相关论文: Universal scaling law of an origami paper spring

Recently, simple scaling laws concerning the mechanical response and mechanical transition of Kirigami have been revealed through agreement between theory and experiment for kirigami made of paper [M. Isobe and K. Okumura, Sci. Rep. 2016].…

Recently a number of empirical "universal" scaling law papers have been published, most notably by OpenAI. `Scaling laws' refers to power-law decreases of training or test error w.r.t. more data, larger neural networks, and/or more compute.…

The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although…

Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is…

We study the lateral deformations of randomly folded elastoplastic and predominantly plastic thin sheets under the uniaxial and radial compressions. We found that the lateral deformations of cylinders folded from elastoplastic sheets of…

A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence…

Universal scaling laws form one of the central issues in physics. A non-standard scaling law or a breakdown of a standard scaling law, on the other hand, can often lead to the finding of a new universality class in physical systems.…

Compressed frictional granular matter cannot flow without dilation. Upon forced shearing to generate flow, the amount of dilation may depend on the initial preparation and a host of material variables. On the basis of both experiments and…

Universal scaling in the power-law size distribution of pelagic fish schools is established. The power-law exponent of size distributions is extracted through the data collapse. The distribution depends on the school size only through the…

The strength of most metals used in daily life scales with either an internal or external length scale. Empirically, this is characterized by power-laws persisting to six orders of magnitude in both strength and length scale. Attempts at…

A scaling relation for the disjoining pressure of strongly confined polymer fluids is proposed for the first time, which yields directly the scaling exponent, nu, of the radius of gyration for polymers. To test the proposed scaling relation…

The statistical properties of turbulence are considered to be universal at sufficiently small length scales, i. e., independent of boundary conditions and large-scale forces acting on the fluid. Analyzing data from numerical simulations of…

The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the…

We show that the law of the three-dimensional uniform spanning tree (UST) is tight under rescaling in a space whose elements are measured, rooted real trees, continuously embedded into Euclidean space. We also establish that the relevant…

We study the power law running of gauge, Yukawa and quartic scalar couplings in the universal extra dimension scenario where the extra dimension is accessed by all the standard model fields. After compactifying on an $S_1 /Z_2$ orbifold, we…

Motivated by the finding that there is some biological universality in the relationship between school geometry and school biomass of various pelagic fishes in various conditions, I here establish a scaling law for school dimensions: the…

Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…

Convergence of order $O(1/\sqrt{n})$ is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in generalized random graphs with random vertex weights. The…

The Family-Vicsek relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational…

The scaling function of the 2D Ising model in a magnetic field on the square and triangular lattices is obtained numerically via Baxter's variational corner transfer matrix approach. The use of the Aharony-Fisher non-linear scaling…