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## ON GENERIC ROTATIONLESS DIFFEOMORPHISMS OF THE ANNULUS

Fonte: AMER MATHEMATICAL SOC
Publicador: AMER MATHEMATICAL SOC

Tipo: Artigo de Revista Científica

ENG

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#Closed connected sets#omega limits#prime end theory#Kupka-Smale diffeomorphisms#Moser generic elliptic points#HOMOCLINIC POINTS#INSTABILITY#HOMEOMORPHISMS#RECURRENCE#REGIONS#Mathematics, Applied

Let f be a C(r)-diffeomorphism of the closed annulus A that preserves the orientation, the boundary components and the Lebesgue measure. Suppose that f has a lift (f) over tilde to the infinite strip (A) over tilde which has zero Lebesgue measure rotation number. If the rotation number of f restricted to both boundary components of (f) over tilde is positive, then for such a generic f (r >= 16), zero is an interior point of its rotation set. This is a partial solution to a conjecture of P. Boyland.; CNPq[301485/03-8]; GNPq[304360/05-8]

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## Quando as memórias são a matéria: memoriais de professoras alfabetizadoras e instabilidade genérica; When the memories are the matter: kindergarten teacher memorials and generic instability

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 13/01/2015
PT

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#Alfabetização e letramento#Formação de professoras#Generic instability#Gêneros do discurso#Instabilidade genérica#Literacy#Memoriais#Memorials#Práticas de ensino e de escrita#Speech genres#Teachers training

Tomando como ponto de partida a crítica às perspectivas que fazem prevalecer os aspectos estáveis dos gêneros discursivos em detrimento da fluidez que os relativiza, a presente pesquisa dá relevo aos elementos instáveis desse processo conjugando, a um só tempo, traços contínuos mais propensos à referida estabilização dos gêneros e descontínuos mais afeitos àquilo que chamo de instabilidade genérica. Do ponto de vista do processo de produção dos gêneros do discurso, a instabilidade genérica se inscreve no texto segundo diferentes marcas enunciativo-discursivas, assinalando pontos de ruptura e evidenciando um funcionamento marcado mais pela permanente incompletude do que pela pretensa fixidez de seus contornos. Parte-se da análise de corpus constituído por um conjunto de 84 textos produzidos, no ano de 2006, por professoras alfabetizadoras em um curso de formação (promovido pela Prefeitura Municipal de Cubatão-SP) chamado Letra e vida. Por ocasião desse curso, foi solicitado às participantes que redigissem, como atividade inicial, suas memórias de alfabetização, textos a partir dos quais elas deveriam reconstruir, preferencialmente de forma literária, as lembranças do tempo em que foram alfabetizadas. A partir dessa proposta...

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## Gravitational instability on the brane: the role of boundary conditions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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An outstanding issue in braneworld theory concerns the setting up of proper
boundary conditions for the brane-bulk system. Boundary conditions (BC's)
employing regulatory branes or demanding that the bulk metric be nonsingular
have yet to be implemented in full generality. In this paper, we take a
different route and specify boundary conditions directly on the brane thereby
arriving at a local and closed system of equations (on the brane). We consider
a one-parameter family of boundary conditions involving the anisotropic stress
of the projection of the bulk Weyl tensor on the brane and derive an exact
system of equations describing scalar cosmological perturbations on a generic
braneworld with induced gravity. Depending upon our choice of boundary
conditions, perturbations on the brane either grow moderately (region of
stability) or rapidly (instability). In the instability region, the evolution
of perturbations usually depends upon the scale: small scale perturbations grow
much more rapidly than those on larger scales. This instability is caused by a
peculiar gravitational interaction between dark radiation and matter on the
brane. Generalizing the boundary conditions obtained by Koyama and Maartens, we
find for the Dvali-Gabadadze-Porrati model an instability...

