A model for the fragmentation kinetics of crumpled thin sheets

As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.Comment: 11 pages, 7 figures (+ Supplemental Materials: 15 pages, 9 figures); introduced a simpler approximation to model, key results unchanged; added references, expanded supplementary information, corrected Fig. 2 and revised Figs. 4 and 7 for clearer presentation of result

A state variable for crumpled thin sheets

Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled sheet can take. Here we experimentally show that key aspects of crumpling have a very simple description; the evolution of the damage in crumpling dynamics can largely be described by a single global quantity, the total length of all creases. We follow the evolution of the damage network in repetitively crumpled elastoplastic sheets, and show that the dynamics of this quantity are deterministic, and depend only on the instantaneous state of the crease network and not at all on the crumpling history. We also show that this global quantity captures the crumpling dynamics of a sheet crumpled for the first time. This leads to a remarkable reduction in complexity, allowing a description of a highly disordered system by a single state parameter. Similar strategies may also be useful in analyzing other systems that evolve under geometric and mechanical constraints, from faulting of tectonic plates to the evolution of proteins

Studies of iron impurities in YxPr1-xBa2Cu3O7-delta

Pr is the only rare earth which, when substituted for Y in YBa2Cu3O7, significantly alters the superconducting transition temperature T(sub c) without changing the crystal structure. For YxPr1-xBa2Cu3O7-delta with delta approx. equal to 0, T(sub c) is reduced rapidly as x is increased, reaching zero for x about 0.5. For x above 0.5 the compound is antiferromagnetic with a Neel temperature that increases with increasing x, rising to above room temperature for x near 1. A similar behavior is observed when the oxygen deficit delta is increased from zero to 1 with x=0. For the case of Pr substitution, the drop in T(sub c) is believed due to magnetic interactions. For the case of varying delta with x=0, the drop can be attributed to a combination of magnetic interactions, band filling, and changes in crystal structure. To study these effects, the Mossbauer effect of 57 Fe atoms substituted for the Cu atoms has been observed as a function of delta, x, and temperature. The observed spectra are all well described by a two quadrupole-split pairs, a central singlet, and a six-line magnetic hyperfine field pattern. For several Pr compositions both delta and temperature were varied, and the results support the hypothesis that a magnetic interaction exists between the Fe in the Cu lattice and the substitutional Pr atoms

Volatility and dividend risk in perpetual American options

American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because some of the most relevant facts that may potentially affect a firm will entail sharp predictable effects. We will analyse the consequences of this potential risk on perpetual American derivatives, a topic connected with a wide class of recurrent problems in physics: holders of American options must look for the fair price and the optimal exercise strategy at once, a typical question of free absorbing boundaries. We present explicit solutions to the most common contract specifications and derive analytical expressions concerning the mean and higher moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep revision, two new appendice

Sliding friction between an elastomer network and a grafted polymer layer: the role of cooperative effects

We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains' penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high grafting density modify the friction force by grafted chain. We develop here a simple model that takes into account those interactions and gives a limit grafting density beyond which the friction no longer increases with the grafting density, in good agreement with the experimental dataComment: Submitted to Europhys. Letter

Dynamic multilateral markets

We study dynamic multilateral markets, in which players' payoffs result from intra-coalitional bargaining. The latter is modeled as the ultimatum game with exogenous (time-invariant) recognition probabilities and unanimity acceptance rule. Players in agreeing coalitions leave the market and are replaced by their replicas, which keeps the pool of market participants constant over time. In this infinite game, we establish payoff uniqueness of stationary equilibria and the emergence of endogenous cooperation structures when traders experience some degree of (heterogeneous) bargaining frictions. When we focus on market games with different player types, we derive, under mild conditions, an explicit formula for each type's equilibrium payoff as the market frictions vanish

Microscopic theory for the glass transition in a system without static correlations

We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l),l=L/a. We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l_c, if v(l_c)=1. We present a variational and a numerically exact evaluation of v(l).Close to l_c the diffusion constant decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a glass transition in the absence of any static correlations, in contrast to present form of mode coupling theory.Comment: 6 pages, 3 figure

Phase transition in nanomagnetite

Recently, the application of nanosized magnetite particles became an area of growing interest for their potential practical applications. Nanosized magnetite samples of 36 and 9 nm sizes were synthesized. Special care was taken on the right stoichiometry of the magnetite particles. Mössbauer spectroscopy measurements were made in 4.2–300 K temperature range. The temperature dependence of the intensities of the spectral components indicated size dependent transition taking place in a broad temperature range. For nanosized samples, the hyperfine interaction values and their relative intensities changed above the Verwey transition temperature value of bulk megnetite. The continuous transition indicated the formation of dendritelike granular assemblies formed during the preparation of the samples

Time Reversal to Localise Multiple Partial Discharges in Power Cables

The paper studies the suitability of the electromagnetic time reversal (EMTR) technique to localise multiple sources of partial discharges (PD) in power cables. In particular, the localisation of two PDs in a homogeneous power line is investigated both in the presence or absence of noise. The investigation, which is based on numerical simulations, shows that an EMTR-based PD localisation method is able to localise two PDs occurring simultaneously in a line using only a measurement at one observation point (OP), indiscriminately collecting the direct and reflected signals coming from the two PD sources. The EMTR procedure to localise multiple PD sources, using a Transmission Line Matrix model digital twin for the time reversal simulations, is described and the challenges that must be addressed to develop an EMTR-based device for the on-line location of multiple PDs are discussed

Variational bounds for the shear viscosity of gelling melts

We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$, which implies that it diverges algebraically with a critical exponent $k\ge 2\nu-\beta$. Here, $\nu$ and $\beta$ are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size.Comment: 5 pages; CHANGES: typos corrected, some references added; version as publishe