Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity

Dynamical ensembles have been introduced to study constrained stochastic processes. In the microcanonical ensemble, the value of a dynamical observable is constrained to a given value. In the canonical ensemble a bias is introduced in the process to move the mean value of this observable. The equivalence between the two ensembles means that calculations in one or the other ensemble lead to the same result. In this paper, we study the physical conditions associated with ensemble equivalence and the consequences of non-equivalence. For continuous time Markov jump processes, we show that ergodicity guarantees ensemble equivalence. For non-ergodic systems or systems with emergent ergodicity breaking, we adapt a method developed for equilibrium ensembles to compute asymptotic probabilities while caring about the initial condition. We illustrate our results on the infinite range Ising model by characterizing the fluctuations of magnetization and activity. We discuss the emergence of non-ergodicity by showing that the initial condition can only be forgotten after a time that scales exponentially with the number of spins.

     

Isometric Uncertainty Relations

Journal of Statistical Physics - We generalize the link between fluctuation theorems and thermodynamic uncertainty relations by deriving a bound on the variance of fluxes that satisfy an isometric...     

Domino portrait generation: a fast and scalable approach

A domino portrait is an approximation of an image using a given number of sets of dominoes. This problem was first formulated in 1981 by Ken Knowlton in a patent application, which was finally granted in 1983. Domino portraits have been generated most often using integer linear programming techniques that provide optimal solutions, but these can be slow and do not scale well to larger portraits. In this paper we propose a new approach that overcomes these limitations and provides high quality portraits. Our approach combines techniques from operations research, artificial intelligence, and computer vision. Starting from a randomly generated template of blank domino shapes, a subsequent optimal placement of dominoes can be achieved in constant time when the problem is viewed as a minimum cost flow. The domino portraits one obtains are good, but not as visually attractive as optimal ones. Combining techniques from computer vision and large neighborhood search we can quickly improve the portraits. Empirically, we show that we obtain many orders of magnitude reduction in search time.     

Theoretical investigation of the uranyl ion sorption on the rutile TiO2(110) face

Canister integrity and radionuclide retention is of first importance for assessing the long-term safety of nuclear waste stored in engineered geologic depositories. Uranyl ion sorption on the TiO(2) rutile (110) face is investigated using periodic density functional theory (DFT) calculations. From experimental observations, only two uranyl surface complexes are observed and characterized. When the pH increases (from 1.5 to 4.5), the relative ratios of these two surface complexes are modified. From a crystallographic point of view, three sorption sites can be considered and have been studied with different protonation states of the surface to account for very acidic and low acidic conditions. The two surface complexes experimentally observed were calculated as the most stable ones, while the evolution of their sorption energies agrees with experimental data.     

What Does Dynamical Systems Theory Teach Us about Fluids?

We use molecular dynamics simulations to compute the Lyapunov spectra of many-particle systems resembling simple fluids in thermal equilibrium and in non-equilibrium stationary states. Here we review some of the most interesting results and point to open questions.     

DEEP RELU NETWORKS OVERCOME THE CURSE OF DIMENSIONALITY FOR GENERALIZED BANDLIMITED FUNCTIONS

We prove a theorem concerning the approximation of generalized bandlimited mul-tivariate functions by deep ReLU networks for which the curse of the dimensionality is overcome.Our theorem is based on a result by Maurey and on the ability of deep ReLU networks to approximate Chebyshev polynomials and analytic functions efficiently.     

Teaching OR: automatic evaluation for linear programming modelling

4OR - Learning how to model a problem described in natural language as a linear program requires students to practice using various and numerous exercises. Moreover, immediate feedback on the...     

Phosphorus‐Stabilized Titanium Carbene Complexes: Synthesis,Reactivity and DFT Studies

The synthesis of two novel titanium carbene complexes from the bis(thiophosphinoyl)methanediide geminal dianion 1 (SCS^2?) is described. Dianion 1 reacts cleanly with 0.5 equivalents of [TiCl₄(thf)₂] to afford the bis‐carbene complex [(SCS)₂Ti] ( 2 ) in 86 % yield. The mono‐carbene complex [(SCS)TiCl₂(thf)] ( 3 ) can also be obtained by using an excess of [TiCl₄(thf)₂]. The structures of 2 and 3 are confirmed by X‐ray crystallography. A strong nucleophilic reactivity towards various electrophiles (ketones and aldehydes) is observed. The reaction of 3 with N,N′‐dicyclohexylcarbodiimide (DCC) and phenyl isocyanate leads to the formation of two novel diphosphinoketenimines 8 a and 8 b . The bis‐titanium guanidinate complex 9 is trapped as the by‐product of the reaction with DCC. The X‐ray crystal structures of 8 a and 9 are presented. The mechanism of the reaction between complex 3 and DCC is rationalized by DFT studies.     

Covariant Lyapunov vectors for rigid disk systems

We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.