Representing fuzzy numbers for fuzzy calculus

In this paper we illustrate the LU representation of fuzzy numbers and present an LU-fuzzy calculator, in order to explain the use of the LU-fuzzy model and to show the advantage of the parametrization. The model can be applied either in the level-cut or in generalized LR frames. The hand-like fuzzy calculator has been developed for the MSWindows platform and produces the basic fuzzy calculus: the arithmetic operations (scalar multiplication, addition, subtraction, multiplication, division) and the fuzzy extension of many univariate functions (exponential, logarithm, power with numeric or fuzzy exponent, sin, arcsin, cos, arccos, tan, arctan, square root, Gaussian, hyperbolic sinh, cosh, tanh and inverses, erf and erfc error functions, cumulative standard normal distribution).Fuzzy Sets, LU-fuzzy Calculator, Fuzzy Calculus, Parametric LU represemtation

An LU-fuzzy calculator for the basic fuzzy calculus

The LU-model for fuzzy numbers has been introduced in [4] and applied to fuzzy calculus in [9]; in this paper we build an LU-fuzzy calculator, in order to explain the use of the LU-fuzzy representation and to show the advantage of the parametrization. The calculator produces the basic fuzzy calculus: the arithmetic operations (scalar multiplication, addition, subtraction, multiplica- tion, division) and the fuzzy extension of many univariate functions (power with integer positive or negative exponent, exponential , logarithm, general power function with numeric or fuzzy exponent, sin, arcsin, cos, arccos, tan, arctan, square root, Gaussian and standard Gaussian functions, hyperbolic sinh, cosh, tanh and inverses, erf error function and complementary erfc error function, cu- mulative standard normal distribution). The use of the calculator is illustrated.Fuzzy Sets, LU-fuzzy Calculator, Fuzzy Calculus

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poissons ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes

Interval LU-fuzzy arithmetic in the Black and Scholes option pricing

In financial markets people have to cope with a lot of uncertainty while making decisions. Many models have been introduced in the last years to handle vagueness but it is very difficult to capture together all the fundamental characteristics of real markets. Fuzzy modeling for finance seems to have some challenging features describing the financial markets behavior; in this paper we show that the vagueness induced by the fuzzy mathematics can be relevant in modelling objects in finance, especially when a flexible parametrization is adopted to represent the fuzzy numbers. Fuzzy calculus for financial applications requires a big amount of computations and the LU-fuzzy representation produces good results due to the fact that it is computationally fast and it reproduces the essential quality of the shape of fuzzy numbers involved in computations. The paper considers the Black and Scholes option pricing formula, as long as many other have done in the last few years. We suggest the use of the LU-fuzzy parametric representation for fuzzy numbers, introduced in Guerra and Stefanini and improved in Stefanini, Sorini and Guerra, in the framework of the Black and Scholes model for option pricing, everywhere recognized as a benchmark; the details of the computations by the interval fuzzy arithmetic approach and an illustrative example are also incuded.Fuzzy Operations, Option Pricing, Black and Scholes

Inhomogeneous Reionization Models in Cosmological Hydrodynamical Simulations

In this work we present a new hybrid method to simulate the thermal effects of the reionization in cosmological hydrodynamical simulations. The method improves upon the standard approach used in simulations of the intergalactic medium (IGM) and galaxy formation without a significant increase of the computational cost allowing for efficient exploration of the parameter space. The method uses a small set of phenomenological input parameters and combines a semi-numerical reionization model to solve for the topology of reionization and an approximate model of how reionization heats the IGM, with the massively parallel \texttt{Nyx} hydrodynamics code, specifically designed to solve for the structure of diffuse IGM gas. We have produced several large-scale high resolution cosmological hydrodynamical simulations ($2048^3$, $L_{\rm box} = 40$ Mpc/h) with different instantaneous and inhomogeneous HI reionization models that use this new methodology. We study the IGM thermal properties of these models and find that large scale temperature fluctuations extend well beyond the end of reionization. Analyzing the 1D flux power spectrum of these models, we find up to $\sim 50\%$ differences in the large scale properties (low modes, $k\lesssim0.01$ s/km) of the post-reionization power spectrum due to the thermal fluctuations. We show that these differences could allow one to distinguish between different reionization scenarios already with existing Ly$\alpha$ forest measurements. Finally, we explore the differences in the small-scale cutoff of the power spectrum and we find that, for the same heat input, models show very good agreement provided that the reionization redshift of the instantaneous reionization model happens at the midpoint of the inhomogeneous model.Comment: 24 pages, 16 figures. Accepted by MNRAS. Minor changes to match published versio

Modeling the Lyman-alpha Forest in Collisionless Simulations

Cosmological hydrodynamic simulations can accurately predict the properties of the intergalactic medium (IGM), but only under the condition of retaining high spatial resolution necessary to resolve density fluctuations in the IGM. This resolution constraint prohibits simulating large volumes, such as those probed by BOSS and future surveys, like DESI and 4MOST. To overcome this limitation, we present Iteratively Matched Statistics (IMS), a novel method to accurately model the Lyman-alpha forest with collisionless N-body simulations, where the relevant density fluctuations are unresolved. We use a small-box, high-resolution hydrodynamic simulation to obtain the probability distribution function (PDF) and the power spectrum of the real-space Lyman-alpha forest flux. These two statistics are iteratively mapped onto a pseudo-flux field of an N-body simulation, which we construct from the matter density. We demonstrate that our method can perfectly reproduce line-of-sight observables, such as the PDF and power spectrum, and accurately reproduce the 3D flux power spectrum (5-20%). We quantify the performance of the commonly used Gaussian smoothing technique and show that it has significantly lower accuracy (20-80%), especially for N-body simulations with achievable mean inter-particle separations in large-volume simulations. In addition, we show that IMS produces reasonable and smooth spectra, making it a powerful tool for modeling the IGM in large cosmological volumes and for producing realistic "mock" skies for Lyman-alpha forest surveys.Comment: 25 pages, 15 figures, submitted to Ap

Orbital Order and Spontaneous Orthorhombicity in Iron Pnictides

A growing list of experiments show orthorhombic electronic anisotropy in the iron pnictides, in some cases at temperatures well above the spin density wave transition. These experiments include neutron scattering, resistivity and magnetoresistance measurements, and a variety of spectroscopies. We explore the idea that these anisotropies stem from a common underlying cause: orbital order manifest in an unequal occupation of $d_{xz}$ and $d_{yz}$ orbitals, arising from the coupled spin-orbital degrees of freedom. We emphasize the distinction between the total orbital occupation (the integrated density of states), where the order parameter may be small, and the orbital polarization near the Fermi level which can be more pronounced. We also discuss light-polarization studies of angle-resolved photoemission, and demonstrate how x-ray absorption linear dichroism may be used as a method to detect an orbital order parameter.Comment: Orig.: 4+ pages; Rev.: 4+ pages with updated content and reference