185 research outputs found
Measuring order in the isotropic packing of elastic rods
The packing of elastic bodies has emerged as a paradigm for the study of
macroscopic disordered systems. However, progress is hampered by the lack of
controlled experiments. Here we consider a model experiment for the isotropic
two-dimensional confinement of a rod by a central force. We seek to measure how
ordered is a folded configuration and we identify two key quantities. A
geometrical characterization is given by the number of superposed layers in the
configuration. Using temporal modulations of the confining force, we probe the
mechanical properties of the configuration and we define and measure its
effective compressibility. These two quantities may be used to build a
statistical framework for packed elastic systems.Comment: 4 pages, 5 figure
A comparative study of crumpling and folding of thin sheets
Crumpling and folding of paper are at rst sight very di erent ways of con
ning thin sheets in a small volume: the former one is random and stochastic
whereas the latest one is regular and deterministic. Nevertheless, certain
similarities exist. Crumpling is surprisingly ine cient: a typical crumpled
paper ball in a waste-bin consists of as much as 80% air. Similarly, if one
folds a sheet of paper repeatedly in two, the necessary force becomes so large
that it is impossible to fold it more than 6 or 7 times. Here we show that the
sti ness that builds up in the two processes is of the same nature, and
therefore simple folding models allow to capture also the main features of
crumpling. An original geometrical approach shows that crumpling is
hierarchical, just as the repeated folding. For both processes the number of
layers increases with the degree of compaction. We nd that for both processes
the crumpling force increases as a power law with the number of folded layers,
and that the dimensionality of the compaction process (crumpling or folding)
controls the exponent of the scaling law between the force and the compaction
ratio.Comment: 5 page
Fourier analysis of wave turbulence in a thin elastic plate
The spatio-temporal dynamics of the deformation of a vibrated plate is
measured by a high speed Fourier transform profilometry technique. The
space-time Fourier spectrum is analyzed. It displays a behavior consistent with
the premises of the Weak Turbulence theory. A isotropic continuous spectrum of
waves is excited with a non linear dispersion relation slightly shifted from
the linear dispersion relation. The spectral width of the dispersion relation
is also measured. The non linearity of this system is weak as expected from the
theory. Finite size effects are discussed. Despite a qualitative agreement with
the theory, a quantitative mismatch is observed which origin may be due to the
dissipation that ultimately absorbs the energy flux of the Kolmogorov-Zakharov
casade.Comment: accepted for publication in European Physical Journal B see
http://www.epj.or
Roughness of moving elastic lines - crack and wetting fronts
We investigate propagating fronts in disordered media that belong to the
universality class of wetting contact lines and planar tensile crack fronts. We
derive from first principles their nonlinear equations of motion, using the
generalized Griffith criterion for crack fronts and three standard mobility
laws for contact lines. Then we study their roughness using the self-consistent
expansion. When neglecting the irreversibility of fracture and wetting
processes, we find a possible dynamic rough phase with a roughness exponent of
and a dynamic exponent of z=2. When including the irreversibility,
we conclude that the front propagation can become history dependent, and thus
we consider the value as a lower bound for the roughness exponent.
Interestingly, for propagating contact line in wetting, where irreversibility
is weaker than in fracture, the experimental results are close to 0.5, while
for fracture the reported values of 0.55--0.65 are higher.Comment: 15 pages, 6 figure
Statistical distributions in the folding of elastic structures
The behaviour of elastic structures undergoing large deformations is the
result of the competition between confining conditions, self-avoidance and
elasticity. This combination of multiple phenomena creates a geometrical
frustration that leads to complex fold patterns. By studying the case of a rod
confined isotropically into a disk, we show that the emergence of the
complexity is associated with a well defined underlying statistical measure
that determines the energy distribution of sub-elements,``branches'', of the
rod. This result suggests that branches act as the ``microscopic'' degrees of
freedom laying the foundations for a statistical mechanical theory of this
athermal and amorphous system
EP-1198: Methylenetetrahfolate reductase C677T polymorphism in patients treated for locally advanced rectal cancer
Scaling of the buckling transition of ridges in thin sheets
When a thin elastic sheet crumples, the elastic energy condenses into a
network of folding lines and point vertices. These folds and vertices have
elastic energy densities much greater than the surrounding areas, and most of
the work required to crumple the sheet is consumed in breaking the folding
lines or ``ridges''. To understand crumpling it is then necessary to understand
the strength of ridges. In this work, we consider the buckling of a single
ridge under the action of inward forcing applied at its ends. We demonstrate a
simple scaling relation for the response of the ridge to the force prior to
buckling. We also show that the buckling instability depends only on the ratio
