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Dynamics that are microscopic in space and time, in which particles commit to a position, so-called excitations, are considered the elementary unit of relaxation in the Dynamic Facilitation (DF) theory of the glass transition. Meanwhile, geometric motifs known as locally favored structures (LFS) are associated with vitrification in many glassformers. Recent work indicates that the probability of particles found both in locally favored structures (LFS) and excitations decreases significantly upon supercooling suggesting that there is an anti-correlation between them [Ortlieb et al, Nature Commun. 14, 2621 (2023)]. However, the spatial relationship between excitations and LFS remains unclear. By employing state-of-the-art GPU computer simulations and colloid experiments, we analyze this relationship between LFS and excitations in model glassformers. We demonstrate that there is a spatial separation between the two in deeply supercooled liquids. This may be due to the fact that LFS are well-packed, thus they are relatively stable.

Many of graphene's remarkable properties are intrinsically linked to its inherent ripples. Defects, whether naturally present or artificially introduced, are known to have a strong impact on the rippling of graphene. However, how defects alter ripple dynamics in two-dimensional (2D) materials in general, and graphene in particular, remains largely unexplored. Here, using machine learning-driven molecular dynamics simulations, we reveal a fundamental connection between defect concentration and ripple dynamics in freestanding graphene sheets. Specifically, we find that at a critical concentration of approximately 0.1%, dynamic rippling undergoes a transition from freely propagating to static ripples. This is in quantitative alignment with the experimentally observed turning point in the non-monotonic scaling of the Young's modulus and emphasises the critical interplay between defects and material dynamics. Our work not only unveils the significant impact of defects on rippling dynamics in graphene but also paves the way to design two-dimensional devices with tailored properties., Comment: 8 pages, 20 pages supplementary information

In this paper, we aim to perform sensitivity analysis of set-valued models and, in particular, to quantify the impact of uncertain inputs on feasible sets, which are key elements in solving a robust optimization problem under constraints. While most sensitivity analysis methods deal with scalar outputs, this paper introduces a novel approach for performing sensitivity analysis with set-valued outputs. Our innovative methodology is designed for excursion sets, but is versatile enough to be applied to set-valued simulators, including those found in viability fields, or when working with maps like pollutant concentration maps or flood zone maps. We propose to use the Hilbert-Schmidt Independence Criterion (HSIC) with a kernel designed for set-valued outputs. After proposing a probabilistic framework for random sets, a first contribution is the proof that this kernel is characteristic, an essential property in a kernel-based sensitivity analysis context. To measure the contribution of each input, we then propose to use HSIC-ANOVA indices. With these indices, we can identify which inputs should be neglected (screening) and we can rank the others according to their influence (ranking). The estimation of these indices is also adapted to the set-valued outputs. Finally, we test the proposed method on three test cases of excursion sets.

Structural defects control the kinetic, thermodynamic and mechanical properties of glasses. For instance, rare quantum tunneling two-level systems (TLS) govern the physics of glasses at very low temperature. Because of their extremely low density, it is very hard to directly identify them in computer simulations. We introduce a machine learning approach to efficiently explore the potential energy landscape of glass models and identify desired classes of defects. We focus in particular on TLS and we design an algorithm that is able to rapidly predict the quantum splitting between any two amorphous configurations produced by classical simulations. This in turn allows us to shift the computational effort towards the collection and identification of a larger number of TLS, rather than the useless characterization of non-tunneling defects which are much more abundant. Finally, we interpret our machine learning model to understand how TLS are identified and characterized, thus giving direct physical insight into their microscopic nature.

The discovery of ultrastable glasses has raised novel challenges about glassy systems. Recent experiments studied the macroscopic devitrification of ultrastable glasses into liquids upon heating but lacked microscopic resolution. We use molecular dynamics simulations to analyse the kinetics of this transformation. In the most stable systems, devitrification occurs after a very large time, but the liquid emerges in two steps. At short times, we observe the rare nucleation and slow growth of isolated droplets containing a liquid maintained under pressure by the rigidity of the surrounding glass. At large times, pressure is released after the droplets coalesce into large domains, which accelerates devitrification. This two-step process produces pronounced deviations from the classical Avrami kinetics and explains the emergence of a giant lengthscale characterising the devitrification of bulk ultrastable glasses. Our study elucidates the nonequilibrium kinetics of glasses following a large temperature jump, which differs from both equilibrium relaxation and aging dynamics, and will guide future experimental studies.

