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1

What is Liquid? [in two dimensions]

Travis K. P., Hoover Wm. G., Hoover C. G., Hass A. B.

Computational Methods in Science and Technology

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2021

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Vol. 27, No. 1

5--23

EN

We consider the practicalities of defining, simulating, and characterizing “Liquids” from a pedagogical standpoint based on atomistic computer simulations. For simplicity and clarity we study two-dimensional systems throughout. In addition to the infinite-ranged Lennard-Jones 12/6 potential we consider two shorter-ranged families of pair potentials. At zero pressure one of them includes just nearest neighbors. The other longer-ranged family includes twelve additional neighbors. We find that these further neighbors can help stabilize the liquid phase. What about liquids? To implement Wikipedia’s definition of liquids as conforming to their container we begin by formulating and imposing smooth-container boundary conditions. To encourage conformation further we add a vertical gravitational field. Gravity helps stabilize the relatively vague liquid-gas interface. Gravity reduces the messiness associated with the curiously-named “spinodal” (tensile) portion of the phase diagram. Our simulations are mainly isothermal. We control the kinetic temperature with Nosé-Hoover thermostating, extracting or injecting heat so as to impose a mean kinetic temperature over time. Our simulations stabilizing density gradients and the temperature provide critical-point estimates fully consistent with previous efforts from free energy and Gibbs ensemble simulations. This agreement validates our approach.

2

The Simplest Viscous Flow

Hoover Wm. G., Hoover C. G.

Computational Methods in Science and Technology

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2021

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Vol. 27, No. 3

109--119

EN

We illustrate an atomistic periodic two-dimensional stationary shear flow, ux = h x˙ i = ˙y, using the simplest possible example, the periodic shear of just two particles! We use a short-ranged “realistic” pair potential, φ(r < 2) = = (2 − r) 6 − 2(2 − r) 3 . Many body simulations with it are capable of modelling the gas, liquid, and solid states of matter. A useful mechanics generating steady shear follows from a special (“Kewpie-Doll” ∼ “qp-Doll”) Hamiltonian based on the Hamiltonian coordinates {q} and momenta {p} : H(q, p) ≡ K(p) + Φ(q) + ˙ Pqp. Choosing qp → ypx the resulting motion equations are consistent with steadily shearing periodic boundaries with a strain rate (dux/dy) = ˙. The occasional x coordinate jumps associated with periodic boundary crossings in the y direction provide a Hamiltonian that is a piecewise-continuous function of time. A time-periodic isothermal steady state results when the Hamiltonian motion equations are augmented with a continuously variable thermostat generalizing Shuichi Nosé’s revolutionary ideas from 1984. The resulting distributions of coordinates and momenta are interesting multifractals, with surprising irreversible consequences from strictly time-reversible motion equations.

3

Compressible Baker Maps and Their Inverses : A Memoir for Francis Hayin Ree [1936–2020]

Hoover Wm. G.

Computational Methods in Science and Technology

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2020

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Vol. 26, No. 1

5--13

EN

This memoir is dedicated to the late Francis Hayin Ree, a formative influence shaping my work in statistical mechanics. Between 1963 and 1968 we collaborated on nine papers published in the Journal of Chemical Physics. Those dealt with the virial series, cell models, and computer simulation. All of them were directed toward understanding the statistical thermodynamics of simple model systems. Our last joint work is also the most cited, with over 1000 citations, “Melting Transition and Communal Entropy for Hard Spheres”, submitted 3 May 1968 and published that October. Here I summarize my own most recent work on compressible time-reversible two-dimensional maps. These simplest of model systems are amenable to computer simulation and are providing stimulating and surprising results.

4

Polish physicists and the progress in physics (1870‒1920)

Wróblewski A. K.

