Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

Viscosity of andesite melts and its implication for magma mixing prior to Unzen 1991-1995 eruption

The viscosity of an iron-bearing melt with composition similar to Unzen andesite was determined experimentally in the high (109-1010.5 Pa·s) and low (5-1000 Pa·s) viscosity range using a parallel plate viscometer and the falling sphere method, respectively. Falling sphere experiments were carried out in an internally heated argon pressure vessel and in a piston cylinder apparatus at 1323 to 1573 K and 200 to 2000 MPa. Creep experiments were performed in the temperature range of 747 - 845 K at 300 MPa. The water content of the melt varies from nominally dry to 6.2 wt% H2O. The Fe2+/Fetot ratio was determined for each sample in the quenched glass using a colorimetric method. Pressure has minor influence on the viscosity compared with the effect of temperature, water content (main compositional parameter controlling the viscosity) or with the Fe2+/Fetot ratio (especially important at low water content of the melt). Based on our new viscosity data and literature data with measured Fe2+/Fetot ratio we propose a new empirical equation to estimate the viscosity η (in Pa·s) of andesitic melts as a function of temperature T (in K), water content w (in wt%) and Fe2+/Fetot ratio. The derived relationship reproduces the experimental data (87 in total) in the viscosity range from 100.5 to 1013 Pa·s with a 1σ standard deviation of 0.17 log units. However, application of this calculation model is limited to Fe2+/Fetot>0.3 and to temperatures above Tg. Moreover, in the high viscosity range the variation of viscosity with water content is constrained only by few experimental data and needs verification by additional measurements. The viscosity data are used to interpret mixing processes in the Unzen magma chamber prior to 1991-1995 eruption. We demonstrate that the viscosities of the rhyolite and andesite melts from the two end-member magmas are nearly identical prior and during mixing, enabling efficient magma mixing

The viscosity of shoshonitic melts (Vulcanello Peninsula, Aeolian Islands, Italy): insight on the magma ascent in dikes

The viscosity of shoshonitic melts from Vulcanello Peninsula (Vulcano Island, Italy) is experimentally determined at temperatures between 733 K and 1673 K. The water content of the melts varies from 0.03 to 4.75 wt% H2O. The micropenetration technique is employed at ambient pressure in the high viscosity range (109-1012 Pa·s). Falling sphere(s) experiments are performed at 500 and 2000 MPa in the low viscosity range (100.5-103 Pa·s). Results show a decrease of about 2 orders of magnitude in viscosity if ~ 3 wt% of water is added to the dry melt at 1300 K. At high temperature the viscosity of Vulcanello melts is intermediate between that of andesitic and basaltic melts. In contrast, at low temperatures (≤1050 K), the shoshonitic melt is characterized by a lower viscosity with respect to the two previous melts. Based on our new data set, a calculation model is proposed to predict the viscosity of the shoshonitic melts as a function of temperature and water content. The viscosity data are used to constrain the ascent velocity of shoshonitic magmas from Vulcanello within dikes. Using petrological data (temperature and crystal content of the magma) and volcanological information (geometrical parameters of the eruptive fissure and depth of magma storage), we estimate the time scale for the ascent of magma from the main reservoir to the surface. Results show time scales in the order of hours to few days. We conclude that the rapid ascent of poorly evolved melts from Moho depths should be taken into account for the hazard assessment of Vulcano Island

Coupled Numerical Analysis of Variations in the Capacity of Driven Energy Piles in Clay

Energy piles are an emerging alternative for the reduction of energy consumption to heat and cool buildings. Most of the research to date has focused on thermodynamic properties or axial and radial stress and strain of piles. This paper focuses on the effects of temperature fluctuation on the capacity of driven energy piles in clayey soils. Consolidation of clay surrounding driven piles affects the pile capacity (i.e., set up in clay). The heating and cooling periods of energy piles can create the excess pore-water pressure (EPWP, ue) or relax the existing one (e.g., due to pile driving or previous thermal loads) in clayey soils (due to the contraction and expansion of water) affecting the pile capacity. In the meantime, the thermal expansion and contraction of the pile also generate or relax the EPWP in the soil, which can be computed using the cavity-expansion theory. This paper studies the resulting changes in the pile capacity due to the daily and seasonal thermal cycles. The results show that thermal cycles in an energy pile can cause a decrease in the pile capacity leading to a delay in reaching the capacity after a complete clay set up

Effective Interactions and Volume Energies in Charged Colloids: Linear Response Theory

Interparticle interactions in charge-stabilized colloidal suspensions, of arbitrary salt concentration, are described at the level of effective interactions in an equivalent one-component system. Integrating out from the partition function the degrees of freedom of all microions, and assuming linear response to the macroion charges, general expressions are obtained for both an effective electrostatic pair interaction and an associated microion volume energy. For macroions with hard-sphere cores, the effective interaction is of the DLVO screened-Coulomb form, but with a modified screening constant that incorporates excluded volume effects. The volume energy -- a natural consequence of the one-component reduction -- contributes to the total free energy and can significantly influence thermodynamic properties in the limit of low-salt concentration. As illustrations, the osmotic pressure and bulk modulus are computed and compared with recent experimental measurements for deionized suspensions. For macroions of sufficient charge and concentration, it is shown that the counterions can act to soften or destabilize colloidal crystals.Comment: 14 pages, including 3 figure

Efficient cosmological parameter sampling using sparse grids

We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the likelihood-evaluation. We obtain excellent results over a large region in parameter space, comprising about 25 log-likelihoods around the peak, and we reproduce the one-dimensional projections of the likelihood almost perfectly. In speed and accuracy, our technique is competitive to existing approaches to accelerate parameter estimation based on polynomial interpolation or neural networks, while having some advantages over them. In our method, there is no danger of creating unphysical wiggles as it can be the case for polynomial fits of a high degree. Furthermore, we do not require a long training time as for neural networks, but the construction of the interpolation is determined by the time it takes to evaluate the likelihood at the sampling points, which can be parallelised to an arbitrary degree. Our approach is completely general, and it can adaptively exploit the properties of the underlying function. We can thus apply it to any problem where an accurate interpolation of a function is needed.Comment: Submitted to MNRAS, 13 pages, 13 figure