Critical scaling of jammed system after quench of temperature

Critical behavior of soft repulsive particles after quench of temperature near the jamming trasition is numerically investigated. It is found that the plateau of the mean square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.Comment: 7 pages, 9 figures, to appear in Phys. Rev.

A theoretical and numerical approach to "magic angle" of stone skipping

We investigate oblique impacts of a circular disk and water surface. An experiment [ Clanet, C., Hersen, F. and Bocquet, L., Nature 427, 29 (2004) ] revealed that there exists a "magic angle" of 20 [deg.] between a disk face and water surface which minimize the required speed for ricochet. We perform 3-dimensional simulation of the water impacts using the Smoothed Particle Hydrodynamics (SPH) and analyze the results with an ordinal differential equation (ODE) model. Our simulation is in good agreement with the experiment. The analysis with the ODE model give us a theoretical insight for the ``magic angle" of stone skipping.Comment: 4 pages, 4figure

Critical behaviors of sheared frictionless granular materials near jamming transition

Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa (Prog. Theor. Phys., 121, 647 (2009)). We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a phenomenology and the simulation.Comment: 13pages, 26 figure

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.Comment: To appear in the Annals of the Institute of Statistical Mathematics, this http://www.ism.ac.jp/editsec/aism-e.htm

A Great Space Weather Event in February 1730

Aims. Historical records provide evidence of extreme magnetic storms with equatorward auroral extensions before the epoch of systematic magnetic observations. One significant magnetic storm occurred on February 15, 1730. We scale this magnetic storm with auroral extension and contextualise it based on contemporary solar activity. Methods. We examined historical records in East Asia and computed the magnetic latitude (MLAT) of observational sites to scale magnetic storms. We also compared them with auroral records in Southern Europe. We examined contemporary sunspot observations to reconstruct detailed solar activity between 1729 and 1731. Results. We show 29 auroral records in East Asian historical documents and 37 sunspot observations. Conclusions. These records show that the auroral displays were visible at least down to 25.8{\deg} MLAT throughout East Asia. In comparison with contemporary European records, we show that the boundary of the auroral display closest to the equator surpassed 45.1{\deg} MLAT and possibly came down to 31.5{\deg} MLAT in its maximum phase, with considerable brightness. Contemporary sunspot records show an active phase in the first half of 1730 during the declining phase of the solar cycle. This magnetic storm was at least as intense as the magnetic storm in 1989, but less intense than the Carrington event.Comment: 30 pages, 5 figures, and 2 tables, accepted for publication in Astronomy & Astrophysics on 25 April 2018. The figures and transcriptions/translations of historical documents are partially omitted in this manuscript due to the condition of reproduction. They are available in the publisher versio

Power-law behavior in the power spectrum induced by Brownian motion of a domain wall

We show that Brownian motion of a one-dimensional domain wall in a large but finite system yields a $\omega^{-3/2}$ power spectrum. This is successfully applied to the totally asymmetric simple exclusion process (TASEP) with open boundaries. An excellent agreement between our theory and numerical results is obtained in a frequency range where the domain wall motion dominates and discreteness of the system is not effective.Comment: 4 pages, 4 figure

Interpretation of percolation in terms of infinity computations

In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor's ideas and describes infinite and infinitesimal numbers in accordance with the principle `The part is less than the whole'. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a computer - the Infinity Computer - introduced recently in by Ya.D. Sergeyev in a number of patents. The new approach does not contradict Cantor. In contrast, it can be viewed as an evolution of his deep ideas regarding the existence of different infinite numbers in a more applied way. Site percolation and gradient percolation have been studied by applying the new computational tools. It has been established that in an infinite system the phase transition point is not really a point as with respect of traditional approach. In light of new arithmetic it appears as a critical interval, rather than a critical point. Depending on "microscope" we use this interval could be regarded as finite, infinite and infinitesimal short interval. Using new approach we observed that in vicinity of percolation threshold we have many different infinite clusters instead of one infinite cluster that appears in traditional consideration.Comment: 22 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1203.4140, arXiv:1203.316

Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension

We present exact results for the density profile of the one dimensional array of N hard spheres of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquid-solid transition occurs at zero temperature, because the close-pakced density, $\phi_c$, is one. However, if we relax this condition slightly such that $phi_c=1-\delta$, we find a series of critical temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th particle undergoes the liquid-solid transition. The functional form of the onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom