ABSTRACT
Understanding the average motion of a multitude of superfluid vortices in the interior of a neutron star is a key ingredient for most theories of pulsar glitches. In this paper, we propose a ...kinetic approach to compute the mutual friction force that is responsible for the momentum exchange between the normal and superfluid components in a neutron star, where the mutual friction is extracted from a suitable average over the motion of many vortex lines. As a first step towards a better modelling of the repinning and depinning processes of many vortex lines in a neutron star, we consider here only straight and non-interacting vortices: we adopt a minimal model for the dynamics of an ensemble of point vortices in two dimensions immersed in a non-homogeneous medium that acts as a pinning landscape. Since the degree of disorder in the inner crust or outer core of a neutron star is unknown, we compare the two possible scenarios of periodic and disordered pinscapes. This approach allows us to extract the mutual friction between the superfluid and the normal component in the star when, in addition to the usual Magnus and drag forces acting on vortex lines, also a pinning force is at work. The effect of disorder on the depinning transition is also discussed.
The internal layers of neutron stars are expected to contain several superfluid components that can significantly affect their dynamics. The description of such objects should rely on hydrodynamic ...models in which it is possible to unambiguously assign the value of the thermodynamic variables from microscopic calculations of the properties of matter. In this work we consider the phenomenological approach to multifluids modelling championed by Carter and, studying the relaxation of the system towards equilibrium, we assign a precise thermodynamic interpretation to its variables. We show that in thermodynamic equilibrium the equation of state contains less state variables than those needed in the phenomenological model, implying the existence of a gauge freedom of the theory that can be used to simplify the hydrodynamic formulation in the non-dissipative limit. Once this is understood, it becomes easy to translate the different multifluid formalisms that have been proposed in the literature into Carter's form. Finally, we show that the usual concepts of affinity and reaction coordinates, as they are introduced in chemistry, are not affected by the presence of superfluid currents. In an effort to make the concepts clear, the formalism is developed step-by-step from first principles, providing model examples and several applications of practical relevance for the study of superfluid neutron star interiors.
The stability conditions of a relativistic hydrodynamic theory can be derived directly from the requirement that the entropy should be maximized in equilibrium. Here, we use a simple geometrical ...argument to prove that, if the hydrodynamic theory is stable according to this entropic criterion, then localized perturbations to the equilibrium state cannot propagate outside their future light cone. In other words, within relativistic hydrodynamics, acausal theories must be thermodynamically unstable, at least close to equilibrium. We show that the physical origin of this deep connection between stability and causality lies in the relationship between entropy and information. Our result may be interpreted as an "equilibrium conservation theorem," which generalizes the Hawking-Ellis vacuum conservation theorem to finite temperature and chemical potential.
The first-order relativistic fluid theories of dissipation proposed by Eckart and Landau-Lifshitz have been proved to be unstable. They admit solutions which start in proximity of equilibrium and ...depart exponentially from it. We show that this behavior is due to the fact that the total entropy of these fluids, restricted to the dynamically accessible states, has no upper bound. As a result, these systems have the tendency to constantly change according to the second law of thermodynamics and the unstable modes represent the directions of growth of the entropy in state space. We, then, verify that the conditions of stability of Israel and Stewart's theory are exactly the requirements for the entropy to have an absolute maximum. Hence, we explain how the instability of the first-order theories is a direct consequence of the truncation of the entropy current at the first order, which turns the maximum into a saddle point of the total entropy. Finally, we show that recently proposed first-order stable theories, constructed using more general frames, do not solve the instability problem by providing a maximum for the entropy, but, rather, are made stable by allowing for small violations of the second law.
Purpose
The EUPHRATES trial examined the impact of polymyxin B hemoperfusion (PMX) on mortality in patients with septic shock and endotoxemia, defined as EAA ≥ 0.60. No difference was found in 28-day ...all-cause mortality. However, the trial showed that in some patients with septic shock the burden of endotoxin activity was extreme (EAA ≥ 0.9). In a post hoc analysis, we evaluated the impact of PMX use in patients with septic shock and endotoxin activity measured between 0.6–0.89.
Methods
Post-hoc analysis of the EUPHRATES trial for the 194 patients with EAA ≥ 0.6–0.89 who completed two treatments (PMX or sham). The primary end point was mortality at 28 days adjusted for APACHE II score and baseline mean arterial pressure (MAP). Additional end points included changes in MAP, cumulative vasopressor index (CVI), median EAA reduction, ventilator-free days (VFD), dialysis-free days (DFD) and hospital length of stay. Subpopulations analyzed were site and type of infection and those with norepinephrine dose > 0.1 mcg/kg/min at baseline.
Results
At 28 days, 23 patients of 88 (26.1%) in the PMX group died versus 39 of 106 (36.8%) in the sham group risk difference 10.7%, OR 0.52, 95% CI (0.27, 0.99),
P
= 0.047. When unadjusted for baseline variables,
P
= 0.11. The 28-day survival time in the PMX group was longer than for the sham group HR 0.56 (95% CI 0.33, 0.95)
P
= 0.03. PMX treatment compared with sham showed greater change in MAP median (IQR) 8 mmHg (− 0.5, 19.5) vs. 4 mmHg (− 4.0, 11)
P
= 0.04 and VFD median (IQR) 20 days (0.5, 23.5) vs. 6 days (0, 20),
P
= 0.004. There were no significant differences in other end points. There was a significant difference in mortality in PMX-treated patients with no bacterial growth on culture PMX, 6/30 (20%) vs. sham, 13/31 (41.9%),
P
= 0.005. The median EAA change in the population was − 12.9% (range: increase 49.2%–reduction 86.3%). The mortality in the above median EAA change group was PMX: 6/38 (15.7%) vs. sham 15/49 (30.6%),
P
= 0.08.