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## On the stratorotational instability in the quasi-hydrostatic semi-geostrophic limit

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The linear normal-mode stratorotational instability (SRI) is analytically
reexamined in the inviscid limit where the length scales of horizontal
disturbances are large compared their vertical and radial counterparts.
Boundary conditions different than channel walls are also considered. This
quasi-hydrostatic, semi-geostrophic (QHSG) approximation allows one to examine
the effect of a vertically varying Brunt-Vaisaila frequency, $N^2$. It is found
that the normal-mode instability persists when $N^2$ increases quadratically
with respect to the disc vertical coordinate. However we also find that the SRI
seems to exist in this inviscid QHSG extreme only for channel wall conditions:
when one or both of the reflecting walls are removed there is no instability in
the asymptotic limit explored here. It is also found that only exponential-type
SRI modes (as defined by Dubrulle et al. 2005) exist under these conditions.
These equations also admit non-normal mode behaviour. Fixed Lagrangian pressure
conditions on both radial boundaries predicts there to be no normal mode
behaviour in the QHSG limit. The mathematical relationship between the results
obtained here and that of the classic Eady (1949) problem for baroclinic
instability is drawn. We conjecture as to the mathematical/physical nature of
the SRI.
The general linear problem...

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## Nonlinear supratransmission as a fundamental instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/10/2003

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The nonlinear supratransmission is the property of a nonlinear system
possessing a natural forbidden band gap to transmit energy of a signal with a
frequency in the gap by means of generation of nonlinear modes (gap solitons).
This process is shown to result from a generic instability of the evanescent
wave profile generated in a nonlinear medium by the incident signal.; Comment: 4 figures, to appear in Physics Letters A

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## The Instability of Charged Black Strings and p-Branes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/04/1994

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We investigate the evolution of small perturbations around charged black
strings and branes which are solutions of low energy string theory. We give the
details of the analysis for the uncharged case which was summarized in a
previous paper. We extend the analysis to the small charge case and give also
an analysis for the generic case, following the behavior of unstable modes as
the charge is modified. We study specifically a magnetically charged black
6-brane, but show how the instability is generic, and that charge does not in
general stabilise black strings and p-branes.; Comment: 41 pages plain TeX, 6 figures appended at end of file,
DAMTP/R-94/7,LA-UR-93-4473

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## Resonance and marginal instability of switching systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/11/2014

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We analyse the so-called Marginal Instability of linear switching systems,
both in continuous and discrete time. This is a phenomenon of unboundedness of
trajectories when the Lyapunov exponent is zero. We disprove two recent
conjectures of Chitour, Mason, and Sigalotti (2012) stating that for generic
systems, the resonance is sufficient for marginal instability and for
polynomial growth of the trajectories. We provide a characterization of
marginal instability under some mild assumptions on the sys- tem. These
assumptions can be verified algorithmically and are believed to be generic.
Finally, we analyze possible types of fastest asymptotic growth of
trajectories. An example of a pair of matrices with sublinear growth is given.

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## Gravitational Instability of de Sitter Compactifications

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/03/2004

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#High Energy Physics - Theory#Astrophysics#General Relativity and Quantum Cosmology#High Energy Physics - Phenomenology

We consider warped compactifications in (4+d)-dimensional theories, with four
dimensional de Sitter dS_4 vacua (with Hubble parameter H) and with a compact
internal space. After introducing a gauge-invariant formalism for the generic
metric perturbations of these backgrounds, we focus on modes which are scalar
with respect to dS_4. The physical eigenmasses of these modes acquire a large
universal tachyonic contribution -12d/(d+2) H^2, independently of the
stabilization mechanism for the compact space, in addition to the usual KK
masses, which instead encode the effects of the stabilization. General
arguments, as well as specific examples, lead us to conjecture that, for
sufficiently large dS curvature, the compactified geometry becomes
gravitationally unstable due to the tachyonic growth of the scalar
perturbations. This mean that for any stabilization mechanism the curvature of
the dS geometry cannot exceed some critical value. We relate this effect to the
anisotropy of the bulk geometry and suggest the end points of the instability.
Of relevance for inflationary cosmology, the perturbations of the bulk metric
inevitably induce a new modulus field, which describes the conformal
fluctuations of the 4 dimensional metric. If this mode is light during
inflation...

