scholarly journals Cheeger bounds on spin-two fields

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
G. Bruno De Luca ◽  
Nicolò De Ponti ◽  
Andrea Mondino ◽  
Alessandro Tomasiello
Keyword(s):  
Lower Bounds ◽  
Degrees Of Freedom ◽  
Small Mass ◽  
Internal Space ◽  
Graviton Mass ◽  
Cheeger Constant ◽  
Massive Spin

Abstract We consider gravity compactifications whose internal space consists of small bridges connecting larger manifolds, possibly noncompact. We prove that, under rather general assumptions, this leads to a massive spin-two field with very small mass. The argument involves a recently-noticed relation to Bakry-Émery geometry, a version of the so-called Cheeger constant, and the theory of synthetic Ricci lower bounds. The latter technique allows generalizations to non-smooth spaces such as those with D-brane singularities. For AdSd vacua with a bridge admitting an AdSd+1 interpretation, the holographic dual is a CFTd with two CFTd−1 boundaries. The ratio of their degrees of freedom gives the graviton mass, generalizing results obtained by Bachas and Lavdas for d = 4. We also prove new bounds on the higher eigenvalues. These are in agreement with the spin-two swampland conjecture in the regime where the background is scale-separated; in the opposite regime we provide examples where they are in naive tension with it.

scholarly journals Group Contractions: Inonu, Wigner, and Einstein

1997 ◽  
Vol 12 (01) ◽  
pp. 71-78 ◽  
Author(s):  
Y.S. Kim
Keyword(s):  
Degrees Of Freedom ◽  
Small Mass ◽  
Space Time ◽  
Internal Space ◽  
Large Momentum ◽  
Energy Relation ◽  
Large Radius ◽  
Massless Particles ◽  
Massive Particles

Einstein's E = mc2 unifies the momentum-energy relation for massive and massless particles. According to Wigner, the internal space–time symmetries of massive and massless particles are isomorphic to O(3) and E(2) respectively. According to Inonu and Wigner, O(3) can be contracted to E(2) in the large-radius limit. It is noted that the O(3)-like little group for massive particles can be contracted to the E(2)-like little group for massless particles in the limit of large momentum and/or small mass. It is thus shown that transverse rotational degress of freedom for massive particles become contracted to gauge degrees of freedom for massless particles.

Mode-crystallography analysis of the crystal structures and the low- and high-temperature phase transitions in Na0.5K0.5NbO3

2015 ◽  
Vol 48 (2) ◽  
pp. 318-333 ◽  
Author(s):  
B. Orayech ◽  
A. Faik ◽  
G. A. López ◽  
O. Fabelo ◽  
J. M. Igartua
Keyword(s):  
Phase Transitions ◽  
High Temperature ◽  
Crystal Structures ◽  
Degrees Of Freedom ◽  
High Temperature Phase ◽  
Structure Evolution ◽  
Internal Space ◽  
Temperature Phase ◽  
Conventional Solid State Reaction ◽  
Space Group

Na0.5K0.5NbO3has been synthesized by the conventional solid-state reaction process. The crystal structures and phase transitions, at low and high temperature, determined from the Rietveld refinements of X-ray and neutron powder diffraction data are reported. The structure evolution of Na0.5K0.5NbO3in the temperature range from 2 to 875 K shows the presence of three phase transitions. The first one, at ∼135 K, is discontinuous from the rhombohedralR3c(No. 161) space group to the room-temperature orthorhombicAmm2 (No. 38) space group; the second is discontinuous from the orthorhombic to the tetragonalP4mmspace group (No. 99) at ∼465 K, and the third is continuous from the tetragonal to the cubic Pm\overline{3}m space group (No. 221) at ∼700 K. The obtained phase-transition sequence isR3c→Amm2 →P4mm→Pm\overline{3}m. No previous studies at low temperature have been carried out on the material with composition Na0.5K0.5NbO3. In the course of the determination of the three experimentally found phases, a novel method of refinement is presented. This is a step forward in the use of the symmetry-adapted modes as degrees of freedom in the refinement process: the parameterization of a direction in the internal space of the, in this case, sole irreducible representation, GM4−, responsible for the symmetry breaking from the parent cubic space group to the polar distorted low-symmetry phases. Eventually, this procedure enables the calculation of the spontaneous polarization.

scholarly journals Expected Logarithm and Negative Integer Moments of a Noncentral χ2-Distributed Random Variable

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 1048
Author(s):  
Stefan Moser
Keyword(s):  
Closed Form ◽  
Lower Bounds ◽  
Degrees Of Freedom ◽  
Random Variable ◽  
Negative Integer ◽  
Upper And Lower Bounds ◽  
Basic Properties

Closed-form expressions for the expected logarithm and for arbitrary negative integer moments of a noncentral χ2-distributed random variable are presented in the cases of both even and odd degrees of freedom. Moreover, some basic properties of these expectations are derived and tight upper and lower bounds on them are proposed.

