2,571 research outputs found
Statistical state dynamics of weak jets in barotropic beta-plane turbulence
Zonal jets in a barotropic setup emerge out of homogeneous turbulence through
a flow-forming instability of the homogeneous turbulent state (`zonostrophic
instability') which occurs as the turbulence intensity increases. This has been
demonstrated using the statistical state dynamics (SSD) framework with a
closure at second order. Furthermore, it was shown that for small
supercriticality the flow-forming instability follows Ginzburg-Landau (G-L)
dynamics. Here, the SSD framework is used to study the equilibration of this
flow-forming instability for small supercriticality. First, we compare the
predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD
dynamics closed at second order for a wide ranges of parameters. A new branch
of jet equilibria is revealed that is not contiguously connected with the G-L
branch. This new branch at weak supercriticalities involves jets with larger
amplitude compared to the ones of the G-L branch. Furthermore, this new branch
continues even for subcritical values with respect to the linear flow-forming
instability. Thus, a new nonlinear flow-forming instability out of homogeneous
turbulence is revealed. Second, we investigate how both the linear flow-forming
instability and the novel nonlinear flow-forming instability are equilibrated.
We identify the physical processes underlying the jet equilibration as well as
the types of eddies that contribute in each process. Third, we propose a
modification of the diffusion coefficient of the G-L dynamics that is able to
capture the asymmetric evolution for weak jets at scales other than the
marginal scale (side-band instabilities) for the linear flow-forming
instability.Comment: 27 pages, 17 figure
Gradient flows and instantons at a Lifshitz point
I provide a broad framework to embed gradient flow equations in
non-relativistic field theory models that exhibit anisotropic scaling. The
prime example is the heat equation arising from a Lifshitz scalar field theory;
other examples include the Allen-Cahn equation that models the evolution of
phase boundaries. Then, I review recent results reported in arXiv:1002.0062
describing instantons of Horava-Lifshitz gravity as eternal solutions of
certain geometric flow equations on 3-manifolds. These instanton solutions are
in general chiral when the anisotropic scaling exponent is z=3. Some general
connections with the Onsager-Machlup theory of non-equilibrium processes are
also briefly discussed in this context. Thus, theories of Lifshitz type in d+1
dimensions can be used as off-shell toy models for dynamical vacuum selection
of relativistic field theories in d dimensions.Comment: 19 pages, 1 figure, contribution to conference proceedings (NEB14);
minor typos corrected in v
TuNet: End-to-end Hierarchical Brain Tumor Segmentation using Cascaded Networks
Glioma is one of the most common types of brain tumors; it arises in the
glial cells in the human brain and in the spinal cord. In addition to having a
high mortality rate, glioma treatment is also very expensive. Hence, automatic
and accurate segmentation and measurement from the early stages are critical in
order to prolong the survival rates of the patients and to reduce the costs of
the treatment. In the present work, we propose a novel end-to-end cascaded
network for semantic segmentation that utilizes the hierarchical structure of
the tumor sub-regions with ResNet-like blocks and Squeeze-and-Excitation
modules after each convolution and concatenation block. By utilizing
cross-validation, an average ensemble technique, and a simple post-processing
technique, we obtained dice scores of 88.06, 80.84, and 80.29, and Hausdorff
Distances (95th percentile) of 6.10, 5.17, and 2.21 for the whole tumor, tumor
core, and enhancing tumor, respectively, on the online test set.Comment: Accepted at MICCAI BrainLes 201
Five-Brane Configurations without a Strong Coupling Regime
Five-brane distributions with no strong coupling problems and high symmetry
are studied. The simplest configuration corresponds to a spherical shell of
branes with S^3 geometry and symmetry. The equations of motions with
delta-function sources are carefully solved in such backgrounds. Various other
brane distributions with sixteen unbroken supercharges are described. They are
associated to exact world-sheet superconformal field theories with domain-walls
in space-time. We study the equations of gravitational fluctuations, find
normalizable modes of bulk 6-d gravitons and confirm the existence of a mass