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## Generic perturbations of linear integrable Hamiltonian systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/11/2015

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In this paper, we investigate perturbations of linear integrable Hamiltonian
systems, with the aim of establishing results in the spirit of the KAM theorem
(preservation of invariant tori), the Nekhoroshev theorem (stability of the
action variables for a finite but long interval of time) and Arnold diffusion
(instability of the action variables). Whether the frequency of the integrable
system is resonant or not, it is known that the KAM theorem does not hold true
for all perturbations; when the frequency is resonant, it is the Nekhoroshev
theorem which does not hold true for all perturbations. Our first result deals
with the resonant case: we prove a result of instability for a generic
perturbation, which implies that the KAM and the Nekhoroshev theorem do not
hold true even for a generic perturbation. The case where the frequency is
non-resonant is more subtle. Our second result shows that for a generic
perturbation, the KAM theorem holds true. Concerning the Nekhrosohev theorem,
it is known that one has stability over an exponentially long interval of time,
and that this cannot be improved for all perturbations. Our third result shows
that for a generic perturbation, one has stability for a doubly exponentially
long interval of time. The only question left unanswered is whether one has
instability for a generic perturbation (necessarily after this very long
interval of time).

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## Semiclassical Instability of the Cauchy Horizon in Self-Similar Collapse

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Generic spherically symmetric self-similar collapse results in strong
naked-singularity formation. In this paper we are concerned with particle
creation during a naked-singularity formation in spherically symmetric
self-similar collapse without specifying the collapsing matter. In the generic
case, the power of particle emission is found to be proportional to the inverse
square of the remaining time to the Cauchy horizon (CH). The constant of
proportion can be arbitrarily large in the limit to marginally naked
singularity. Therefore, the unbounded power is especially striking in the case
that an event horizon is very close to the CH because the emitted energy can be
arbitrarily large in spite of a cutoff expected from quantum gravity. Above
results suggest the instability of the CH in spherically symmetric self-similar
spacetime from quantum field theory and seem to support the existence of a
semiclassical cosmic censor. The divergence of redshifts and blueshifts of
emitted particles is found to cause the divergence of power to positive or
negative infinity, depending on the coupling manner of scalar fields to
gravity. On the other hand, it is found that there is a special class of
self-similar spacetimes in which the semiclassical instability of the CH is not
efficient. The analyses in this paper are based on the geometric optics
approximation...

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## Instability, Intermittency and Multiscaling in Discrete Growth Models of Kinetic Roughening

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 28/07/1996

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We show by numerical simulations that discretized versions of commonly
studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang
equation and the Lai-Das Sarma equation) and related atomistic models of
epitaxial growth have a generic instability in which isolated pillars (or
grooves) on an otherwise flat interface grow in time when their height (or
depth) exceeds a critical value. Depending on the details of the model, the
instability found in the discretized version may or may not be present in the
truly continuum growth equation, indicating that the behavior of discretized
nonlinear growth equations may be very different from that of their continuum
counterparts. This instability can be controlled either by the introduction of
higher-order nonlinear terms with appropriate coefficients or by restricting
the growth of pillars (or grooves) by other means. A number of such
``controlled instability'' models are studied by simulation. For appropriate
choice of the parameters used for controlling the instability, these models
exhibit intermittent behavior, characterized by multiexponent scaling of height
fluctuations, over the time interval during which the instability is active.
The behavior found in this regime is very similar to the ``turbulent'' behavior
observed in recent simulations of several one- and two-dimensional atomistic
models of epitaxial growth. [pacs{61.50.Cj...

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## Instability driven by boundary inflow across shear: a way to circumvent Rayleigh's stability criterion in accretion disks?

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We investigate the 2D instability recently discussed by Gallet et al. (2010)
and Ilin \& Morgulis (2013) which arises when a radial crossflow is imposed on
a centrifugally-stable swirling flow. By finding a simpler rectilinear example
of the instability - a sheared half plane, the minimal ingredients for the
instability are identified and the destabilizing/stabilizing effect of
inflow/outflow boundaries clarified. The instability - christened `boundary
inflow instability' here - is of critical layer type where this layer is either
at the inflow wall and the growth rate is $O(\sqrt{\eta})$ (as found by Ilin \&
Morgulis 2013), or in the interior of the flow and the growth rate is $O(\eta
\log 1/\eta)$ where $\eta$ measures the (small) inflow-to-tangential-flow
ratio. The instability is robust to changes in the rotation profile even to
those which are very Rayleigh-stable and the addition of further physics such
as viscosity, 3-dimensionality and compressibility but is sensitive to the
boundary condition imposed on the tangential velocity field at the inflow
boundary. Providing the vorticity is not fixed at the inflow boundary, the
instability seems generic and operates by the inflow advecting vorticity
present at the boundary across the interior shear. Both the primary bifurcation
to 2D states and secondary bifurcations to 3D states are found to be
supercritical. Assuming an accretion flow driven by molecular viscosity only so
$\eta=O(Re^{-1})$...