Conclusions
These hypothesis-generating results, based on an exploratory post hoc analysis of the EUPHRATES trial, suggest measurable responses in patients with septic shock and an EAA ≥ 0.6 to 0.89 on changes in mean arterial pressure, ventilator-free days and mortality.
Trial registration
Clinicaltrials.gov Identifier: NCT01046669. Funding Spectral Medical Incorporated.
Abstract
The approach of extended irreversible thermodynamics consists of promoting the dissipative fluxes to non-equilibrium thermodynamic variables. In a relativistic context, this naturally leads ...to the formulation of the theory of Israel and Stewart (1979), which is, to date, one of the most successful theories for relativistic dissipation. Although the generality of the principle makes it applicable to any dissipative fluid, a connection of the Israel–Stewart theory with microphysics has been established, through kinetic theory, only for the case of ideal quantum gases. By performing a convenient change of variables, we provide, for the case of bulk viscosity, an equivalent reformulation of the equations at the basis of extended irreversible thermodynamics. This approach maps any thermodynamic process which contributes to the bulk viscosity into a set of chemical reactions, whose reaction coordinates are abstract parameters describing the displacement from local thermodynamic equilibrium of the fluid element. We apply our new formalism to the case of the relativistic fluids, showing that the Israel–Stewart model for bulk viscosity is just the second-order expansion of a minimal model belonging to a larger class of non-perturbative theories for bulk viscosity which include the nuclear-reaction-mediated bulk viscosity of neutron star matter as a particular case. Furthermore, we show with concrete examples that our formalism provides new ways of computing the bulk viscosity directly and defines a simple prescription for constructing the Israel–Stewart model for a generic bulk-viscous fluid.
Abstract
We study the GENERIC hydrodynamic theory for relativistic liquids formulated by Öttinger and collaborators. We use the maximum entropy principle to derive its conditions for linear stability ...(in an arbitrary reference frame) and for relativistic causality. In addition, we show that, in the linear regime, its field equations can be recast into a symmetric-hyperbolic form. Once rewritten in this way, the linearised field equations turn out to be a particular realisation of the Israel–Stewart theory, where some of the Israel–Stewart free parameters are constrained. This also allows us to reinterpret the GENERIC framework in view of the principles of extended irreversible thermodynamics and to discuss its physical relevance to model (possibly viscoelastic) fluids.
During the spin-up phase of a large pulsar glitch – a sudden decrease of the rotational period of a neutron star – the angular velocity of the star may overshoot, namely reach values greater than ...that observed for the new post-glitch equilibrium. These transient phenomena are expected on the basis of theoretical models for pulsar internal dynamics, and their observation has the potential to provide an important diagnostic for glitch modelling. In this article, we present a simple criterion to assess the presence of an overshoot, based on the minimal analytical model that is able to reproduce an overshooting spin-up. We employed it to fit the data of the 2016 glitch of the Vela pulsar, obtaining estimates of the fractional moments of inertia of the internal superfluid components involved in the glitch, of the rise and decay timescales of the overshoot, and of the mutual friction parameters between the superfluid components and the normal one. We studied the cases with and without strong entrainment in the crust: in the former, we found an indication of a large inner core strongly coupled to the observable component, and of a reservoir of angular momentum extending into the core to densities below nuclear saturation; while in the latter, a large reservoir extending above nuclear saturation and a standard normal component without inner core were found.
The coupling of a small-scale Multi-Effect Distillation system for seawater desalination with a waste heat recovery Organic Rankine Cycle was studied. Two configurations were analysed: a hybrid ...serial-cascade and a cascade configuration. The heat source was a generic waste heat flow at 200 °C. Four sizes were considered for the Multi-Effect Distillation, from 500 to 2000 m3/day. The second law efficiency decreased with the desalination unit size for the hybrid configuration, while presented a maximum value in size range 500–2000 m3/day for the cascade configuration. For the serial-hybrid configuration, the second law efficiency decreased from 43.1% to 15.5% when passing from a Multi-Effect Distillation size of 500 to 2000 m3/day, while for the cascade, the values had a reduced variation between 26.2 and 21.4%. The economic analysis showed that the hybrid configuration reduced to a serial configuration, which was largely more profitable. Moreover, when the size of the Multi-Effect Distillation was smaller, the investment could be convenient also for a water price of 0.8 $/m3, and the profitability index in some configurations reached 2.4 with this water price. In most of the cases, the coupling with an Organic Rankine Cycle improved the investment and reduced the payback time.
ABSTRACT
Observations of pulsar glitches may provide insights on the internal physics of neutron stars and recent studies show how it is in principle possible to constrain pulsar masses with timing ...observations. The reliability of these estimates depends on the current uncertainties about the structure of neutron stars and on our ability to model the dynamics of the superfluid neutrons in the internal layers. We assume a simplified model for the rotational dynamics of a neutron star and estimate an upper bound to the mass of 25 pulsars from their largest glitch and average activity: the aim is to understand to which extent the mass constraints are sensitive to the choice of the unknown structural properties of neutron stars, like the extension of the superfluid region and the equation of state. Reasonable values, within the range measured for neutron star masses, are obtained only if the superfluid domain extends for at least a small region inside the outer core, which is compatible with calculations of the neutron S-wave pairing gap. Moreover, the mass constraints stabilize when the superfluid domain extends to densities over nuclear saturation, irrespective of the equation of state tested.
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