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Order of magnitude
About: Order of magnitude is a research topic. Over the lifetime, 1164 publications have been published within this topic receiving 36107 citations.
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TL;DR: In this article, a 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.
Abstract: We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.
3,758 citations
TL;DR: Gas and water flow measurements through microfabricated membranes in which aligned carbon nanotubes with diameters of less than 2 nanometers serve as pores enable fundamental studies of mass transport in confined environments, as well as more energy-efficient nanoscale filtration.
Abstract: We report gas and water flow measurements through microfabricated membranes in which aligned carbon nanotubes with diameters of less than 2 nanometers serve as pores. The measured gas flow exceeds predictions of the Knudsen diffusion model by more than an order of magnitude. The measured water flow exceeds values calculated from continuum hydrodynamics models by more than three orders of magnitude and is comparable to flow rates extrapolated from molecular dynamics simulations. The gas and water permeabilities of these nanotube-based membranes are several orders of magnitude higher than those of commercial polycarbonate membranes, despite having pore sizes an order of magnitude smaller. These membranes enable fundamental studies of mass transport in confined environments, as well as more energy-efficient nanoscale filtration.
2,637 citations
TL;DR: A relatively new class of materials has been found in which exhibit unusual temperature dependences in their low-temperature properties, including several examples in which the specific heat divided by temperature shows a singular $\mathrm{log}T$ temperature dependence over more than two orders of magnitude as mentioned in this paper.
Abstract: A relatively new class of materials has been found in which the basic assumption of Landau Fermi-liquid theory---that at low energies the electrons in a metal should behave essentially as a collection of weakly interacting particles---is violated. These ``non-Fermi-liquid'' systems exhibit unusual temperature dependences in their low-temperature properties, including several examples in which the specific heat divided by temperature shows a singular $\mathrm{log}T$ temperature dependence over more than two orders of magnitude, from the lowest measured temperatures in the milliKelvin regime to temperatures over 10 K. These anomalous properties, with their often pure power-law or logarithmic temperature dependences over broad temperature ranges and inherent low characteristic energies, have attracted active theoretical interest from the first experimental report in 1991. This article first describes the various theoretical approaches to trying to understand the source of strong temperature- and frequency-dependent electron-electron interactions in non-Fermi-liquid systems. It then discusses the current experimental body of knowledge, including a compilation of data on non-Fermi-liquid behavior in over 50 systems. The disparate data reveal some interesting correlations and trends and serve to point up a number of areas where further theoretical and experimental work is needed.
1,289 citations
TL;DR: In this paper, the authors used the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal.
Abstract: Work function is experimentally known to be different for different faces of a crystal by amounts ranging from one-tenth to half a volt. For tungsten the faces can be arranged according to decreasing work function as follows: 110, 211, 100 and finally 111. The explanations so far suggested for the differences of the work function are discussed and shown to give either an incorrect sequence or a wrong order of magnitude of the observed differences. The author uses the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal. The origin of the latter can be described in the following manner. With every atom one can associate a polyhedron ("$s$-polyhedron") with the atom at its center, such that it contains all points nearer to the atom under consideration than to any other atom. If the distribution of the electron density within these polyhedra of the surface atoms was the same as for the inside atoms then there would be no double layer on the surface. However, this is not the case since the total energy is lowered by a redistribution of the electron cloud on the surface. There are two effects: the first is a partial spread of the charge out of the $s$-polyhedra and the second is a tendency to smooth out the surface of the polyhedra. In consequence of the second effect the surfaces of equal charge density are more nearly plane than in the original picture. The two effects have opposite influences and since they are comparable in magnitude, it is not possible to predict the sign of the total double layer without numerical computations. Some general formulae for the double layers are derived and discussed more fully in the case of a simple cubic and a body-centered cubic lattice. The minimum problem of the surface energy is solved for four faces of a body-centered crystal and the results are applied to the case of tungsten. One obtains the differences between the work functions for different directions. The results agree satisfactorily with the experimental data: assuming a reasonable density of the free electrons, one obtains the correct sequence of faces and the correct differences of the work function. The surface energies are calculated an d found in agreement with the observed stability of certain crystal faces.
1,117 citations
TL;DR: Spin precession measurements in the polar molecule thorium monoxide indicate a nearly spherical charge distribution of an electron, which constrains T-violating physics at the TeV energy scale.
Abstract: The Standard Model of particle physics is known to be incomplete. Extensions to the Standard Model, such as weak-scale supersymmetry, posit the existence of new particles and interactions that are asymmetric under time reversal (T) and nearly always predict a small yet potentially measurable electron electric dipole moment (EDM), d(e), in the range of 10(-27) to 10(-30) e·cm. The EDM is an asymmetric charge distribution along the electron spin (S(→)) that is also asymmetric under T. Using the polar molecule thorium monoxide, we measured d(e) = (-2.1 ± 3.7stat ± 2.5syst) × 10(-29) e·cm. This corresponds to an upper limit of |d(e)| < 8.7 × 10(-29) e·cm with 90% confidence, an order of magnitude improvement in sensitivity relative to the previous best limit. Our result constrains T-violating physics at the TeV energy scale.
1,040 citations