Granular cooling of hard needles

We have developed a kinetic theory of hard needles undergoing binary collisions with loss of energy due to normal and tangential restitution. In addition, we have simulated many particle systems of granular hard needles. The theory, based on the assumption of a homogeneous cooling state, predicts that granular cooling of the needles proceeds in two stages: An exponential decay of the initial configuration to a state where translational and rotational energies take on a time independent ratio (not necessarily unity), followed by an algebraic decay of the total kinetic energy $\sim t^{-2}$. The simulations support the theory very well for low and moderate densities. For higher densities, we have observed the onset of the formation of clusters and shear bands.Comment: 7 pages, 8 figures; major changes, extended versio

Homogeneous cooling of rough, dissipative particles: Theory and simulations

We investigate freely cooling systems of rough spheres in two and three dimensions. Simulations using an event driven algorithm are compared with results of an approximate kinetic theory, based on the assumption of a generalized homogeneous cooling state. For short times $t$, translational and rotational energy are found to change linearly with $t$. For large times both energies decay like $t^{-2}$ with a ratio independent of time, but not corresponding to equipartition. Good agreement is found between theory and simulations, as long as no clustering instability is observed. System parameters, i.e. density, particle size, and particle mass can be absorbed in a rescaled time, so that the decay of translational and rotational energy is solely determined by normal restitution and surface roughness.Comment: 10 pages, 10 eps-figure

Effects of Velocity Correlation on Early Stage of Free Cooling Process of Inelastic Hard Sphere System

The free cooling process in the inelastic hard sphere system is studied by analysing the data from large scale molecular dynamics simulations on a three dimensional system. The initial energy decay, the velocity distribution function, and the velocity correlation functions are calculated to be compared with theoretical predictions. The energy decay rate in the homogeneous cooling state is slightly but distinctively smaller than that expected from the independent collision assumption. The form of the one particle velocity distribution is found not to be stationary. These contradict to the predictions of the kinetic theory based on the Enskog-Boltzmann equation and suggest that the velocity correlation is already important in the early stage of homogeneous cooling state. The energy decay rate is analysed in terms of the velocity correlation.Comment: 9 pages (figures included). To be published in J. Phys. Soc. Jpn. Vol. 73 No. 1 (2004) Added two references and removed one. Changed the name of T_{L}. Added unit constants in Sec. 5 and

Dynamics of inelastically colliding rough spheres: Relaxation of translational and rotational energy

We study the exchange of kinetic energy between translational and rotational degrees of freedom for inelastic collisions of rough spheres. Even if equipartition holds in the initial state it is immediately destroyed by collisions. The simplest generalisation of the homogeneous cooling state allows for two temperatures, characterizing translational and rotational degrees of freedom separately. For times larger than a crossover frequency, which is determined by the Enskog frequency and the initial temperature, both energies decay algebraically like $t^{-2}$ with a fixed ratio of amplitudes, different from one.Comment: 5 pages, RevTeX, 2 eps figures, slightly expanded discussion, new figures with dimensionless units, added references, accepted for publication in PRE as a Rapid Com

Universality and its Origins at the Amorphous Solidification Transition

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling functions that describe the order parameter and (equivalently) the statistical distribution of localization lengths for these localized particles. The purpose of this Paper is to discuss the origins and consequences of this universality, and in doing so, three themes are explored. First, a replica-Landau-type approach is formulated for the universality class of systems that are composed of extended objects connected by permanent random constraints and undergo amorphous solidification at a critical density of constraints. This formulation generalizes the cases of randomly cross-linked and end-linked macromolecular systems, discussed previously. The universal replica free energy is constructed, in terms of the replica order parameter appropriate to amorphous solidification, the value of the order parameter is obtained in the liquid and amorphous solid states, and the chief universal characteristics are determined. Second, the theory is reformulated in terms of the distribution of local static density fluctuations rather than the replica order parameter. It is shown that a suitable free energy can be constructed, depending on the distribution of static density fluctuations, and that this formulation yields precisely the same conclusions as the replica approach. Third, the universal predictions of the theory are compared with the results of extensive numerical simulations of randomly cross-linked macromolecular systems, due to Barsky and Plischke, and excellent agreement is found.Comment: 10 pages, including 3 figures (REVTEX

Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure

Elasticity near the vulcanization transition

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.Comment: REVTEX, 5 pages. Minor change

Self-diffusion in granular gases

The coefficient of self-diffusion for a homogeneously cooling granular gas changes significantly if the impact-velocity dependence of the restitution coefficient $\epsilon$ is taken into account. For the case of a constant $\epsilon$ the particles spread logarithmically slow with time, whereas the velocity dependent coefficient yields a power law time-dependence. The impact of the difference in these time dependences on the properties of a freely cooling granular gas is discussed.Comment: 6 pages, no figure

Hydrodynamics and transport coefficients for Granular Gases

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.Comment: 16 pages, 4 figure

EPIdemiology of Surgery-Associated Acute Kidney Injury (EPIS-AKI) : Study protocol for a multicentre, observational trial

More than 300 million surgical procedures are performed each year. Acute kidney injury (AKI) is a common complication after major surgery and is associated with adverse short-term and long-term outcomes. However, there is a large variation in the incidence of reported AKI rates. The establishment of an accurate epidemiology of surgery-associated AKI is important for healthcare policy, quality initiatives, clinical trials, as well as for improving guidelines. The objective of the Epidemiology of Surgery-associated Acute Kidney Injury (EPIS-AKI) trial is to prospectively evaluate the epidemiology of AKI after major surgery using the latest Kidney Disease: Improving Global Outcomes (KDIGO) consensus definition of AKI. EPIS-AKI is an international prospective, observational, multicentre cohort study including 10 000 patients undergoing major surgery who are subsequently admitted to the ICU or a similar high dependency unit. The primary endpoint is the incidence of AKI within 72 hours after surgery according to the KDIGO criteria. Secondary endpoints include use of renal replacement therapy (RRT), mortality during ICU and hospital stay, length of ICU and hospital stay and major adverse kidney events (combined endpoint consisting of persistent renal dysfunction, RRT and mortality) at day 90. Further, we will evaluate preoperative and intraoperative risk factors affecting the incidence of postoperative AKI. In an add-on analysis, we will assess urinary biomarkers for early detection of AKI. EPIS-AKI has been approved by the leading Ethics Committee of the Medical Council North Rhine-Westphalia, of the Westphalian Wilhelms-University Münster and the corresponding Ethics Committee at each participating site. Results will be disseminated widely and published in peer-reviewed journals, presented at conferences and used to design further AKI-related trials. Trial registration number NCT04165369