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements., Comment: 17 pages, 12 figures

We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics simulations to analyse the equilibrium relaxation dynamics of model supercooled liquids over a time window covering ten orders of magnitude for temperatures down to the experimental glass transition temperature $T_g$. The analysis of \rev{several} time correlation functions coupled to spatio-temporal resolution of particle motion allow us to elucidate the nature of the equilibrium dynamics in deeply supercooled liquids. We find that structural relaxation starts at early times in rare localised regions characterised by a waiting time distribution that develops a power law near $T_g$. At longer times, relaxation events accumulate with increasing probability in these regions as $T_g$ is approached. This accumulation leads to a power-law growth of the linear extension of relaxed domains with time with a large, temperature-dependent dynamic exponent. Past the average relaxation time, unrelaxed domains slowly shrink with time due to relaxation events happening at their boundaries. Our results provide a complete microscopic description of the particle motion responsible for key experimental signatures of glassy dynamics, from the shape and temperature evolution of relaxation spectra to the core features of dynamic heterogeneity. They also provide a microscopic basis to understand the emergence of dynamic facilitation in deeply supercooled liquids and allow us to critically reassess theoretical descriptions of the glass transition., Comment: 22 pages, 21 figures

Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The maintenance of diversity in large ecosystems is a longstanding puzzle, towards which recent progress has been made by the derivation of dynamical mean-field theories of random models. In particular, it has recently been shown that these random models have a chaotic phase in which abundances display wild fluctuations. When modest spatial structure is included, these fluctuations are stabilized and diversity is maintained. If and how these phenomena have parallels in biochemical reaction networks is currently unknown. Making this connection is of interest since life requires cooperation among a large number of molecular species. In this work, we find a reaction network whose large-scale behavior recovers the random Lotka-Volterra model recently considered in theoretical ecology. We clarify the assumptions necessary to derive its large-scale description, and reveal the underlying assumptions made on the noise to recover previous dynamical mean-field theories. Then, we show how local detailed balance and the positivity of reaction rates, which are key physical requirements of chemical reaction networks, provide obstructions towards the construction of an associated dynamical mean-field theory of biochemical reaction networks. Finally, we outline prospects and challenges for the future.

We consider chance constrained optimization where it is sought to optimize a function while complying with constraints, both of which are affected by uncertainties. The high computational cost of realistic simulations strongly limits the number of evaluations and makes this type of problems particularly challenging. In such a context, it is common to rely on Bayesian optimization algorithms. Assuming, without loss of generality, that the uncertainty comes from some of the inputs, it becomes possible to build a Gaussian process model in the joint space of design and uncertain variables. A two-step acquisition function is then used to provide, both, promising optimization variables associated to relevant uncertain samples. Our overall contribution is to correlate the constraints in the GP model and exploit this to optimally decide, at each iteration, which constraint should be evaluated and at which point. The coupled Gaussian model of the constraints relies on an output-as-input encoding. The constraint selection idea is developed by enabling that each constraint can be evaluated for a different uncertain input, thus improving the refinement efficiency. Constraints coupling and selection are gradually implement in 3 algorithm variants which are compared to a reference Bayesian approach. The results are promising in terms of convergence speed, accuracy and stability as observed on a 2, a 4 and a 27-dimensional problems.

Medicines and agricultural biocides are often discovered using large phenotypic screens across hundreds of compounds, where visible effects of whole organisms are compared to gauge efficacy and possible modes of action. However, such analysis is often limited to human-defined and static features. Here, we introduce a novel framework that can characterize shape changes (morphodynamics) for cell-drug interactions directly from images, and use it to interpret perturbed development of Phakopsora pachyrhizi, the Asian soybean rust crop pathogen. We describe population development over a 2D space of shapes (morphospace) using two models with condition-dependent parameters: a top-down Fokker-Planck model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. We discover a variety of landscapes, describing phenotype transitions during growth, and identify possible perturbations in the tip growth machinery that cause this variation. This demonstrates a widely-applicable integration of unsupervised learning and biophysical modeling.

In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by these findings, we construct a minimal empirical model to describe this physics and introduce dynamic facilitation in the trap model, which was initially developed to capture the thermally-activated dynamics of glassy systems. We fully characterise the relaxation dynamics of this facilitated trap model varying the functional form of energy distributions and the strength of dynamic facilitation, combining numerical results and analytic arguments. Dynamic facilitation generically accelerates the relaxation of the deepest traps, thus making relaxation spectra strongly asymmetric, with an apparent "excess" signal at high frequencies. For well-chosen values of the parameters, the obtained spectra mimic experimental results for organic liquids displaying an excess wing. Overall, our results identify the minimal physical ingredients needed to describe excess processes in relaxation spectra of supercooled liquids., Comment: 11 pages, 9 figures

