Analytical continuum mechanics \`a la Hamilton-Piola: least action principle for second gradient continua and capillary fluids

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta.Comment: 52 page

Transverse surface waves on a cylindrical surface with coating

We discuss the propagation of transverse surface waves that are so-called whispering-gallery waves along a surface of an elastic cylinder with coating. The coating is modelled in the framework of linearized Gurtin–Murdoch surface elasticity. Other interpretations of the surface shear modulus are given and relations to so-called stiff interface and stiff skin model are discussed. The dispersion relations are obtained and analyzed

Combination of rainfall thresholds and susceptibility maps for dynamic landslide hazard assessment at regional scale

We propose a methodology to couple rainfall thresholds and susceptibility maps for dynamic landslide hazard assessment at regional scale. Both inputs are combined in a purposely-built hazard matrix to get a spatially and temporally variable definition of landslide hazard: while statistical rainfall thresholds are used to accomplish a temporal forecasting with very coarse spatial resolution, landslide susceptibility maps provide static spatial information about the probability of landslide occurrence at fine spatial resolution. The test site is the Northern part of Tuscany (Italy), where a recent landslide susceptibility map and a set of recently updated rainfall thresholds are available. These products were modified and updated to meet the requirements of the proposed procedure: the susceptibility map was reclassified and the threshold set was expanded defining additional thresholds. The hazard matrix combines three susceptibility classes (S1, low susceptibility; S2 medium susceptibility; S3 high susceptibility) and three rainfall rate classes (R1, R2, R3), defining five hazard classes, from H0 (null hazard) to H4 (high hazard). A key passage of the procedure is the appropriate calibration and validation of the matrix, letting the hazard classes have a precise meaning in terms of expected consequences and hazard management. The employ of the proposed procedure in a regional warning system brings two main advantages: (i) it is possible to better hypothesize when and where landslide are expected and with which hazard degree, thus fostering a more effective hazard and risk management (e.g., setting priorities of intervention); (ii) the spatial resolution of the regional scale warning system is markedly refined because from time to time the areas where landslides are expected represent only a fraction of the alert zone

Microfiltration and ultra-high-pressure homogenization for extending the shelf-storage stability of UHT milk

Fat separation, gelation or sedimentation of UHT milk during shelf-storage represent instability phenomena causing the product rejection by consumers. Stability of UHT milk is of increasing concern because access to emerging markets currently implies for this product to be stable during shipping and prolonged storage, up to 12 months. The role of microfiltration prior to UHT process in avoiding or retarding the gelation or sediment formation was studied by comparing microfiltered UHT milk to conventional UHT milk. A second trial was set up to study the effects of double ultra-high pressure homogenization in delaying the cream rising and UHT milk homogenized once at lower pressure was taken as control. All milk samples were produced at industrial plant level. Milk packages were stored at 22 \ub0C, opened monthly for visually inspecting the presence of cream layer, gel or sediment and then analysed. Microfiltration markedly delayed the formation of both gel particles and sediment, with respect to the control, and slowed down the proteolysis in terms of accumulation of peptides although no correlation was observed between the two phenomena. The double homogenization, also evaluated at ultra-structural level, narrowed the fat globule distribution and the second one (400 MPa), performed downstream to the sterilization step, disrupted the fat-protein aggregates produced in the first one (250 MPa). The adopted conditions avoided the appearance of the cream layer in the UHT milk up to 18 months. This study contributes important knowledge for developing strategies to delay instability phenomena in UHT milk destined to extremely long shelf storage

Galactic Binary Gravitational Wave Noise within LISA Frequency Band

Gravitational wave noise associated with unresolved binary stars in the Galaxy is studied with the special aim of determining the upper frequency at which it stops to contribute at the rms noise level of the proposed space-born interferometer (LISA). The upper limit to this background is derived from the statistics of SN Ia explosions, part of which can be triggered by binary white dwarf coalescences. The upper limiting frequency at which binary stochastic noise crosses LISA rms sensitivity is found to lie within the range 0.03-0.07 Hz, depending on the galactic binary white dwarf coalescence rate. To be reliably detectable by LISA, the energy density of relic cosmological background per logarithmic frequency interval should be Omega_{GW}h_{100}^2>10^{-8} at f>0.03 Hz.Comment: 16 pages with 1 eps figure, aasms4.sty, to appear in the ApJ vol. 494 February 20, 1998 issu

Changes in the soluble nitrogen fraction of milk throughout PDO Grana Padano cheese-making

The behaviour of soluble nitrogen compounds during Grana Padano cheese-making was studied at eight dairies. Raw milk, skimmed milk, sweet whey and the derived natural whey culture, collected from 24 processes, were analysed for soluble whey proteins (\u3b1-lactalbumin and \u3b2-lactoglobulin), proteose-peptones (PP), small peptides (SP), caseinomacropeptides (CMPs), and free amino acids (FAAs). The PP fraction increased during milk natural creaming, then part of it was selectively retained in the curd and the rest degraded in the first few hours of whey fermentation, together with \u3b1-lactalbumin, CMPs and part of SP. Features outlined for the whey culture were confirmed on 30 samples collected at six different dairies. A time course study of the whey fermentation showed that degradation of \u3b1-lactalbumin began when the pH dropped below 4, whereas \u3b2-lactoglobulin content did not change. Uptake of specific FAAs was shown to support the initial growth of lactic acid bacteria in whey