Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

Thermodynamic instabilities in one dimensional particle lattices: a finite-size scaling approach

One-dimensional thermodynamic instabilities are phase transitions not prohibited by Landau's argument, because the energy of the domain wall (DW) which separates the two phases is infinite. Whether they actually occur in a given system of particles must be demonstrated on a case-by-case basis by examining the (non-) analyticity properties of the corresponding transfer integral (TI) equation. The present note deals with the generic Peyrard-Bishop model of DNA denaturation. In the absence of exact statements about the spectrum of the singular TI equation, I use Gauss-Hermite quadratures to achieve a single-parameter-controlled approach to rounding effects; this allows me to employ finite-size scaling concepts in order to demonstrate that a phase transition occurs and to derive the critical exponents.Comment: 5 pages, 6 figures, subm. to Phys. Rev.

Variational Calculations for 3^3He Impurities on 4^4He Droplets

Variational Monte Carlo method is used to calculate ground state properties of $^4$He droplets, containing 70, 112, 168, 240, 330, and 728 particles. The resulting particle and kinetic energy densities are used as an input in the Feynman-Lekner theory for $^3$He impurities. The kinetic energy density of $^4$He atoms and the energy of the $^3$He surface states are compared with the results of previous phenomenological calculations.Comment: 12 pages, in revtex 3.0, with 5 .ps figure

Apparent phase transitions in finite one-dimensional sine-Gordon lattices

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.Comment: 7 pages, 4 figure

Superfluidity of a perfect quantum crystal

In recent years, experimental data were published which point to the possibility of the existence of superfluidity in solid helium. To investigate this phenomenon theoretically we employ a hierarchy of equations for reduced density matrices which describes a quantum system that is in thermodynamic equilibrium below the Bose-Einstein condensation point, the hierarchy being obtained earlier by the author. It is shown that the hierarchy admits solutions relevant to a perfect crystal (immobile) in which there is a frictionless flow of atoms, which testifies to the possibility of superfluidity in ideal solids. The solutions are studied with the help of the bifurcation method and some their peculiarities are found out. Various physical aspects of the problem, among them experimental ones, are discussed as well.Comment: 24 pages with 2 figures, version accepted for publication in Eur.Phys.J.

Variational Monte Carlo study of the ground state properties and vacancy formation energy of solid para-H2 using a shadow wave function

A Shadow Wave Function (SWF) is employed along with Variational Monte Carlo techniques to describe the ground state properties of solid molecular para-hydrogen. The study has been extended to densities below the equilibrium value, to obtain a parameterization of the SWF useful for the description of inhomogeneous phases. We also present an estimate of the vacancy formation energy as a function of the density, and discuss the importance of relaxation effects near the vacant site

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Nondestructive monitoring of ageing of Alkali resistant Glass fiber reinforced cement (GRC)