Experimental Comparison of Two Degrees-of-Freedom Vortex-Induced Vibration on High and Low Aspect Ratio Cylinders with Small Mass Ratio

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Rodolfo T. Gonçalves ◽  
Guilherme F. Rosetti ◽  
André L. C. Fujarra ◽  
Guilherme R. Franzini ◽  
César M. Freire ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Degrees Of Freedom ◽  
Small Mass ◽  
Experimental Comparison ◽  
Small Scale ◽  
Mass Ratio ◽  
Vortex Induced Vibration ◽  
Two Degrees Of Freedom ◽  
Low Aspect Ratio ◽  
Aspect Ratios

Vortex-induced motion (VIM) is a specific way for naming the vortex-induced vibration (VIV) acting on floating units. The VIM phenomenon can occur in monocolumn production, storage and offloading system (MPSO) and spar platforms, structures presenting aspect ratio lower than 4 and unity mass ratio, i.e., structural mass equal to the displaced fluid mass. These platforms can experience motion amplitudes of approximately their characteristic diameters, and therefore, the fatigue life of mooring lines and risers can be greatly affected. Two degrees-of-freedom VIV model tests based on cylinders with low aspect ratio and small mass ratio have been carried out at the recirculating water channel facility available at NDF-EPUSP in order to better understand this hydro-elastic phenomenon. The tests have considered three circular cylinders of mass ratio equal to one and different aspect ratios, respectively L/D = 1.0, 1.7, and 2.0, as well as a fourth cylinder of mass ratio equal to 2.62 and aspect ratio of 2.0. The Reynolds number covered the range from 10 000 to 50 000, corresponding to reduced velocities from 1 to approximately 12. The results of amplitude and frequency in the transverse and in-line directions were analyzed by means of the Hilbert-Huang transform method (HHT) and then compared to those obtained from works found in the literature. The comparisons have shown similar maxima amplitudes for all aspect ratios and small mass ratio, featuring a decrease as the aspect ratio decreases. Moreover, some changes in the Strouhal number have been indirectly observed as a consequence of the decrease in the aspect ratio. In conclusion, it is shown that comparing results of small-scale platforms with those from bare cylinders, all of them presenting low aspect ratio and small mass ratio, the laboratory experiments may well be used in practical investigation, including those concerning the VIM phenomenon acting on platforms.

scholarly journals On the mean and dispersion of the Moore-Penrose generalized inverse of a Wishart matrix

2020 ◽  
Vol 36 (36) ◽  
pp. 124-133
Author(s):  
Shinpei Imori ◽  
Dietrich Von Rosen
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Degrees Of Freedom ◽  
Generalized Inverse ◽  
Upper And Lower Bounds ◽  
Exact Results ◽  
Identity Matrix ◽  
Wishart Matrix ◽  
The Mean ◽  
Scale Matrix

The Moore-Penrose inverse of a singular Wishart matrix is studied. When the scale matrix equals the identity matrix the mean and dispersion matrices of the Moore-Penrose inverse are known. When the scale matrix has an arbitrary structure no exact results are available. The article complements the existing literature by deriving upper and lower bounds for the expectation and an upper bound for the dispersion of the Moore-Penrose inverse. The results show that the bounds become large when the number of rows (columns) of the Wishart matrix are close to the degrees of freedom of the distribution.

scholarly journals Massive islands

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Hao Geng ◽  
Andreas Karch
Keyword(s):  
Simple Model ◽  
Degrees Of Freedom ◽  
Graviton Mass ◽  
Island Formation ◽  
Crucial Ingredient

Abstract We comment on the role of the graviton mass in recent calculations of the Page curve using holographic ideas. All reliable calculations of the Page curve in more than 2+1 spacetime dimensions have been performed in systems with massive gravitons. A crucial ingredient in these calculations is the formation of islands, regions that contribute to the entropy of degrees of freedom located elsewhere. While most often simply ignored, it is indeed true that mass of the graviton does not appear to significantly affect the calculations that appeared in the literature. We use the freedom to change the graviton mass to give an extremely simple model of analytically tractable island formation in general dimensions. We do however note that if one attempts to take the limit of zero graviton mass, any contribution from the islands disappears. This raises the question to what extent entanglement islands can play a role in standard massless gravity.

scholarly journals NEW ESTIMATES FOR EVANS' VARIATIONAL APPROACH TO WEAK KAM THEORY

2013 ◽  
Vol 15 (02) ◽  
pp. 1250055 ◽  
Author(s):  
OLGA BERNARDI ◽  
FRANCO CARDIN ◽  
MASSIMILIANO GUZZO
Keyword(s):  
Variational Principle ◽  
Hamiltonian Systems ◽  
Lower Bounds ◽  
Variational Approach ◽  
Degrees Of Freedom ◽  
Kam Theory ◽  
Weak Kam Theory ◽  
One Dimensional ◽  
Dynamic Interpretation ◽  
Geometric Content

We consider a recent approximate variational principle for weak KAM theory proposed by Evans. As in the case of classical integrability, for one-dimensional mechanical Hamiltonian systems all the computations can be carried out explicitly. In this setting, we illustrate the geometric content of the theory and prove new lower bounds for the estimates related to its dynamic interpretation. These estimates also extend to the case of n degrees of freedom.

NEWTON'S GRAVITATIONAL COUPLING CONSTANT FROM A QUANTUM OF AREA

2011 ◽  
Vol 26 (17) ◽  
pp. 1301-1308 ◽  
Author(s):  
F. R. KLINKHAMER
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Internal Space ◽  
Gravitational Coupling ◽  
Coupling Constant ◽  
Range Interaction ◽  
Gravitational Coupling Constant ◽  
Final Formula ◽  
Equipartition Law ◽  
Energy Equipartition

A previous calculation of Newton's gravitational coupling constant G is generalized. This generalization makes it possible to have "atoms of two-dimensional space" with an integer dimension d atom of the internal space, where the case d atom = 1 is found to be excluded. Given the quantum of area l2, the final formula for G is inversely proportional to the logarithm of the integer d atom . The generalization used may be interpreted as a modification of the energy equipartition law of the microscopic degrees of freedom responsible for gravity, suggesting some form of long-range interaction between these degrees of freedom themselves.

Innovative Designs for the Suspension System of Horizontal-Axis Washing Machines: Secondary Suspensions and Tuned Mass Dampers

2013 ◽  
Author(s):  
T. Argentini ◽  
M. Belloli ◽  
F. C. Robustelli ◽  
L. Martegani ◽  
G. Fraternale
Keyword(s):  
Dry Friction ◽  
Degrees Of Freedom ◽  
Low Cost ◽  
Small Mass ◽  
Suspension System ◽  
Shaking Table ◽  
Mode Shapes ◽  
Friction Dampers ◽  
Washing Machines ◽  
Secondary Suspension

Cabinet vibrations during spinning cycles of washing machines are often perceived negatively by customers, both in acoustic and visual terms. Therefore, in a market that is more and more oriented towards customer satisfaction and appliance efficiency, reducing cabinet vibrations and noise is a very attractive target. Previous experimental campaigns have highlighted that currently installed dry-friction dampers have highly non-linear characteristics and they are the main source of broadband forcing on the cabinet panels. To overcome these negative effects, two innovative designs for the suspension system have been studied and are here presented: the first solution is a secondary suspension system, designed to filter out the high frequency force components introduced by the dampers and therefore to mitigate panel vibrations; the second solution is more radical and it consists in removing the existing dampers and to substitute them with a tuned mass damper (TMD), directly fixed to the oscillating group. These solutions are a compromise between cost and efficiency, since a linear oil damper would impact excessively on the final cost of the appliance. The secondary suspension system has been designed to meet the very strict requirements of the manufacturer: low cost (which implies small mass) and applicable to the existing machine without any modification of any part other than the dampers themselves. The desired results have been achieved increasing the mass of the damper rod and introducing a fixed-fixed (or hinged-hinged) beam spring. The prototype of the secondary suspension has been tested independently and assembled in the washing machine, and the vibratory and acoustic results will be reported. The introduction of a TMD and the contextual removal of the dry-friction dampers, on the contrary, requires the modification of the oscillating group in order to work efficiently. As a matter of fact, a principle for the design of oscillating groups is the space optimization, which usually leads to asymmetric distributions of mass of the oscillating group, that in their turn lead to asymmetrically coupled mode shapes. This dynamic characteristic does not suit the design of a simple and compact TMD, with a limited number of degrees of freedom. We show that careful mass distribution and a specifically designed 2-dofs TMD can efficiently substitute the original dampers. An elemental prototype of the so defined TMD has been tested on a shaking table, and it seems an effective alternative to classical suspension systems.

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