We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly challenging because of their inherent computational cost. To tackle such problems, we propose a new Bayesian optimization method. It applies to the situation where the uncertainty comes from some of the inputs, so that it becomes possible to define an acquisition criterion in the joint controlled-uncontrolled input space. The main contribution of this work is an acquisition criterion that accounts for both the average improvement in objective function and the constraint reliability. The criterion is derived following the Stepwise Uncertainty Reduction logic and its maximization provides both optimal controlled and uncontrolled parameters. Analytical expressions are given to efficiently calculate the criterion. Numerical studies on test functions are presented. It is found through experimental comparisons with alternative sampling criteria that the adequation between the sampling criterion and the problem contributes to the efficiency of the overall optimization. As a side result, an expression for the variance of the improvement is given., Comment: to appear in SMAI Journal of Computational Mathematics, Vol.9, pp. 285-309

Glass formation is encountered in diverse materials. Experiments have revealed that dynamic relaxation spectra of supercooled liquids generically become asymmetric near the glass transition temperature, $T_g$, where an extended power law emerges at high frequencies. The microscopic origin of this "wing" remains unknown, and was so far inaccessible to simulations. Here, we develop a novel computational approach and study the equilibrium dynamics of model supercooled liquids near $T_g$. We demonstrate the emergence of a power law wing in numerical spectra, which originates from relaxation at rare, localised regions over broadly-distributed timescales. We rationalise the asymmetric shape of relaxation spectra by constructing an empirical model associating heterogeneous activated dynamics with dynamic facilitation, which are the two minimal physical ingredients revealed by our simulations. Our work offers a glimpse of the molecular motion responsible for glass formation at relevant experimental conditions., Comment: 5 pages, 4 figures, supplementary materials

Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create {\it in silico} glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than $k_{B}T_Q$, with $T_Q$ the temperature below which quantum effects are relevant ($T_Q \approx 1 \,$K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it is probed tend to deplete the density of tunneling defects, as observed in recent experiments. We explore the real-space nature of tunneling defects, and find that they are mostly localized to a few atoms, but are occasionally dramatically delocalized., Comment: 6 pages, 4 figures + Supplementary Material

The nature of defects in amorphous materials, analogous to vacancies and dislocations in crystals, remains elusive. Here we explore their nature in a three-dimensional microscopic model glass-former which describes granular, colloidal, atomic and molecular glasses by changing the temperature and density. We find that all glasses evolve in a very rough energy landscape, with a hierarchy of barrier sizes corresponding to both localized and delocalized excitations. Collective excitations dominate in the jamming regime relevant for granular and colloidal glasses. By moving gradually to larger densities describing atomic and molecular glasses, the system crosses over to a regime dominated by localized defects and relatively simpler landscapes. We quantify the energy and temperature scales associated to these defects and their evolution with density. Our result pave the way to a systematic study of low-temperature physics in a broad range of physical conditions and glassy materials., Comment: 11 pages, 8 figures

We perform stringent tests of thermodynamic theories of the glass transition over the experimentally relevant temperature regime for several simulated glass-formers. The swap Monte Carlo algorithm is used to estimate the configurational entropy and static point-to-set lengthscale, and careful extrapolations are used for the relaxation times. We first quantify the relation between configurational entropy and the point-to-set lengthscale in two and three dimensions. We then show that the Adam-Gibbs relation is generally violated in simulated models for the experimentally relevant time window. Collecting experimental data for several supercooled molecular liquids, we show that the same trends are observed experimentally. Deviations from the Adam-Gibbs relation remain compatible with random first order transition theory, and may account for the reported discrepancies between Kauzmann and Vogel-Fulcher-Tammann temperatures. Alternatively, they may also indicate that even near $T_g$ thermodynamics is not the only driving force for slow dynamics., Comment: 13 pages, 8 figures

We show numerically that a three-dimensional model for structural glass displays aging, rejuvenation and memory effects when submitted to a temperature cycle. These effects indicate that the free energy landscape of structural glasses may possess the complex hierarchical structure that characterize materials such as spin and polymer glasses. We use the theoretical concept of marginal stability to interpret our results, and explain in which physical conditions a complex aging dynamics can emerge in dense supercooled liquids, paving the way for future experimental studies of complex aging dynamics in colloidal and granular glasses., Comment: 5 pages, 7 figures

