There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

National Institute of Standards and Technology における超伝導研究及び生活

Analysis of correlations between various physical properties of solids provides a formulation of simple criteria applicable to the search for new superhard materials. The prospects for the synthesis of new substances with the key elastic moduli, whose values approach or even exceed those of diamond are also discussed. We introduce the concept of ideal hardness and strength, which relates the elastic properties of materials to the corresponding mechanical characteristics, the concepts that are less unambiguously determined and that depend on the conditions of measurements. The control of material nanostructure makes it possible to approach the ideal hardness. The formulation of trends interrelating physical properties is expected to allow an essential guidance in the synthesis of new classes of superhard materials.

Harder than diamond: Dreams and reality

The Toroid type high-pressure device and its predecessor, the Chechevitsa (lentil) type high-pressure device, are known to be used efficiently for the synthesis of new materials in recent decades. It was through the Chechevitsa device the first ultradense modification of silica, ‘stishovite’, was obtained. Both devices were essential for the industrial production of superhard materials in the USSR and other socialist countries. In 1980s, almost half of the world synthetic diamond and c-BN products were manufactured by these devices. However, the application of the Toroid device for examining the structure and physical properties of highly compressed substances has been considerably less appreciated. Meanwhile, the device has some unique features that have made possible 35-years of an extensive investigation of physical properties of substances at pressures up to 150 kbar, including electron transport and thermodynamic properties, elastic characteristics, viscosity, thermo-conductivity and other physical p...

Toroid type high-pressure device: history and prospects

It is generally agreed that the supercritical region of a liquid consists of one single state (supercritical fluid). On the other hand, we show here that liquids in this region exist in two qualitatively different states: ``rigid'' and ``nonrigid'' liquids. Rigid to nonrigid transition corresponds to the condition $\ensuremath{\tau}\ensuremath{\approx}{\ensuremath{\tau}}_{0}$, where $\ensuremath{\tau}$ is the liquid relaxation time and ${\ensuremath{\tau}}_{0}$ is the minimal period of transverse quasiharmonic waves. This condition defines a new dynamic crossover line on the phase diagram and corresponds to the loss of shear stiffness of a liquid at all available frequencies and, consequently, to the qualitative change in many important liquid properties. We analyze this line theoretically as well as in real and model fluids and show that the transition corresponds to the disappearance of high-frequency sound, to the disappearance of roton minima, qualitative changes in the temperature dependencies of sound velocity, diffusion, viscous flow, and thermal conductivity, an increase in particle thermal speed to half the speed of sound, and a reduction in the constant volume specific heat to 2${k}_{\mathrm{B}}$ per particle. In contrast to the Widom line that exists near the critical point only, the new dynamic line is universal: It separates two liquid states at arbitrarily high pressure and temperature and exists in systems where liquid-gas transition and the critical point are absent altogether. We propose to call the new dynamic line on the phase diagram ``Frenkel line''.

https://ccmmp.ph.qmul.ac.uk/~kostya/Frenkel-line.pdf

Two liquid states of matter: a dynamic line on a phase diagram.

We discuss the fluid state of matter at high temperature and pressure. We review the existing ways in which the boundary between a liquid and a quasigas fluid above the critical point are discussed. We show that the proposed 'thermodynamic' continuation of the boiling line, the 'Widom line', exists as a line near the critical point only, but becomes a bunch of short lines at a higher temperature. We subsequently propose a new 'dynamic' line separating a liquid and a gas-like fluid. The dynamic line is related to different types of particle trajectories and different diffusion mechanisms in liquids and dense gases. The location of the line on the phase diagram is determined by the equality of the liquid relaxation time and the minimal period of transverse acoustic excitations. Crossing the line results in the disappearance of transverse waves at all frequencies, the diffusion coefficient acquiring a value close to that at the critical point, the speed of sound becoming twice the particle thermal speed, and the specific heat reaching 2. In the high-pressure limit, the temperature on the dynamic line depends on pressure in the same way as does the melting temperature. In contrast to the Widom line, the proposed dynamic line separates liquid and gas-like fluids above the critical point at arbitrarily high pressure and temperature. We propose calling the new dynamic line the 'Frenkel line'.

https://iopscience.iop.org/article/10.3367/UFNe.0182.201211a.1137/pdf

Where is the supercritical fluid on the phase diagram

Strongly interacting, dynamically disordered and with no small parameter, liquids took a theoretical status between gases and solids with the historical tradition of hydrodynamic description as the starting point. We review different approaches to liquids as well as recent experimental and theoretical work, and propose that liquids do not need classifying in terms of their proximity to gases and solids or any categorizing for that matter. Instead, they are a unique system in their own class with a notably mixed dynamical state in contrast to pure dynamical states of solids and gases. We start with explaining how the first-principles approach to liquids is an intractable, exponentially complex problem of coupled non-linear oscillators with bifurcations. This is followed by a reduction of the problem based on liquid relaxation time τ representing non-perturbative treatment of strong interactions. On the basis of τ, solid-like high-frequency modes are predicted and we review related recent experiments. We demonstrate how the propagation of these modes can be derived by generalizing either hydrodynamic or elasticity equations. We comment on the historical trend to approach liquids using hydrodynamics and compare it to an alternative solid-like approach. We subsequently discuss how collective modes evolve with temperature and how this evolution affects liquid energy and heat capacity as well as other properties such as fast sound. Here, our emphasis is on understanding experimental data in real, rather than model, liquids. Highlighting the dominant role of solid-like high-frequency modes for liquid energy and heat capacity, we review a wide range of liquids: subcritical low-viscous liquids, supercritical state with two different dynamical and thermodynamic regimes separated by the Frenkel line, highly-viscous liquids in the glass transformation range and liquid-glass transition. We subsequently discuss the fairly recent area of liquid–liquid phase transitions, the area where the solid-like properties of liquids have become further apparent. We then discuss gas-like and solid-like approaches to quantum liquids and theoretical issues that are similar to the classical case. Finally, we summarize the emergent view of liquids as a unique system with a mixed dynamical state, and list several areas where interesting insights may appear and continue the extraordinary liquid story.

https://iopscience.iop.org/article/10.1088/0034-4885/79/1/016502/pdf

Vadim V. Brazhkin

Papers

Harder than diamond: Dreams and reality

Toroid type high-pressure device: history and prospects

Two liquid states of matter: a dynamic line on a phase diagram.

Where is the supercritical fluid on the phase diagram

Collective modes and thermodynamics of the liquid state