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## Accurate simulations of the dynamical bar-mode instability in full General Relativity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We present accurate simulations of the dynamical bar-mode instability in full
General Relativity focussing on two aspects which have not been investigated in
detail in the past. Namely, on the persistence of the bar deformation once the
instability has reached its saturation and on the precise determination of the
threshold for the onset of the instability in terms of the parameter
$\beta={T}/{|W|}$. We find that generic nonlinear mode-coupling effects appear
during the development of the instability and these can severely limit the
persistence of the bar deformation and eventually suppress the instability. In
addition, we observe the dynamics of the instability to be strongly influenced
by the value $\beta$ and on its separation from the critical value $\beta_c$
marking the onset of the instability. We discuss the impact these results have
on the detection of gravitational waves from this process and provide evidence
that the classical perturbative analysis of the bar-mode instability for
Newtonian and incompressible Maclaurin spheroids remains qualitatively valid
and accurate also in full General Relativity.; Comment: RevTeX4, 23 pages, 19 figures. Version in print

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## Onset of fingering instability in a finite slice of adsorbed solute

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/05/2015

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The effect of a linear adsorption isotherm on the onset of fingering
instability in a miscible displacement in the application of liquid
chromatography, pollutant contamination in aquifers etc. is investigated. Such
fingering instability on the solute dynamics arise due to the miscible viscus
fingering (VF) between the displacing fluid and sample solvent. We use a
Fourier pseudo-spectral method to solve the initial value problem appeared in
the linear stability analysis. The present linear stability analysis is of
generic type and it captures the early time diffusion dominated region which
was never expressible through the quasi-steady state analysis (QSSA). In
addition, it measures the onset of instability more accurately than the QSSA
methods. It is shown that the onset time depends non-monotonically on the
retention parameter of the solute adsorption. This qualitative influence of the
retention parameter on the onset of instability resemblances with the results
obtained from direct numerical simulations of the nonlinear equations.
Moreover, the present linear stability method helps for an appropriate
characterisation of the linear and the nonlinear regimes of miscible VF
instability and also can be useful for the fluid flow problems with the
unsteady base-state.; Comment: 30 pages...

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## Elliptical instability in terrestrial planets and moons

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 08/03/2012

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The presence of celestial companions means that any planet may be subject to
three kinds of harmonic mechanical forcing: tides, precession/nutation, and
libration. These forcings can generate flows in internal fluid layers, such as
fluid cores and subsurface oceans, whose dynamics then significantly differ
from solid body rotation. In particular, tides in non-synchronized bodies and
libration in synchronized ones are known to be capable of exciting the
so-called elliptical instability, i.e. a generic instability corresponding to
the destabilization of two-dimensional flows with elliptical streamlines,
leading to three-dimensional turbulence. We aim here at confirming the
relevance of such an elliptical instability in terrestrial bodies by
determining its growth rate, as well as its consequences on energy dissipation,
on magnetic field induction, and on heat flux fluctuations on planetary scales.
Previous studies and theoretical results for the elliptical instability are
re-evaluated and extended to cope with an astrophysical context. In particular,
generic analytical expressions of the elliptical instability growth rate are
obtained using a local WKB approach, simultaneously considering for the first
time (i) a local temperature gradient due to an imposed temperature contrast
across the considered layer or to the presence of a volumic heat source and
(ii) an imposed magnetic field along the rotation axis...

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## Final State of Gregory-Laflamme Instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/06/2011

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We describe the behavior of a perturbed 5-dimensional black string subject to
the Gregory-Laflamme instability. We show that the horizon evolves in a
self-similar manner, where at any moment in the late-time development of the
instability the horizon can be described as a sequence of 3-dimensional
spherical black holes of varying size, joined by black string segments of
similar radius. As with the initial black string, each local string segment is
itself unstable, and this fuels the self-similar cascade to (classically)
arbitrarily small scales; in the process the horizon develops a fractal
structure. In finite asymptotic time, the remaining string segments shrink to
zero-size, yielding a naked singularity. Since no fine-tuning is required to
excite the instability, this constitutes a generic violation of cosmic
censorship. We further discuss how this behavior is related to satellite
formation in low-viscosity fluid streams subject to the Rayleigh-Plateau
instability, and estimate the fractal dimension of the horizon prior to
formation of the naked singularity.; Comment: 27 pages, 6 Figures. Chapter of the book `Black Holes in Higher
Dimensions' to be published by Cambridge University Press (editor: G.
Horowitz)

