that for strong interactions the Poincar\'e map is piecewise contractive.
Using this contraction property, we prove that there exist a countable number
of limit cycles attracting all the orbits dropping into the stable subset of
the phase space. This result applies not only to the Poincar\'e map under
study, but also to a wide class of general n-dimensional piecewise contractive
maps.Comment: 46 pages. In this version we added many comments suggested by the
referees all along the paper, we changed the introduction and the section
containing the conclusions. The final version will appear in Journal of
Mathematical Biology of SPRINGER and will be available at
http://www.springerlink.com/content/0303-681
Ultra-short pulses in linear and nonlinear media
We consider the evolution of ultra-short optical pulses in linear and
nonlinear media. For the linear case, we first show that the initial-boundary
value problem for Maxwell's equations in which a pulse is injected into a
quiescent medium at the left endpoint can be approximated by a linear wave
equation which can then be further reduced to the linear short-pulse equation.
A rigorous proof is given that the solution of the short pulse equation stays
close to the solutions of the original wave equation over the time scales
expected from the multiple scales derivation of the short pulse equation. For
the nonlinear case we compare the predictions of the traditional nonlinear
Schr\"odinger equation (NLSE) approximation which those of the short pulse
equation (SPE). We show that both equations can be derived from Maxwell's
equations using the renormalization group method, thus bringing out the
contrasting scales. The numerical comparison of both equations to Maxwell's
equations shows clearly that as the pulse length shortens, the NLSE
approximation becomes steadily less accurate while the short pulse equation
provides a better and better approximation
Middle-out reasoning for synthesis and induction
We develop two applications of middle-out reasoning in inductive proofs: Logic program synthesis and the selection of induction schemes. Middle-out reasoning as part of proof planning was first suggested by Bundy et al [Bundy et al 90a]. Middle-out reasoning uses variables to represent unknown terms and formulae. Unification instantiates the variables in the subsequent planning, while proof planning provides the necessary search control. Middle-out reasoning is used for synthesis by planning the verification of an unknown logic program: The program body is represented with a meta-variable. The planning results both in an instantiation of the program body and a plan for the verification of that program. If the plan executes successfully, the synthesized program is partially correct and complete. Middle-out reasoning is also used to select induction schemes. Finding an appropriate induction scheme during synthesis is difficult, because the recursion of the program, which is un..
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