A minimum principle for superharmonic functions subject to interface conditions

AbstractLet D be a bounded domain in R2 with smooth boundary. Let B1, …, Bm be non-intersecting smooth Jordan curves contained in D, and let D′ denote the complement of ∪i − 1m Bi respect to D. Suppose that u ϵ C2(D′) ∩ C(D̄) and Δu ⩽ 0 in D′ (where Δ is the Laplacian), while across each “interface” Bi, i = 1,…, m, there is “continuity of flux” (as suggested by the theory of heat conduction). It is proved here that the presence of the interfaces does not alter the conclusions of the classical minimum principle (for Δu ⩽ 0 in D). The result is extended in several regards. Also it is applied to an elliptic free boundary problem and to the proof of uniqueness for steady-state heat conduction in a composite medium. Finally this minimum principle (which assumes “continuity of flux”) is compared with one due to Collatz and Werner which employs an alternative interface condition

Long-Time Behavior of Quasilinear Thermoelastic Kirchhoff-Love Plates with Second Sound

We consider an initial-boundary-value problem for a thermoelastic Kirchhoff & Love plate, thermally insulated and simply supported on the boundary, incorporating rotational inertia and a quasilinear hypoelastic response, while the heat effects are modeled using the hyperbolic Maxwell-Cattaneo-Vernotte law giving rise to a 'second sound' effect. We study the local well-posedness of the resulting quasilinear mixed-order hyperbolic system in a suitable solution class of smooth functions mapping into Sobolev $H^{k}$-spaces. Exploiting the sole source of energy dissipation entering the system through the hyperbolic heat flux moment, provided the initial data are small in a lower topology (basic energy level corresponding to weak solutions), we prove a nonlinear stabilizability estimate furnishing global existence & uniqueness and exponential decay of classical solutions.Comment: 46 page

The Borexino Thermal Monitoring & Management System and simulations of the fluid-dynamics of the Borexino detector under asymmetrical, changing boundary conditions

A comprehensive monitoring system for the thermal environment inside the Borexino neutrino detector was developed and installed in order to reduce uncertainties in determining temperatures throughout the detector. A complementary thermal management system limits undesirable thermal couplings between the environment and Borexino's active sections. This strategy is bringing improved radioactive background conditions to the region of interest for the physics signal thanks to reduced fluid mixing induced in the liquid scintillator. Although fluid-dynamical equilibrium has not yet been fully reached, and thermal fine-tuning is possible, the system has proven extremely effective at stabilizing the detector's thermal conditions while offering precise insights into its mechanisms of internal thermal transport. Furthermore, a Computational Fluid-Dynamics analysis has been performed, based on the empirical measurements provided by the thermal monitoring system, and providing information into present and future thermal trends. A two-dimensional modeling approach was implemented in order to achieve a proper understanding of the thermal and fluid-dynamics in Borexino. It was optimized for different regions and periods of interest, focusing on the most critical effects that were identified as influencing background concentrations. Literature experimental case studies were reproduced to benchmark the method and settings, and a Borexino-specific benchmark was implemented in order to validate the modeling approach for thermal transport. Finally, fully-convective models were applied to understand general and specific fluid motions impacting the detector's Active Volume.Comment: arXiv admin note: substantial text overlap with arXiv:1705.09078, arXiv:1705.0965

Some remarks on the fast spatial growth/decay in exterior regions

In this paper we investigate the spatial behavior of the solutions to several partial differential equations/systems for exterior or cone-like regions. Under certain conditions for the equations we prove that the growth/decay estimates are faster than any exponential depending linearly on the distance to the origin. This kind of spatial behavior has not been noticed previously for parabolic problems and exterior or cone-like regions. The results obtained in this work apply in particular for the linear case.Peer ReviewedPostprint (author's final draft