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## Pattern generation by dissipative parametric instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/12/2015

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Nonlinear instabilities are responsible for spontaneous pattern formation in
a vast number of natural and engineered systems ranging from biology to
galaxies build-up. We propose a new instability mechanism leading to pattern
formation in spatially extended nonlinear systems based on a periodic antiphase
modulation of spectrally-dependent losses arranged in a zig-zag way: an
effective filtering is imposed at symmetrically located wavenumbers k and -k in
alternating order. The properties of the dissipative parametric instability
differ from the features of the both key classical concepts of modulation
instabilities: the Benjamin-Feir, and the Faraday instability. We demonstrate
how dissipative parametric instability can lead to the formation of stable
patterns in one and two-dimensional systems. The proposed instability mechanism
is generic and can naturally occur or can be implemented in various physical
systems.

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## Libration driven elliptical instability

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/06/2012

Relevância na Pesquisa

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The elliptical instability is a generic instability which takes place in any
rotating flow whose streamlines are elliptically deformed. Up to now, it has
been widely studied in the case of a constant, non-zero differential rotation
between the fluid and the elliptical distortion with applications in
turbulence, aeronautics, planetology and astrophysics. In this letter, we
extend previous analytical studies and report the first numerical and
experimental evidence that elliptical instability can also be driven by
libration, i.e. periodic oscillations of the differential rotation between the
fluid and the elliptical distortion, with a zero mean value. Our results
suggest that intermittent, space-filling turbulence due to this instability can
exist in the liquid cores and sub-surface oceans of so-called synchronized
planets and moons.

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## Proof of linear instability of the Reissner-Nordstr\"om Cauchy horizon under scalar perturbations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/01/2015

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It has long been suggested that solutions to linear scalar wave equation
$$\Box_g\phi=0$$ on a fixed subextremal Reissner-Nordstr\"om spacetime with
non-vanishing charge are generically singular at the Cauchy horizon. We prove
that generic smooth and compactly supported initial data on a Cauchy
hypersurface indeed give rise to solutions with infinite nondegenerate energy
near the Cauchy horizon in the interior of the black hole. In particular, the
solution generically does not belong to $W^{1,2}_{loc}$. This instability is
related to the celebrated blue shift effect in the interior of the black hole.
The problem is motivated by the strong cosmic censorship conjecture and it is
expected that for the full nonlinear Einstein-Maxwell system, this instability
leads to a singular Cauchy horizon for generic small perturbations of
Reissner-Nordstr\"om spacetime. Moreover, in addition to the instability
result, we also show as a consequence of the proof that Price's law decay is
generically sharp along the event horizon.

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## Generic Features of Modulational Instability in Nonlocal Kerr Media

Fonte: American Physical Society
Publicador: American Physical Society

Tipo: Artigo de Revista Científica

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#Keywords: Bandwidth#Bifurcation (mathematics)#Fourier transforms#Light propagation#Nonlinear optics#Optical beam splitters#Optical transfer function#Plasma waves#Polarization#Raman scattering#Refractive index

The modulational instability (MI) of plane waves in nonlocal Kerr media is studied for a general response function. Several generic properties are proven mathematically, with emphasis on how new gain bands are formed through a bifurcation process when the degree of nonlocality, σ, passes certain bifurcation values and how the bandwidth and maximum of each individual gain band depends on σ. The generic properties of the MI gain spectrum, including the bifurcation phenomena, are then demonstrated for the exponential and rectangular response functions. For a focusing nonlinearity the nonlocality tends to suppress MI, but can never remove it completely, irrespectively of the shape of the response function. For a defocusing nonlinearity the stability properties depend sensitively on the profile of the response function. For response functions with a positive-definite spectrum, such as Gaussians and exponentials, plane waves are always stable, whereas response functions with spectra that are not positive definite (such as the rectangular) will lead to MI if σ exceeds a certain threshold. For the square response function, in both the focusing and defocusing case, we show analytically and numerically how new gain bands that form at higher wave numbers when σ increases will eventually dominate the existing gain bands at lower wave numbers and abruptly change the length scale of the periodic pattern that may be observed in experiments.

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