Glass fiber reinforced cement (GRC) is a composite material made of portland cement mortar and alkali resistant (AR) fibers. AR fibers are added to portland cement to give the material additional flexural strength and toughness. However, ageing deteriorates the fibers and as a result the improvement in the mechanical properties resulted from the fiber addition disappears as the structure becomes old. The aim of this paper is monitoring GRC ageing by nondestructive evaluation (NDE) techniques. Two different NDE techniques (1) nonlinear impact resonant acoustic spectroscopy analysis and (2) propagating ultrasonic guided waves are used for this purpose. Both techniques revealed a reduction of the nonlinear behavior in the GRC material with ageing. Specimens are then loaded to failure to obtain their strength and stiffness. Compared to the un-aged specimens, the aged specimens are found to exhibit more linear behavior, have more stiffness but less toughness. Finally, undisturbed fragments on the fracture surface from mechanical tests are inspected under the electron microscope, to understand the fundamental mechanisms that cause the change in the GRC behavior with ageing.The authors want to acknowledge the financial support of the Ministerio de Ciencia e Innovacion MICINN, Spain, and FEDER funding (Ondacem Project: BIA 2010-19933) and BES-2011-044624. Also thanks to PAID-02-11 Program from Universitat Politecnica de Valencia.Eiras Fernández, JN.; Kundu, T.; Bonilla Salvador, MM.; Paya Bernabeu, JJ. (2013). Nondestructive monitoring of ageing of Alkali resistant Glass fiber reinforced cement (GRC). Journal of Nondestructive Evaluation - NDT and E International. 32:300-314. https://doi.org/10.1007/s10921-013-0183-yS30031432Bentur, A., Fibre, M.S.: Reinforced Cementitious Composites, 2nd edn. Taylor and Francis, New York (2007)Purnell, P., Short, N.R., Page, C.L.: A static fatigue model for the durability of glass fibre reinforced cement. J. Mater. Sci. 36(22), 5385–5390 (2001)Ferreira, J.G., Branco, F.A.: Structural application of GRC in telecommunication towers. Constr. Build. Mater. 21(1), 19–28 (2007)Bentur, A., Ben-Bassat, M., Schneider, D.: Durability of glass-fiber-reinforced cements with different alkali-resistant glass fibers. J. Am. Ceram. Soc. 68(4), 203–208 (1985)Cheng, J., Liang, W., Hu, Y., Chen, Q., Frischat, G.H.: Development of a new alkali resistant coating. J. Sol-Gel Sci. Technol. 27(3), 309–313 (2003)Liang, W., Cheng, J., Hu, Y., Luo, H.: Improved properties of GRC composites using commercial E-glass fibers with new coatings. Mater. Res. Bull. 37(4), 641–646 (2002)Payá, J., Bonilla, M., Borrachero, M.V., Monzó, J., Peris-Mora, E., Lalinde, L.F.: Reusing fly ash in glass fibre reinforced cement: a new generation of high-quality GRC composites. Waste Manag. 27(10), 1416–1421 (2007)Zhang, Y., Sun, W., Shang, L., Pan, G.: The effect of high content of fly ash on the properties of glass fiber reinforced cementitious composites. Cem. Concr. Res. 27(12), 1885–1891 (1997)Purnell, P., Short, N., Page, C.: Super-critical carbonation of glass-fibre reinforced cement. Part 1: mechanical testing and chemical analysis. Composites, Part A, Appl. Sci. Manuf. 32(12), 1777–1787 (2001)EN 1170-8:2008. Test method for glass-fibre reinforced cement. Cyclic weathering type testPurnell, P.: Interpretation of climatic temperature variations for accelerated ageing models. J. Mater. Sci. 39(1), 113–118 (2004)Enfedaque, A., Sánchez Paradela, L., Sánchez-Gálvez, V.: An alternative methodology to predict aging effects on the mechanical properties of glass fiber reinforced cements (GRC). Constr. Build. Mater. 27(1), 425–431 (2012)Litherland, K.L., Maguire, P., Proctor, B.A.: A test method for the strength of glass fibres in cement. Int. J. Cem. Compos. Lightweight Concr. 6(1), 39–45 (1984)Itterbeeck, P., Cuypers, H., Orlowsky, J., Wastiels, J.: Evaluation of the strand in cement (SIC) test for GRCs with improved durability. Mater. Struct. 41(6), 1109–1116 (2007)Guyer, R.A., Johnson, P.A.: Nonlinear mesoscopic elasticity: evidence for a new class of materials. Phys. Today 52, 30 (1999)Johnson, P.A.: Nonequilibrium nonlinear dynamics in solids: state of the art. In: Delsanto, P.P. (ed.) Universality of Nonclassical Nonlinearity, pp. 49–69. Springer, New York (2006)Guyer, R.A., McCall, K.R., Boitnott, G.N.: Hysteresis, discrete memory, and nonlinear wave propagation in rock: a new paradigm. Phys. Rev. Lett. 74(17), 3491–3494 (1995)Mayergoyz, I.D.: Mathematical Models of Hysteresis and Their Applications. Academic Press, New York (2003)Van Den Abeele, K.E.A., Carmeliet, J., Ten Cate, J.A., Johnson, P.A.: Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part II: single-mode nonlinear resonance acoustic spectroscopy. Res. Nondestruct. Eval. 12(1), 31–42 (2000)Chen, J., Jayapalan, A.R., Kim, J.Y., Kurtis, K.E., Jacobs, L.J.: Rapid evaluation of alkali–silica reactivity of aggregates using a nonlinear resonance spectroscopy technique. Cem. Concr. Res. 40(6), 914–923 (2010)Leśnicki, K.J., Kim, J.Y., Kurtis, K.E., Jacobs, L.J.: Characterization of ASR damage in concrete using nonlinear impact resonance acoustic spectroscopy technique. Nondestruct. Test. Eval. Int. 44(8), 721–727 (2011)Bouchaala, F., Payan, C., Garnier, V., Balayssac, J.P.: Carbonation assessment in concrete by nonlinear ultrasound. Cem. Concr. Res. 41(5), 557–559 (2011)Eiras, J.N., Popovics, J.S., Borrachero, M.V., Monzó, J., Payá, J.: Nonlinear impact resonant acoustic spectroscopy to discern mechanical damage in cement based materials. In: 15th International Conference on Experimental Mechanics, Porto, Portugal (2012)Kundu, T.: Ultrasonic Nondestructive Evaluation: Engineering and Biological Material Characterization. CRC Press, Boca Raton (2004)Kundu, T.: Ultrasonic and Electromagnetic NDE for Structure and Material Characterization—Engineering and Biomedical Applications. CRC Press, Boca Raton (2012)Dutta, D., Sohn, H., Harries, K.A., Rizzo, P.: A nonlinear acoustic technique for crack detection in metallic structures. Struct. Health Monit. 8(3), 251–262 (2009)Aymerich, F., Staszewski, W.J.: Impact damage detection in composite laminates using nonlinear acoustics. Composites, Part A, Appl. Sci. Manuf. 41(9), 1084–1092 (2010)EN 1170-1:1998. Precast concrete products. Test method for glass-fibre reinforced cement. Measuring the consistency of the matrix, “Slump test” methodMontgomery, P.L.: A block Lanczos algorithm for finding dependencies over GF(2). In: EUROCRYPT ’95. Lecture Notes in Computer Science, vol. 921, pp. 106–120. Springer, Berlin (1995)EN 1170-5:1998. Precast concrete products. Test method for glass-fibre reinforced cement. Measuring bending strength, “complete bending test” methodRomero, R., Zúnica, L.R.: Métodos Estadísticos en Ingeniería. Universitat Politècnica València, Valencia (2005)Kundu, T.: Fundamentals of Fracture Mechanics. CRC Press, Boca Raton (2008)ASTM C 215:08. Standard Test Method for Fundamental Transverse, Longitudinal, and Torsional Frequencies of Concrete Specimens (2008)Hewlett, P.C.: Lea’s Chemistry of Cement and Concrete, 4th edn. Butterworth-Heinemann, Oxford (2003)Zhu, W., Bartos, P.J.M.: Assessment of interfacial microstructure and bond properties in aged GRC using a novel microindentation method. Cem. Concr. Res. 27(11), 1701–1711 (1997)Purnell, P., Buchanan, A.J., Short, N.R., Page, C.L., Majumdar, A.J.: Determination of bond strength in glass fibre reinforced cement using petrography and image analysis. J. Mater. Sci. 35(18), 4653–4659 (2000)Visalvanich, K., Naaman, A.E.: Fracture model for fiber reinforced concrete. J. ACI Proc. 80(2), 128–138 (1983)Kundu, T., Jang, H.S., Cha, Y.H., Desai, C.S.: A simple model to predict the effect of volume fraction, diameter, and length of fibers on strength variation of fiber reinforced brittle matrix composites. Int. J. Numer. Anal. Methods Geomech. 24, 655–673 (2000)Li, V.C., Maalej, M.: Toughening in cement based composites. Part II: fiber reinforced composites. Cem. Concr. Compos. 18, 239–249 (1996)Van Den Abeele, K.E.A., Johnson, P.A., Sutin, A.: Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part I: nonlinear wave modulation spectroscopy (NWMS). Res. Nondestruct. Eval. 12(1), 17–30 (2000