gap. We also study the moduli of the configurations and derive their
(normalizable) wave-functions. We use our results to calculate in a
controllable fashion using holography, the two-point function of the stress
tensor of little string theory in these vacua.Comment: LateX, 32 pages, 4 figures; (v2) A reference adde
Applications of Partial Supersymmetry
I examine quantum mechanical Hamiltonians with partial supersymmetry, and
explore two main applications. First, I analyze a theory with a logarithmic
spectrum, and show how to use partial supersymmetry to reveal the underlying
structure of this theory. This method reveals an intriguing equivalence between
two formulations of this theory, one of which is one-dimensional, and the other
of which is infinite-dimensional. Second, I demonstrate the use of partial
supersymmetry as a tool to obtain the asymptotic energy levels in
non-relativistic quantum mechanics in an exceptionally easy way. In the end, I
discuss possible extensions of this work, including the possible connections
between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on
title pag
Duality in deformed coset fermionic models
We study the -parafermion model perturbed by its first thermal
operator. By formulating the theory in terms of a (perturbed) fermionic coset
model we show that the model is equivalent to interacting WZW fields modulo
free fields. In this scheme, the order and disorder operators of the
parafermion theory are constructed as gauge invariant composites. We find that
the theory presents a duality symmetry that interchanges the roles of the spin
and dual spin operators. For two particular values of the coupling constant we
find that the theory recovers conformal invariance and the gauge symmetry is
enlarged. We also find a novel self-dual point.Comment: 13 pages, LaTex. Minor corrections. One reference added. Version to
appear in Nuc. Phys.
Dirichlet sigma models and mean curvature flow
The mean curvature flow describes the parabolic deformation of embedded
branes in Riemannian geometry driven by their extrinsic mean curvature vector,
which is typically associated to surface tension forces. It is the gradient
flow of the area functional, and, as such, it is naturally identified with the
boundary renormalization group equation of Dirichlet sigma models away from
conformality, to lowest order in perturbation theory. D-branes appear as fixed
points of this flow having conformally invariant boundary conditions. Simple
running solutions include the paper-clip and the hair-pin (or grim-reaper)
models on the plane, as well as scaling solutions associated to rational (p, q)
closed curves and the decay of two intersecting lines. Stability analysis is
performed in several cases while searching for transitions among different
brane configurations. The combination of Ricci with the mean curvature flow is
examined in detail together with several explicit examples of deforming curves
on curved backgrounds. Some general aspects of the mean curvature flow in
higher dimensional ambient spaces are also discussed and obtain consistent
truncations to lower dimensional systems. Selected physical applications are
mentioned in the text, including tachyon condensation in open string theory and
the resistive diffusion of force-free fields in magneto-hydrodynamics.Comment: 77 pages, 21 figure
Mixmaster universe in Horava-Lifshitz gravity
We consider spatially homogeneous (but generally non-isotropic) cosmologies
in the recently proposed Horava-Lifshitz gravity and compare them to those of
general relativity using Hamiltonian methods. In all cases, the problem is
described by an effective point particle moving in a potential well with
exponentially steep walls. Focusing on the closed-space cosmological model
(Bianchi type IX), the mixmaster dynamics is now completely dominated by the
quadratic Cotton tensor potential term for very small volume of the universe.
Unlike general relativity, where the evolution towards the initial singularity
always exhibits chaotic behavior with alternating Kasner epochs, the
anisotropic universe in Horava-Lifshitz gravity (with parameter lambda > 1/3)
is described by a particle moving in a frozen potential well with fixed (but
arbitrary) energy E. Alternating Kasner epochs still provide a good description
of the early universe for very large E, but the evolution appears to be
non-ergodic. For very small E there are harmonic oscillations around the fully
isotropic model. The question of chaos remains open for intermediate energy
levels.Comment: 1+35 pages, 4 figure
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