of strain along the ridge to curvature across it. Numerically, we find for a
wide range of boundary conditions that ridges buckle when our forcing has
increased their elastic energy by 20% over their resting state value. We also
observe a correlation between neighbor interactions and the location of initial
buckling. Analytic arguments and numerical simulations are employed to prove
these results. Implications for the strength of ridges as structural elements
are discussed.Comment: 42 pages, latex, doctoral dissertation, to be submitted to Phys Rev
Anomalous strength of membranes with elastic ridges
We report on a simulational study of the compression and buckling of elastic
ridges formed by joining the boundary of a flat sheet to itself. Such ridges
store energy anomalously: their resting energy scales as the linear size of the
sheet to the 1/3 power. We find that the energy required to buckle such a ridge
is a fixed multiple of the resting energy. Thus thin sheets with elastic ridges
such as crumpled sheets are qualitatively stronger than smoothly bent sheets.Comment: 4 pages, REVTEX, 3 figure
Using Representation Theorems for Proving Polynomials Non-negative
Proving polynomials non-negative when variables range on a
subset of numbers (e.g., [0, +â)) is often required in many applications
(e.g., in the analysis of program termination). Several representations for
univariate polynomials P that are non-negative on [0, +â) have been
investigated. They can often be used to characterize the property, thus
providing a method for checking it by trying a match of P against the
representation. We introduce a new characterization based on viewing
polynomials P as vectors, and find the appropriate polynomial basis B
in which the non-negativeness of the coordinates [P]B representing P in
B witnesses that P is non-negative on [0, +â). Matching a polynomial
against a representation provides a way to transform universal sentences
âx â [0, +â) P(x) â„ 0 into a constraint solving problem which can be
solved by using efficient methods. We consider different approaches to
solve both kind of problems and provide a quantitative evaluation of
performance that points to an early result by PÂŽolya and Szegšoâs as an
appropriate basis for implementations in most cases.Lucas Alba, S. (2014). Using Representation Theorems for Proving Polynomials Non-negative. En Artificial Intelligence and Symbolic Computation: 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings. Springer Verlag (Germany). 21-33. doi:10.1007/978-3-319-13770-4_4S2133AlarcĂłn, B., GutiĂ©rrez, R., Lucas, S., Navarro-Marset, R.: Proving Termination Properties with mu-term. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 201â208. Springer, Heidelberg (2011)Basu, S., Pollack, R., Roy, M.-F.: Algorithms in Real Algebraic Geometry. Springer, Berlin (2006)Bernstein, S.: DĂ©monstration du thĂ©orĂšme de Weierstrass fondĂ©e sur le calcul des probabilitĂ©s. Communic. Soc. Math. de Kharkow 13(2), 1â2 (1912)Bernstein, S.: Sur la rĂ©presentation des polynĂŽmes positifs. Communic. Soc. Math. de Kharkow 14(2), 227â228 (1915)Borralleras, C., Lucas, S., Oliveras, A., RodrĂguez, E., Rubio, A.: SAT Modulo Linear Arithmetic for Solving Polynomial Constraints. Journal of Automated Reasoning 48, 107â131 (2012)Boudaoud, F., Caruso, F., Roy, M.-F.: Certificates of Positivity in the Bernstein Basis. Discrete Computational Geometry 39, 639â655 (2008)Choi, M.D., Lam, T.Y., Reznick, B.: Sums of squares of real polynomials. In: Proc. of the Symposium on Pure Mathematics, vol. 4, pp. 103â126. American Mathematical Society (1995)Contejean, E., MarchĂ©, C., TomĂĄs, A.-P., Urbain, X.: Mechanically proving termination using polynomial interpretations. Journal of Automated Reasoning 32(4), 315â355 (2006)Hilbert, D.: Ăber die Darstellung definiter Formen als Summe von Formenquadraten. Mathematische Annalen 32, 342â350 (1888)Hong, H., JakuĆĄ, D.: Testing Positiveness of Polynomials. Journal of Automated Reasoning 21, 23â38 (1998)Karlin, S., Studden, W.J.: Tchebycheff systems: with applications in analysis and statistics. Interscience, New York (1966)Lucas, S.: Polynomials over the reals in proofs of termination: from theory to practice. RAIRO Theoretical Informatics and Applications 39(3), 547â586 (2005)Polya, G., Szegö, G.: Problems and Theorems in Analysis II. Springer (1976)Powers, V., Reznick, B.: Polynomials that are positive on an interval. Transactions of the AMS 352(10), 4677â4692 (2000)Powers, V., Wörmann, T.: An algorithm for sums of squares of real polynomials. Journal of Pure and Applied Algebra 127, 99â104 (1998
Energy distributions and effective temperatures in the packing of elastic sheets
The packing of elastic sheets is investigated in a quasi two-dimensional
experimental setup: a sheet is pulled through a rigid hole acting as a
container, so that its configuration is mostly prescribed by the cross-section
of the sheet in the plane of the hole. The characterisation of the packed
configuration is made possible by using refined image analysis. The geometrical
properties and energies of the branches forming the cross-section are broadly
distributed. We find distributions of energy with exponential tails. This setup
naturally divides the system into two sub-systems: in contact with the
container and within the bulk. While the geometrical properties of the
sub-systems differ, their energy distributions are identical, indicating
'thermal' homogeneity and allowing the definition of effective temperatures
from the characteristic scales of the energy distributions.Comment: 6 page
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