Dynamics of liquid He-4 in confined geometries from Time-Dependent Density Functional calculations

We present numerical results obtained from Time-Dependent Density Functional calculations of the dynamics of liquid He-4 in different environments characterized by geometrical confinement. The time-dependent density profile and velocity field of He-4 are obtained by means of direct numerical integration of the non-linear Schrodinger equation associated with a phenomenological energy functional which describes accurately both the static and dynamic properties of bulk liquid He-4. Our implementation allows for a general solution in 3-D (i.e. no symmetries are assumed in order to simplify the calculations). We apply our method to study the real-time dynamics of pure and alkali-doped clusters, of a monolayer film on a weakly attractive surface and a nano-droplet spreading on a solid surface.Comment: q 1 tex file + 9 Ps figure

Integrating sequence and array data to create an improved 1000 Genomes Project haplotype reference panel

A major use of the 1000 Genomes Project (1000GP) data is genotype imputation in genome-wide association studies (GWAS). Here we develop a method to estimate haplotypes from low-coverage sequencing data that can take advantage of single-nucleotide polymorphism (SNP) microarray genotypes on the same samples. First the SNP array data are phased to build a backbone (or 'scaffold') of haplotypes across each chromosome. We then phase the sequence data 'onto' this haplotype scaffold. This approach can take advantage of relatedness between sequenced and non-sequenced samples to improve accuracy. We use this method to create a new 1000GP haplotype reference set for use by the human genetic community. Using a set of validation genotypes at SNP and bi-allelic indels we show that these haplotypes have lower genotype discordance and improved imputation performance into downstream GWAS samples, especially at low-frequency variants. © 2014 Macmillan Publishers Limited. All rights reserved