289,802 research outputs found
Minimum description length with local geometry
pre-printEstablishing optimal correspondence across object populations is essential to statistical shape analysis. Minimizing the description length (MDL) is a popular method for finding correspondence. In this work, we extend the MDL method by incorporating various local curvature metrics. Using local curvature can improve performance by ensuring that corresponding points exhibit similar local geometric characteristics that can't always be captured by mere point locations. We illustrate results on a variety of anatomical structures. The MDL method with a combination of point locations and curvature outperforms all the other methods we analyzed, including traditional MDL and spherical harmonics (SPHARM) correspondence, when the analyzed object population exhibits complex structure. When the objects are of simple nature, however, there's no added benefit to using the local curvature. In our experiments, we did not observe a significant difference in the correspondence quality when different curvature metrics (e.g. principal curvatures, mean curvature, Gaussian curvature) were used
3D FEM model development from 3D optical measurement technique applied to corroded steel bars
Understanding the mechanical effects of the corrosion pits on the steel surface requires an accurate definition of their geometry and distribution along the rebar. 3D optical measurement technique is used to obtain the outer geometry of artificially corroded bars tested under cyclic or monotonic loads. 3D FEM model development from the 3D scanning results were carried out in order to investigate the failure process and local effects on the pits, which are responsible of the variation of the mechanical properties in corroded steel reinforcement. In addition, a validation of a simplified model, which allows the mechanical steel properties determination given an estimated corrosion level, is presented. 3D models were convenient to observe and measure the local effects on the pits.Peer ReviewedPostprint (author's final draft
D3 branes in a Melvin universe: a new realm for gravitational holography
The decoupling limit of a certain configuration of D3 branes in a Melvin
universe defines a sector of string theory known as Puff Field Theory (PFT) - a
theory with non-local dynamics but without gravity. In this work, we present a
systematic analysis of the non-local states of strongly coupled PFT using
gravitational holography. And we are led to a remarkable new holographic
dictionary. We show that the theory admits states that may be viewed as brane
protrusions from the D3 brane worldvolume. The footprint of a protrusion has
finite size - the scale of non-locality in the PFT - and corresponds to an
operator insertion in the PFT. We compute correlators of these states, and we
demonstrate that only part of the holographic bulk is explored by this
computation. We then show that the remaining space holographically encodes the
dynamics of the D3 brane tentacles. The two sectors are coupled: in this
holographic description, this is realized via quantum entanglement across a
holographic screen - a throat in the geometry - that splits the bulk into the
two regions in question. We then propose a description of PFT through a direct
product of two Fock spaces - akin to other non-local settings that employ
quantum group structures.Comment: 44 pages, 13 figures; v2: minor corrections, citations added; v3:
typos corrected in section on local operators, some asymptotic expansions
improved and made more consistent with rest of paper in section on non-local
operator
The Hawking-Page crossover in noncommutative anti-deSitter space
We study the problem of a Schwarzschild-anti-deSitter black hole in a
noncommutative geometry framework, thought to be an effective description of
quantum-gravitational spacetime. As a first step we derive the noncommutative
geometry inspired Schwarzschild-anti-deSitter solution. After studying the
horizon structure, we find that the curvature singularity is smeared out by the
noncommutative fluctuations. On the thermodynamics side, we show that the black
hole temperature, instead of a divergent behavior at small scales, admits a
maximum value. This fact implies an extension of the Hawking-Page transition
into a van der Waals-like phase diagram, with a critical point at a critical
cosmological constant size in Plank units and a smooth crossover thereafter. We
speculate that, in the gauge-string dictionary, this corresponds to the
confinement "critical point" in number of colors at finite number of flavors, a
highly non-trivial parameter that can be determined through lattice
simulations.Comment: 24 pages, 6 figure, 1 table, version matching that published on JHE
Force dipoles and stable local defects on fluid vesicles
An exact description is provided of an almost spherical fluid vesicle with a
fixed area and a fixed enclosed volume locally deformed by external normal
forces bringing two nearby points on the surface together symmetrically. The
conformal invariance of the two-dimensional bending energy is used to identify
the distribution of energy as well as the stress established in the vesicle.
While these states are local minima of the energy, this energy is degenerate;
there is a zero mode in the energy fluctuation spectrum, associated with area
and volume preserving conformal transformations, which breaks the symmetry
between the two points. The volume constraint fixes the distance , measured
along the surface, between the two points; if it is relaxed, a second zero mode
appears, reflecting the independence of the energy on ; in the absence of
this constraint a pathway opens for the membrane to slip out of the defect.
Logarithmic curvature singularities in the surface geometry at the points of
contact signal the presence of external forces. The magnitude of these forces
varies inversely with and so diverges as the points merge; the
corresponding torques vanish in these defects. The geometry behaves near each
of the singularities as a biharmonic monopole, in the region between them as a
surface of constant mean curvature, and in distant regions as a biharmonic
quadrupole. Comparison of the distribution of stress with the quadratic
approximation in the height functions points to shortcomings of the latter
representation. Radial tension is accompanied by lateral compression, both near
the singularities and far away, with a crossover from tension to compression
occurring in the region between them.Comment: 26 pages, 10 figure
The Hawking-Page crossover in noncommutative anti-deSitter space
We study the problem of a Schwarzschild-anti-deSitter black hole in a
noncommutative geometry framework, thought to be an effective description of
quantum-gravitational spacetime. As a first step we derive the noncommutative
geometry inspired Schwarzschild-anti-deSitter solution. After studying the
horizon structure, we find that the curvature singularity is smeared out by the
noncommutative fluctuations. On the thermodynamics side, we show that the black
hole temperature, instead of a divergent behavior at small scales, admits a
maximum value. This fact implies an extension of the Hawking-Page transition
into a van der Waals-like phase diagram, with a critical point at a critical
cosmological constant size in Plank units and a smooth crossover thereafter. We
speculate that, in the gauge-string dictionary, this corresponds to the
confinement "critical point" in number of colors at finite number of flavors, a
highly non-trivial parameter that can be determined through lattice
simulations.Comment: 24 pages, 6 figure, 1 table, version matching that published on JHE
Thermodynamical phases of a regular SAdS black hole
This paper studies the thermodynamical stability of regular BHs in AdS5
background. We investigate off-shell free energy of the system as a function of
temperature for different values of a "coupling constant" L=4 theta/l^2, where
the cosmological constant is Lambda = -3/l^2 and \sqrt{theta} is a "minimal
length". The parameter L admits a critical value, L_{inf}=0.2, corresponding to
the appearance of an inflexion point in the Hawking temperature. In the
weak-coupling regime L < L_{inf}, there are first order phase transitions at
different temperatures. Unlike the Hawking-Page case, at temperature 0\le T \le
T_{min} the ground state is populated by "cold" near-extremal BHs instead of a
pure radiation. On the other hand, for L \g L_{inf} only large,
thermodynamically stable, BHs exist.Comment: 12 pages; 6 Figures; accepted for publication in Int. J. Mod. Phys.
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