NVU dynamics. II. Comparing to four other dynamics

In the companion paper [Ingebrigtsen et al., arXiv:1012.3447] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here simulations of this NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Gaussian Lennard-Jones liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are then presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular to leading order in 1/N these two dynamics give identical time-autocorrelation functions. In the final section NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nose-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make their single-particle diffusion constants identical to those of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times

Isomorphs in model molecular liquids

Isomorphs are curves in the phase diagram along which a number of static and dynamic quantities are invariant in reduced units. A liquid has good isomorphs if and only if it is strongly correlating, i.e., the equilibrium virial/potential energy fluctuations are more than 90% correlated in the NVT ensemble. This paper generalizes isomorphs to liquids composed of rigid molecules and study the isomorphs of two systems of small rigid molecules, the asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for both systems we find that the isochoric heat capacity, the excess entropy, the reduced molecular center-of-mass self part of the intermediate scattering function, the reduced molecular center-of-mass radial distribution function to a good approximation are invariant along an isomorph. In agreement with theory, we also find that an instantaneous change of temperature and density from an equilibrated state point to another isomorphic state point leads to no relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be more approximative than those of the asymmetric dumbbell model, which is consistent with the OTP model being less strongly correlating. For both models we find "master isomorphs", i.e., isomorphs have identical shape in the virial/potential energy phase diagram.Comment: 20 page

Invariants in the Yukawa system’s thermodynamic phase diagram

This paper shows that several known properties of the Yukawa system can be derived from the isomorph theory, which applies to any system that has strong correlations between its virial and potential-energy equilibrium fluctuations. Such "Roskilde-simple" systems have a simplified thermodynamic phase diagram deriving from the fact that they have curves (isomorphs) along which structure and dynamics in reduced units are invariant to a good approximation. We show that the Yukawa system has strong virial potential-energy correlations and identify its isomorphs by two different methods. One method, the so-called direct isomorph check, identifies isomorphs numerically from jumps of relatively small density changes (here 10%). The second method identifies isomorphs analytically from the pair potential. The curves obtained by the two methods are close to each other; these curves are confirmed to be isomorphs by demonstrating the invariance of the radial distribution function, the static structure factor, the mean-square displacement as a function of time, and the incoherent intermediate scattering function. Since the melting line is predicted to be an isomorph, the theory provides a derivation of a known approximate analytical expression for this line in the temperature-density phase diagram. The paper's results give the first demonstration that the isomorph theory can be applied to systems like dense colloidal suspensions and strongly coupled dusty plasmas.Comment: 12 pages, 12 figure

Excess-entropy scaling in supercooled binary mixtures

Supercooled liquids near the glass transition show remarkable non-Arrhenius transport phenomena, whose origin is yet to be clarified. Here, the authors use GPU molecular dynamics simulations for various binary mixtures in the supercooled regime to show the validity of a quasiuniversal excess-entropy scaling relation for viscosity and diffusion

Explaining why simple liquids are quasi-universal

It has been known for a long time that many simple liquids have surprisingly similar structure as quantified, e.g., by the radial distribution function. A much more recent realization is that the dynamics are also very similar for a number of systems with quite different pair potentials. Systems with such non-trivial similarities are generally referred to as "quasi-universal". From the fact that the exponentially repulsive pair potential has strong virial potential-energy correlations in the low-temperature part of its thermodynamic phase diagram, we here show that a liquid is quasi-universal if its pair potential can be written approximately as a sum of exponential terms with numerically large prefactors. Based on evidence from the literature we moreover conjecture the converse, i.e., that quasi-universality only applies for systems with this property

Does the principle of minimum work apply at the carotid bifurcation: a retrospective cohort study

<p>Abstract</p> <p>Background</p> <p>There is recent interest in the role of carotid bifurcation anatomy, geometry and hemodynamic factors in the pathogenesis of carotid artery atherosclerosis. Certain anatomical and geometric configurations at the carotid bifurcation have been linked to disturbed flow. It has been proposed that vascular dimensions are selected to minimize energy required to maintain blood flow, and that this occurs when an exponent of 3 relates the radii of parent and daughter arteries. We evaluate whether the dimensions of bifurcation of the extracranial carotid artery follow this principle of minimum work.</p> <p>Methods</p> <p>This study involved subjects who had computed tomographic angiography (CTA) at our institution between 2006 and 2007. Radii of the common, internal and external carotid arteries were determined. The exponent was determined for individual bifurcations using numerical methods and for the sample using nonlinear regression.</p> <p>Results</p> <p>Mean age for 45 participants was 56.9 ± 16.5 years with 26 males. Prevalence of vascular risk factors was: hypertension-48%, smoking-23%, diabetes-16.7%, hyperlipidemia-51%, ischemic heart disease-18.7%.</p> <p>The value of the exponent ranged from 1.3 to 1.6, depending on estimation methodology.</p> <p>Conclusions</p> <p>The principle of minimum work (defined by an exponent of 3) may not apply at the carotid bifurcation. Additional factors may play a role in the relationship between the radii of the parent and daughter vessels.</p

Understanding practice: the factors that influence management of mild traumatic brain injury in the emergency department-a qualitative study using the Theoretical Domains Framework

Background: Mild traumatic brain injury is a frequent cause of presentation to emergency departments. Despite the availability of clinical practice guidelines in this area, there is variation in practice. One of the aims of the Neurotrauma Evidence Translation program is to develop and evaluate a targeted, theory- and evidence-informed intervention to improve the management of mild traumatic brain injury in Australian emergency departments. This study is the first step in the intervention development process and uses the Theoretical Domains Framework to explore the factors perceived to influence the uptake of four key evidence-based recommended practices for managing mild traumatic brain injury. Methods: Semi-structured interviews were conducted with emergency staff in the Australian state of Victoria. The interview guide was developed using the Theoretical Domains Framework to explore current practice and to identify the factors perceived to influence practice. Two researchers coded the interview transcripts using thematic content analysis. Results: A total of 42 participants (9 Directors, 20 doctors and 13 nurses) were interviewed over a seven-month period. The results suggested that (i) the prospective assessment of post-traumatic amnesia was influenced by: knowledge; beliefs about consequences; environmental context and resources; skills; social/professional role and identity; and beliefs about capabilities; (ii) the use of guideline-developed criteria or decision rules to inform the appropriate use of a CT scan was influenced by: knowledge; beliefs about consequences; environmental context and resources; memory, attention and decision processes; beliefs about capabilities; social influences; skills and behavioral regulation; (iii) providing verbal and written patient information on discharge was influenced by: beliefs about consequences; environmental context and resources; memory, attention and decision processes; social/professional role and identity; and knowledge; (iv) the practice of providing brief, routine follow-up on discharge was influenced by: environmental context and resources; social/professional role and identity; knowledge; beliefs about consequences; and motivation and goals. Conclusions: Using the Theoretical Domains Framework, factors thought to influence the management of mild traumatic brain injury in the emergency department were identified. These factors present theoretically based targets for a future intervention