Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the Miller-Robert-Sommeria (MRS) entropy under these sole constraints. The vorticity fluctuations are Gaussian while the mean flow is characterized by a linear $\bar{\omega}-\psi$ relationship. Furthermore, the maximization of entropy at fixed energy, circulation and microscopic enstrophy is equivalent to the minimization of macroscopic enstrophy at fixed energy and circulation. This provides a justification of the minimum enstrophy principle from statistical mechanics when only the microscopic enstrophy is conserved among the infinite class of Casimir constraints. A new class of relaxation equations towards the statistical equilibrium state is derived. These equations can provide an effective description of the dynamics towards equilibrium or serve as numerical algorithms to determine maximum entropy or minimum enstrophy states. We use these relaxation equations to study geometry induced phase transitions in rectangular domains. In particular, we illustrate with the relaxation equations the transition between monopoles and dipoles predicted by Chavanis and Sommeria [J. Fluid. Mech. 314, 267 (1996)]. We take into account stable as well as metastable states and show that metastable states are robust and have negative specific heats. This is the first evidence of negative specific heats in that context. We also argue that saddle points of entropy can be long-lived and play a role in the dynamics because the system may not spontaneously generate the perturbations that destabilize them.Comment: 26 pages, 10 figure

Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations

We characterize the thermodynamical equilibrium states of axisymmetric Euler-Beltrami flows. They have the form of coherent structures presenting one or several cells. We find the relevant control parameters and derive the corresponding equations of state. We prove the coexistence of several equilibrium states for a given value of the control parameter like in 2D turbulence [Chavanis and Sommeria, J. Fluid Mech. 314, 267 (1996)]. We explore the stability of these equilibrium states and show that all states are saddle points of entropy and can, in principle, be destabilized by a perturbation with a larger wavenumber, resulting in a structure at the smallest available scale. This mechanism is therefore reminiscent of the 3D Richardson energy cascade towards smaller and smaller scales. Therefore, our system is truly intermediate between 2D turbulence (coherent structures) and 3D turbulence (energy cascade). We further explore numerically the robustness of the equilibrium states with respect to random perturbations using a relaxation algorithm in both canonical and microcanonical ensembles. We show that saddle points of entropy can be very robust and therefore play a role in the dynamics. We evidence differences in the robustness of the solutions in the canonical and microcanonical ensembles. A scenario of bifurcation between two different equilibria (with one or two cells) is proposed and discussed in connection with a recent observation of a turbulent bifurcation in a von Karman experiment [Ravelet et al., Phys. Rev. Lett. 93, 164501 (2004)].Comment: 25 pages; 16 figure

Genetic Algorithms in Supply Chain Scheduling of Ready-Mixed Concrete

The coordination of just-in-time production and transportation in a network of partially independent facilities to guarantee timely delivery to distributed customers is one of the most challenging aspects of supply chain management. From the theoretical perspective, the timely production/distribution can be viewed as a hybrid combination of planning, scheduling and routing problem, each notoriously affected by nearly prohibitive combinatorial complexity. From a practical viewpoint, the problem calls for a trade-off between risks and profits. This paper focuses on the ready-made concrete delivery: in addition to the mentioned complexity, strict time-constraints forbid both earliness and lateness of the supply. After developing a detailed model of the considered problem, we propose a novel meta-heuristic approach based on a hybrid genetic algorithm combined with constructive heuristics. A detailed case study derived from industrial data is used to illustrate the potential of the proposed approach

Neuropathic pain after thoracotomy: tracking signs and symptoms before and at monthly intervals following surgery

Background: Because the development of neuropathic symptoms contributes to pain severity and chronification after surgery, their early prediction is important to allow targeted treatment. Objectives: We longitudinally investigated trajectories of signs and symptoms in patients undergoing thoracotomy and assessed whether and at which time they were related to the development of neuropathic pain symptoms six months after surgery. Methods: Presurgical and six, monthly postsurgical assessments included questionnaires for mental and physical well-being (e.g. depression/anxiety, pain catastrophizing, sleep quality, neuropathic pain symptoms), and quantitative sensory testing (QST). Results: QST trajectories indicated nerve impairment of the surgery site with predominant loss of function. Signs of recovery towards the end of the assessment period were observed for some tests. Unsupervised cluster analysis with NPSI scores six months after surgery as clustering variable identified one group with no/low levels of neuropathic symptoms and one with moderate levels. The two groups differed w.r.t. several signs and symptoms already at early time points. Notably, neuropathic pain anywhere in the body differed already preoperatively and sleep impairment differentiated the two groups at all time points. Regression analysis revealed three factors that seemed particularly suited to predicted six months NPSI scores, namely preoperative neuropathic pain symptoms, with contributions from sleep impairment one month after surgery and the presence of dynamic mechanical allodynia three months after surgery. Conclusions: Clinical routine should focus on the individual’s physiological state, including pre-existing neuropathic pain and sleep quality to identify patients early who might be at risk to develop chronic post-surgical neuropathic pain

design optimization of a distributed energy system through cost and exergy assessments

Abstract In recent years, Distributed Energy Systems (DESs) have been recognized as a good option for sustainable development of future energy systems. With growing environmental concerns, design optimization of DESs through economic assessments only is not sufficient. To achieve long-run sustainability of energy supply, the key idea of this paper is to investigate exergy assessments in DES design optimization to attain rational use of energy resources while considering energy qualities of supply and demand. By using low-temperature sources for low-quality thermal demand, the waste of high-quality energy can be reduced, and the overall exergy efficiency can be increased. Based on a pre-established superstructure, the aim is to determine numbers and sizes of energy devices in the DES and the corresponding operation strategies. A multi-objective linear problem is formulated to reduce the total annual cost and increase the overall exergy efficiency. The Pareto frontier is found to provide different design options for planners based on economic and sustainability priorities, through minimizing a weighted-sum of the total annual cost and primary exergy input, by using branch-and-cut. Numerical results demonstrate that different optimized DES configurations can be found according to the two objectives. Moreover, results also show that the total annual cost and primary exergy input are reduced by 20% - 30% as compared with conventional energy supply systems

Statistical mechanics of Fofonoff flows in an oceanic basin

We study the minimization of potential enstrophy at fixed circulation and energy in an oceanic basin with arbitrary topography. For illustration, we consider a rectangular basin and a linear topography h=by which represents either a real bottom topography or the beta-effect appropriate to oceanic situations. Our minimum enstrophy principle is motivated by different arguments of statistical mechanics reviewed in the article. It leads to steady states of the quasigeostrophic (QG) equations characterized by a linear relationship between potential vorticity q and stream function psi. For low values of the energy, we recover Fofonoff flows [J. Mar. Res. 13, 254 (1954)] that display a strong westward jet. For large values of the energy, we obtain geometry induced phase transitions between monopoles and dipoles similar to those found by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)] in the absence of topography. In the presence of topography, we recover and confirm the results obtained by Venaille and Bouchet [Phys. Rev. Lett. 102, 104501 (2009)] using a different formalism. In addition, we introduce relaxation equations towards minimum potential enstrophy states and perform numerical simulations to illustrate the phase transitions in a rectangular oceanic basin with linear topography (or beta-effect).Comment: 26 pages, 28 figure

Effect of polyglucosamine on weight loss and metabolic parameters in overweight and obesity: A systemic review and meta-analysis

The use of dietary supplements for weight loss has gained significant momentum. Polyglucosamine, a chitosan derivative, is a dietary supplement increasingly used for weight loss. In this meta-analysis, we systematically summarized and quantified the key findings of four randomized, placebo-controlled clinical trials examining the effects of polyglucosamine supplementation and caloric restriction, and physical activity on body weight, body mass index (BMI), and waist circumference in subjects with overweight and obesity. The control group was set with a physical activity from 6–7 MET-h/week activity and up to 21 MET-h/week activity with caloric restriction. Compliance in the latter trials was reported via a follow-up questionnaire with the individual participants. The analysis included 399 subjects followed for a period ranging from 12 weeks to one year. Subjects’ age ranged from 21–75 years, BMI from 26–45 kg/m2, and all were white European or Caucasian in ethnicity. The meta-analyzed mean differences for random effects showed that polyglucosamine supplementation improves weight loss by −1.78 kg [−2.78, −0.79], BMI by −1.52 kg/m2 [−3.58, 0.54], and improves waist circumference reduction by −1.45 cm [−2.77, −0.12]. In conclusion, the use of polyglucosamine supplementation in conjunction with lifestyle behavioral therapies can be effective for weight reduction. Further studies are needed to examine the long-term effects of polyglucosamine supplementation on weight loss and other metabolic parameters

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [Ellis, Haven, Turkington, Nonlin., 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D, 237, 1998 (2008)]. They can provide a small-scale parametrization of 2D turbulence or serve as numerical algorithms to compute maximum entropy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.Comment: 21 pages, 9 figure