Tail Entropy Research Articles

Generalized Beta-Generated Distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also have tractable properties: we present various expansions for moments, generating function, quantiles, deviations and reliability. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

A direct proof of the tail variational principle and its extension to maps

AbstractDownarowicz [Entropy structure. J. Anal.96 (2005), 57–116] stated a variational principle for the tail entropy for invertible continuous dynamical systems of a compact metric space. We give here an elementary proof of this variational principle. Furthermore, we extend the result to the non-invertible case.

Anomalous Phase Sequences in Lyotropic Liquid Crystals

We present a coarse-grained model in order to describe the unusual sequence of mesophases observed in aqueous solutions of nonionic lipids, such as monoolein. The lipid molecules are modeled as a rigid head and a flexible Gaussian tail, and water is treated explicitly. A key component of the model is thermally reversible hydrogen bonding between the lipid head and water resulting in changes in both head volume and the interactions of the hydrated head with its surroundings. Phase diagrams obtained from unit-cell self-consistent field simulations capture the qualitative thermotropic and lyotropic phase behavior of the monoolein-water system. The unusual phase sequences result from a competition between hydrogen bond formation, changes in head volume and interactions, lipid tail entropy, and the hydrophobic effect.

Maximizing Entropy by Minimizing Area: Towards a New Principle of Self-Organization

We propose a heuristic explanation for the numerous non-close-packed crystal structures observed in various colloidal systems. By developing an analogy between soap froths and the soft coronas of fuzzy colloids, we provide a geometrical interpretation of the free energy of soft spheres. Within this picture, we show that the close-packing rule associated with hard-core interactions and positional entropy of particles is frustrated by a minimum-area principle associated with the soft tail and internal entropy of the soft coronas. We also discuss these ideas in terms of crystal architecture and pair distribution functions and analyze the phase diagram of a model hard-sphere−square-shoulder system within the cellular theory. We find that the A15 lattice, known to be area minimizing, is favored for a reasonable range of model parameters and so it is among the possible equilibrium states for a variety of colloidal systems. We also show that in the case of short-range convex potentials the A15 and other non-clos...

Structural reliability estimation using Monte Carlo simulation and Pearson's curves

At present Level 2 and importance sampling methods are the main tools used to estimate reliability of structural systems. But sometimes application of these techniques to realistic problems involves certain difficulties. In order to overcome the difficulties it is suggested to use Monte Carlo simulation in combination with two other techniques-extreme value and tail entropy approximations; an appropriate Pearson's curve is fit to represent simulation results. On the basis of this approach an algorithm and computer program for structural reliability estimation are developed. A number of specially chosen numerical examples are considered with the aim of checking the accuracy of the approach and comparing it with the Level 2 and importance sampling methods. The field of application of the approach is revealed.

Tail entropy approximations

A three parameter tail entropy approximation ( TEA) suitable for reliability and risk analysis is described and illustrated by examples. The TEA is determined directly from sample data. It combines the best features of tail approximation and entropy optimization for structural safety analysis. Estimation of the distributions of basic random variables from sample data is a critical step in the analysis of structural safety and other random phenomena. Standard estimation methods may be simple, but results are sensitive to the necessary but arbitrary assumptions about distribution type. The method of minimum relative entropy is more objective and less sensitive to arbitrary assumptions, but requires optimization procedures and some of the results are mathematically intractable. The TEA method is a tractable and accurate combination, useful when a tail approximation is appropriate.

Entropy estimation of hydrological extremes

The method of Relative Entropy with Fractile constraints (REF method) is explained and applied to model extreme compound hydrological phenomena, such as extreme sea levels under storm conditions. Also presented is a simple method of Tail Entropy Approximation (TEA), which amounts to a correction of traditional statistical estimates for extreme observations.

Ordered phases of rigid cores having semiflexible tails. II. Model for smectic-Aand reentrant-nematic phases with hard repulsions

The general partition function of the preceding paper is applied to the special cases of smectic-$A$ and nematic liquid crystals and isotropic liquids in bulk phases. The relative stabilities of the isotropic, nematic, smectic-$A$, and reentrant-nematic phases are studied as a fucntion of temperature, pressure, tail flexibility, and tail length. The following thermodynamic and molecular ordering properties are studied in these phases and at the phase transitions: smectic-$A$ order parameter, core and tail intermolecular orientational order parameters, tail intramolecular orientational order parameter, density, and entropy. The role of the semiflexible tails in stabilizing the smectic-$A$ and reentrant-nematic phases is explicitly elucidated.