Search results for "Entropy"
showing 10 items of 496 documents
Six Matrix Adjustment Problems Solved by Some Fundamental Theorems on Biproportion
2011
After defining biproportion (or RAS) rigorously, we recall two fundamental theorems: unicity of biproportion (any biproportional algorithm leads to the same solution than biproportion, which turns biproportion into a mathematical tool as indisputable than proportion), ineffectiveness of separability (premultiplying or post multiplying the initial matrix by a diagonal matrix does not change the biproportional solution) and its corollary (it is equivalent to do a separable modification of the initial matrix or to do a proportional change of each biproportional factors). We then apply these theorems to show immediately that: i) no difficulties are encountered when solving the biproportional pr…
A first estimate of $\eta/s$ in Au+Au reactions at E$_{\rm lab}=1.23$ $A$GeV
2020
The HADES experiment at GSI has recently provided data on the flow coefficients $v_1,...,v_4$ for protons in Au+Au reactions at $E_{\rm lab} = 1.23$~$A$GeV (or $\sqrt{s_\mathrm{NN}}=2.4$ GeV). This data allows to estimate the shear viscosity over entropy ratio, $\eta/s$ at low energies via a coarse graining analysis of the UrQMD transport simulations of the flow harmonics in comparison to the experimental data. By this we can provide for the first time an estimate of $\eta/s\approx0.65\pm0.15$ (or $(8\pm2)\,(4\pi)^{-1}$) at such low energies.
Measurements of Higher Order Flow Harmonics inAu+AuCollisions atsNN=200 GeV
2011
Flow coefficients nu(n) for n = 2, 3, 4, characterizing the anisotropic collective flow in Au + Au collisions at root s(NN) = 200 GeV, are measured relative to event planes Psi(n), determined at large rapidity. We report nu(n) as a function of transverse momentum and collision centrality, and study the correlations among the event planes of different order n. The nu(n) are well described by hydrodynamic models which employ a Glauber Monte Carlo initial state geometry with fluctuations, providing additional constraining power on the interplay between initial conditions and the effects of viscosity as the system evolves. This new constraint can serve to improve the precision of the extracted …
Towards a Thermodynamic Description of Supercontinuum Generation
2009
Based on the kinetic wave theory, we describe continuous-wave supercontinuum generation as a thermalization process, i.e., an irreversible evolution of the optical field towards a state of maximum nonequilibrium entropy.
Comparison between Entropy and Resilience as Indirect Measures of Reliability in the Framework of Water Distribution Network Design
2014
Abstract The aim of this paper is to investigate which between the entropy and resilience indices represents a better indirect measure of reliability in the framework of water distribution network design. The methodology adopted consisted of (a) multi-objective optimizations performed in order to minimize costs and maximize reliability, expressed by means of one of the indirect indices at time; (b) retrospective performance assessment of the solutions of Pareto fronts obtained. Two case studies of different topological complexity were considered. Results showed that indices based on energetic concepts (resilience and modified resilience) represent a better compact estimate of reliability th…
Water quality sensor placement: a multi-objective and multi-criteria approach
2021
[EN] To satisfy their main goal, namely providing quality water to consumers, water distribution networks (WDNs) need to be suitably monitored. Only well designed and reliable monitoring data enables WDN managers to make sound decisions on their systems. In this belief, water utilities worldwide have invested in monitoring and data acquisition systems. However, good monitoring needs optimal sensor placement and presents a multi-objective problem where cost and quality are conflicting objectives (among others). In this paper, we address the solution to this multi-objective problem by integrating quality simulations using EPANET-MSX, with two optimization techniques. First, multi-objective op…
An algorithmic construction of entropies in higher-order nonlinear PDEs
2006
A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can …
Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation
2021
Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a…
Quantum Critical Scaling under Periodic Driving
2016
Universality is key to the theory of phase transition stating that the equilibrium properties of observables near a phase transition can be classified according to few critical exponents. These exponents rule an universal scaling behaviour that witnesses the irrelevance of the model's microscopic details at criticality. Here we discuss the persistence of such a scaling in a one-dimensional quantum Ising model under sinusoidal modulation in time of its transverse magnetic field. We show that scaling of various quantities (concurrence, entanglement entropy, magnetic and fidelity susceptibility) endures up to a stroboscopic time $\tau_{bd}$, proportional to the size of the system. This behavio…
A Wigner molecule at extremely low densities: a numerically exact study
2019
In this work we investigate Wigner localization at very low densities by means of the exact diagonalization of the Hamiltonian. This yields numerically exact results. In particular, we study a quasi-one-dimensional system of two electrons that are confined to a ring by three-dimensional gaussians placed along the ring perimeter. To characterize the Wigner localization we study several appropriate observables, namely the two-body reduced density matrix, the localization tensor and the particle-hole entropy. We show that the localization tensor is the most promising quantity to study Wigner localization since it accurately captures the transition from the delocalized to the localized state an…