The Homily at the Mass Commemorating the 700th Anniversary of the Death of Thomas Aquinas, Immaculate Conception Chapel, University of Dayton, March 7, 1974

Thomas Aquinas was a true intellectual. He was intensely interested in science. philosophy and theology — all of which, after a rather long dormant period, were beginning to come to life and to attract attention during his formative years. It soon became evident to Thomas that God had given him great talents, and he chose to serve God and the Church by developing and using those talents to the fullest extent possible. Never did he consider intellectualism to be an obstacle to the Church\u27s mission. On the contrary, by his prodigious research and writing, he proved that the intellectual life can be an important and indeed indispensable aspect of the Church\u27s life and mission. This can indeed be an important lesson for us

Dinner Address Commemorating the 30th Anniversary of the Marian Library

The liturgical renewal of the post-Vatican II period has sometimes given the unfortunate impression that Mary\u27s place has been downgraded in the Church. The laudable effort to bring our devotional life into closer harmony with sound liturgical principles has not always achieved its purpose. Sometimes this has been due to misunderstanding; sometimes to a misplaced zeal which did not always make the necessary connection between the old and the new. Surely this was not intended by the Council. Both the Constitution on the Church in its eighth chapter and the Constitution on the Sacred Liturgy reaffirm our traditional understanding of Mary\u27s role in the mystery of Christ and the Church and point out how we might give expression to that understanding in a way that is eminently meaningful for the times in which we live

Transport Properties of a Chain of Anharmonic Oscillators with random flip of velocities

We consider the stationary states of a chain of $n$ anharmonic coupled oscillators, whose deterministic hamiltonian dynamics is perturbed by random independent sign change of the velocities (a random mechanism that conserve energy). The extremities are coupled to thermostats at different temperature $T_\ell$ and $T_r$ and subject to constant forces $\tau_\ell$ and $\tau_r$. If the forces differ $\tau_\ell \neq \tau_r$ the center of mass of the system will move of a speed $V_s$ inducing a tension gradient inside the system. Our aim is to see the influence of the tension gradient on the thermal conductivity. We investigate the entropy production properties of the stationary states, and we prove the existence of the Onsager matrix defined by Green-kubo formulas (linear response). We also prove some explicit bounds on the thermal conductivity, depending on the temperature.Comment: Published version: J Stat Phys (2011) 145:1224-1255 DOI 10.1007/s10955-011-0385-

Green-Kubo formula for weakly coupled system with dynamical noise

We study the Green-Kubo (GK) formula $\kappa (\varepsilon, \xi)$ for the heat conductivity of an infinite chain of $d$-dimensional finite systems (cells) coupled by a smooth nearest neighbour potential $\varepsilon V$. The uncoupled systems evolve according to Hamiltonian dynamics perturbed stochastically by an energy conserving noise of strength $\xi$. Noting that $\kappa (\varepsilon, \xi)$ exists and is finite whenever $\xi> 0$, we are interested in what happens when the strength of the noise $\xi \to 0$. For this, we start in this work by formally expanding $\kappa (\varepsilon, \xi)$ in a power series in $\varepsilon$, $\kappa (\varepsilon, \xi) = \varepsilon^2 \sum_{n\ge 2} \varepsilon^{n-2} \kappa_n (\xi)$ and investigating the (formal) equations satisfied by $\kappa_n (\xi$. We show in particular that $\kappa_2 (\xi)$ is well defined when no pinning potential is present, and coincides formally with the heat conductivity obtained in the weak coupling (van Hove) limit, where time is rescaled as $\varepsilon^{-2}t$, for the cases where the latter has been established \cite{LO, DL}. For one-dimensional systems, we investigate $\kappa_2 (\xi)$ as $\xi\to 0$ in three cases: the disordered harmonic chain, the rotor chain and a chain of strongly anharmonic oscillators. Moreover, we formally identify $\kappa_2 (\xi)$ with the conductivity obtained by having the chain between two reservoirs at temperature $T$ and $T+\delta T$, in the limit $\delta T\to 0$, $N \to \infty$, $\varepsilon \to 0$.Comment: New version with many improvement

Harmonic Systems With Bulk Noises

We consider a harmonic chain in contact with thermal reservoirs at different temperatures and subject to bulk noises of different types: velocity flips or self-consistent reservoirs. While both systems have the same covariances in the nonequilibrium stationary state (NESS) the measures are very different. We study hydrodynamical scaling, large deviations, fluctuations, and long range correlations in both systems. Some of our results extend to higher dimensions

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Nonequilibrium stationary states of harmonic chains with bulk noises

We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.Peer reviewe

Anomalous diffusion for a class of systems with two conserved quantities

We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative stochastic noise so that it becomes ergodic. System of conservation laws are derived as hydrodynamic limits of the modified dynamics. Numerical evidence shows these models are still super-diffusive. This is proven rigorously for harmonic potentials