Czasopismo Techniczne. Nauki Podstawowe

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2014

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R. 111, z. 1-NP

255--273

EN

The Polish-Lithuanian Commonwealth lost independence in 1795 and was partitioned among her three powerful neighbours: Austria, Prussia and Russia. The two old Polish universities in Cracow and Lvov enjoyed relatively liberals laws in the Austrian partition. It was there that Polish physicists (Karol Olszewski, Zygmunt Wróblewski, Marian Smoluchowski, Władysław Natanson, Wojciech Rubinowicz, Czesław Białobrzeski, and others) made most important discoveries and original contributions. There was no possibility of career for Poles living in the oppressive Russian and Prussian partitions where even the use of Polish language was forbidden in schools. Thus many bright Polish students such as e.g. Kazimierz Fajans, Stefan Pieńkowski, Maria Skłodowska, and Mieczysław Wolfke, went abroad to study in foreign universities. In spite of unfavourable conditions under which they had to live and act in the period 1870‒1920, Polish scholars were not only passive recipients of new ideas in physics, but made essential contributions to several fields such as e.g. cryogenics, electromagnetism, statistical physics, relativity, radioactivity, quantum physics, and astrophysics.

PL

Rzeczpospolita Obojga Narodów straciła niepodległość w 1795 r. i została podzielona między trzech potężnych sąsiadów: Austrię, Prusy i Rosję. Dwa stare polskie uniwersytety w Krakowie i Lwowie mogły działać w stosunkowo liberalnych stosunkach w zaborze austriackim. Właśnie tam fizycy polscy (Karol Olszewski, Zygmunt Wróblewski, Marian Smoluchowski, Władysław Natanson, Wojciech Rubinowicz, Czesław Białobrzeski i inni) dokonali największych i najbardziej oryginalnych odkryć. W represyjnych zaborach pruskim i rosyjskim, w których język polski był nawet zabroniony w szkołach, nie było możliwości kariery naukowej dla Polaków. Z tego powodu wielu zdolnych polskich studentów, jak Kazimierz Fajans, Stefan Pieńkowski, Maria Skłodowska czy Mieczysław Wolfke emigrowało, by studiować zagranicą. Mimo niesprzyjających warunków, w jakich przyszło im żyć i działać w okresie 1870‒1920, uczeni polscy nie byli tylko biernymi odbiorcami nowych idei w fizyce, ale wnieśli znaczący wkład do wielu dziedzin, jak np. kriogenika, elektromagnetyzm, fizyka statystyczna, teoria względności, promieniotwórczość, fizyka kwantowa i astrofizyka.

5

U źródeł geologicznych zainteresowań Mariana Smoluchowskiego

Miecznik J. B.

Przegląd Geologiczny

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2013

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Vol. 61, nr 5

286--289

EN

Marian Smoluchowski (1872-1917) was an eminent physicist of international renown. His research in the field of the Kinetic Theory of Matter (e.g. the Brownian motion) contributed to strengthen the nuclear science. He is considered a pioneer of the statistical physics. Childhood and the years of study he spent in Vienna. From an early age, he was associated with mountains and was a prominent mountaineer. Along with his brother, Tadeusz, he climbed many unclimbed peaks in the Eastern Alps: Dolomites, Ortler group and Hohe Tauern. Those achievements passed into the history of Alpine mountaineering. In addition to sports and aesthetic aspects (he painted mountain landscapes), Smoluchowski found his scientific inspirations in the mountains. He was interested in the mechanics of tectonic movements and joined the discussion on the concepts concerning the nappe structure of orogens at the beginning of the 20th century (1909). Research on the physicalfoundations of tectonic movements in the Tatra Mountains, that he planned to undertake, was thwarted by the outbreak of World War I in 1914, and his premature death in 1917.

6

Statistical physics of string-like objects in condensed matter. Dislocations and superconducting vortices

Rogula D.

Journal of Technical Physics

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2002

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Vol. 43, no 3

231-239

EN

Material media containing dense distributions of linear, string-like objects are considered. Dislocation lines in structured solids and supercurrent vortices in type-II superconductors are exemplifications of such objects. The strings are assumed to carry a quantized Abelian topological charge, such as the Burgers vector or magnetic flux. The basic formulations of statistical physics of such systems are discussed. Contrary to the special cases of rectilinear strings, which reduce effectively to 2D systems of point-like particles, the statistical physics of 3D networks of flexible strings is treated on a stand alone basis from the first principles. The presented description takes into account the quenched, thermal, and quantum disorder in a unified way. Implications for the macroscopic setting are discussed.