3,054 research outputs found
Rim curvature anomaly in thin conical sheets revisited
This paper revisits one of the puzzling behaviors in a developable cone
(d-cone), the shape obtained by pushing a thin sheet into a circular container
of radius by a distance [E. Cerda, S. Chaieb, F. Melo, and L.
Mahadevan, {\sl Nature} {\bf 401}, 46 (1999)]. The mean curvature was reported
to vanish at the rim where the d-cone is supported [T. Liang and T. A. Witten,
{\sl Phys. Rev. E} {\bf 73}, 046604 (2006)]. We investigate the ratio of the
two principal curvatures versus sheet thickness over a wider dynamic range
than was used previously, holding and fixed. Instead of tending
towards 1 as suggested by previous work, the ratio scales as .
Thus the mean curvature does not vanish for very thin sheets as previously
claimed. Moreover, we find that the normalized rim profile of radial curvature
in a d-cone is identical to that in a "c-cone" which is made by pushing a
regular cone into a circular container. In both c-cones and d-cones, the ratio
of the principal curvatures at the rim scales as ,
where is the pushing force and is the Young's modulus. Scaling
arguments and analytical solutions confirm the numerical results.Comment: 25 pages, 12 figures. Added references. Corrected typos. Results
unchange
Optimal strategies for a game on amenable semigroups
The semigroup game is a two-person zero-sum game defined on a semigroup S as
follows: Players 1 and 2 choose elements x and y in S, respectively, and player
1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the
semigroup is amenable in the sense of Day and von Neumann, one can extend the
set of classical strategies, namely countably additive probability measures on
S, to include some finitely additive measures in a natural way. This extended
game has a value and the players have optimal strategies. This theorem extends
previous results for the multiplication game on a compact group or on the
positive integers with a specific payoff. We also prove that the procedure of
extending the set of allowed strategies preserves classical solutions: if a
semigroup game has a classical solution, this solution solves also the extended
game.Comment: 17 pages. To appear in International Journal of Game Theor
Light-Cone Quantization of the Liouville Model
We present the quantization of the Liouville model defined in light-cone
coordinates in (1,1) signature space. We take advantage of the representation
of the Liouville field by the free field of the Backl\"{u}nd transformation and
adapt the approch by Braaten, Curtright and Thorn.
Quantum operators of the Liouville field ,
, , are constructed consistently in
terms of the free field. The Liouville model field theory space is found to be
restricted to the sector with field momentum , , which
is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6
Properties of Ridges in Elastic Membranes
When a thin elastic sheet is confined to a region much smaller than its size
the morphology of the resulting crumpled membrane is a network of straight
ridges or folds that meet at sharp vertices. A virial theorem predicts the
ratio of the total bending and stretching energies of a ridge. Small strains
and curvatures persist far away from the ridge. We discuss several kinds of
perturbations that distinguish a ridge in a crumpled sheet from an isolated
ridge studied earlier (A. E. Lobkovsky, Phys. Rev. E. 53 3750 (1996)). Linear
response as well as buckling properties are investigated. We find that quite
generally, the energy of a ridge can change by no more than a finite fraction
before it buckles.Comment: 13 pages, RevTeX, acknowledgement adde
Relaxation and reconstruction on (111) surfaces of Au, Pt, and Cu
We have theoretically studied the stability and reconstruction of (111)
surfaces of Au, Pt, and Cu. We have calculated the surface energy, surface
stress, interatomic force constants, and other relevant quantities by ab initio
electronic structure calculations using the density functional theory (DFT), in
a slab geometry with periodic boundary conditions. We have estimated the
stability towards a quasi-one-dimensional reconstruction by using the
calculated quantities as parameters in a one-dimensional Frenkel-Kontorova
model. On all surfaces we have found an intrinsic tensile stress. This stress
is large enough on Au and Pt surfaces to lead to a reconstruction in which a
denser surface layer is formed, in agreement with experiment. The
experimentally observed differences between the dense reconstruction pattern on
Au(111) and a sparse structure of stripes on Pt(111) are attributed to the
details of the interaction potential between the first layer of atoms and the
substrate.Comment: 8 pages, 3 figures, submitted to Physical Review
Effects of horizontal whole-body vibration and standing posture on activity interference
The role of social capital in participatory arts for wellbeing: findings from a qualitative systematic review
BACKGROUND:Social capital is often cited as shaping impacts of participatory arts, although the concept has not been systematically mapped in arts, health and wellbeing contexts. In wider health inequalities research, complex, differential, and sometimes negative impacts of social capital have been recognised. METHODS:This paper maps of social capital concepts in qualitative research as part of the UK What Works for Wellbeing evidence review programme on culture, sport and wellbeing. RESULTS:Studies often cite positive impacts of bonding and, to a lesser extent, bridging social capital. However, reported challenges suggest the need for a critical approach. Forms of linking social capital, such as reframing and political engagement to address social divisions, are less often cited but may be important in participatory arts and wellbeing. CONCLUSIONS:Future research should further specify dimensions of social capital as well as their nuanced effects in arts, and wellbeing contexts
Resourcefulness, reciprocity and reflexivity: the three Rs of partnership in sport for public health research
This paper explores the dynamics of research–policy–practice (RPP) partnerships in sport. Such partnerships, involving a diverse range of groups, have emerged as a response to: (1) a contemporary political prioritisation in the use of sport for health and wellbeing and (2) a parallel requirement for robust evidence of effectiveness and cost-effectiveness. A conceptual framework for understanding such RPP partnerships is proposed and discussed in relation to three overlapping characteristics; resourcefulness, reciprocity and reflexivity. The paper concludes that understanding these three Rs of RPP partnerships is a way to demythologise the role of sport in public health and present theoretically informed analyses about processes of knowledge production, dissemination and use. It is a conceptual framework which might also further an understanding of, and make public, issues concerning the legitimation of some forms of evidence over others, and potentially maximise the impact of the co-production of knowledge about sport for public health and wellbeing
Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory
We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory.
The proof uses a shift acting on all external momenta, and we show that every
N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this
shift. The MHV vertex expansion allows us to derive compact and efficient
generating functions for all N^kMHV tree amplitudes of the theory. We also
derive an improved form of the anti-NMHV generating function. The proof leads
to a curious set of sum rules for the diagrams of the MHV vertex expansion.Comment: 40 pages, 7 figure
Comparison of machine learning algorithms in restaurant revenue prediction
In this paper, we address several aspects of applying classical machine learning algorithms to a regression problem. We compare the predictive power to validate our approach on a data about revenue of a large Russian restaurant chain. We pay special attention to solve two problems: data heterogeneity and a high number of correlated features. We describe methods for considering heterogeneity—observations weighting and estimating models on subsamples. We define a weighting function via Mahalanobis distance in the space of features and show its predictive properties on following methods: ordinary least squares regression, elastic net, support vector regression, and random forest.</p
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