The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely accepted definition of the configurational entropy is missing, its quantitative characterization remains fraud with difficulties, misconceptions and paradoxes, and its physical relevance is vividly debated. Motivated by recent computational progress, we offer a pedagogical perspective on the configurational entropy in glass-forming liquids. We first explain why the configurational entropy has become a key quantity to describe glassy materials, from early empirical observations to modern theoretical treatments. We explain why practical measurements necessarily require approximations that make its physical interpretation delicate. We then demonstrate that computer simulations have become an invaluable tool to obtain precise, non-ambiguous, and experimentally-relevant measurements of the configurational entropy. We describe a panel of available computational tools, offering for each method a critical discussion. This perspective should be useful to both experimentalists and theoreticians interested in glassy materials and complex systems., Comment: 20 pages, 11 figures

It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the efficiency of particle swaps into equilibrium molecular dynamics (MD) simulations. We first develop a hybrid MD/MC scheme combining molecular dynamics with the original swap Monte Carlo. We implement this hybrid method in LAMMPS, a software package employed by a large community of users. Secondly, we define a continuous time version of the swap algorithm where both the positions and diameters of the particles evolve via Hamilton's equations of motion. For both algorithms, we discuss in detail various technical issues as well as the optimisation of simulation parameters. We compare the numerical efficiency of all available swap algorithms and discuss their relative merits., Comment: 16 pages, 13 figures

A novel form of amorphous matter characterized by marginal stability was recently discovered in the mean-field theory of structural glasses. Using this approach, we provide complete phase diagrams delimiting the location of the marginally stable glass phase for a large variety of pair interactions and physical conditions, extensively exploring physical regimes relevant to granular matter, foams, emulsions, hard and soft colloids, and molecular glasses. We find that all types of glasses may become marginally stable, but the extent of the marginally stable phase highly depends on the preparation protocol. Our results suggest that marginal phases should be observable for colloidal and non-Brownian particles near jamming, and poorly annealed glasses. For well-annealed glasses, two distinct marginal phases are predicted. Our study unifies previous results on marginal stability in mean-field models, and will be useful to guide numerical simulations and experiments aimed at detecting marginal stability in finite dimensional amorphous materials., Comment: 10 pages, 7 figures

Electromagnetic radiation (photons) or particle beam (protons or heavy ions) have similar biological effects, i.e. damage to human cell DNA that eventually leads to cell death if not correctly repaired. The biological effects at the level of organs or organisms are explained by a progressive depletion of constitutive cells; below a given threshold, cell division is no longer sufficient to compensate for cell loss, up to a point where the entire organism (or organ) breaks down. The quantitative aspects of the biological effects are modulated by the microscopic distribution of energy deposits along the beam or particle tracks. In particular, the ionization density, i.e. the amount of energy deposited by unit path length (measured in keV/{\mu}m), has an influence on the biological effectiveness, i.e. the amount of damage per energy unit deposited (measured in gray or Gy, equivalent to 1 joule/kg). The ionization density is usually represented by the Linear Energy Transfer or LET, also expressed in keV/{\mu}m. Photon beams (X-rays, g-rays) are low-LET radiation, with a sparsely ionising characteristic. Particle beams have a higher LET, with a more dense distribution of energy deposits along the particle tracks. Protons are intermediary, with a LET larger than the photon one, but still belong to the 'radiobiological' group of low LET. The higher the ionization density, the higher the biological effectiveness per unit of dose., Comment: 11 pages, contribution to the CAS-CERN Accelerator School on Accelerators for Medical Applications. Senec, V\"osendorf, Austria, 26 May-5 June 2015

This paper proposes a stochastic approach to model temperature dynamic and study related risk measures. The dynamic of temperatures can be modelled by a mean-reverting process such as an Ornstein-Uhlenbeck one. In this study, we estimate the parameters of this process thanks to daily observed suprema of temperatures, which are the only data gathered by some weather stations. The expression of the cumulative distribution function of the supremum is obtained thanks to the law of the hitting time. The parameters are estimated by a least square method quantiles based on this function. Theoretical results, including mixing property and consistency of model parameters estimation, are provided. The parameters estimation is assessed on simulated data and performed on real ones. Numerical illustrations are given for both data. This estimation will allow us to estimate risk measures, such as the probability of heat wave and the mean duration of an heat wave.

Marginally stable solids have peculiar physical properties that were discovered and analyzed in the context of the jamming transition. We theoretically investigate the existence of marginal stability in a prototypical model for structural glass-formers, combining analytical calculations in infinite dimensions to computer simulations in three dimensions. While mean-field theory predicts the existence of a Gardner phase transition towards a marginally stable glass phase at low temperatures, simulations show no hint of diverging timescales or lengthscales, but reveal instead the presence of sparse localized defects. Our results suggest that the Gardner transition is deeply affected by finite dimensional fluctuations, and raise issues about the relevance of marginal stability in structural glasses far away from jamming., Comment: 5 pages, 3 figures

A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency $\sim 10$ Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies $f$, a tail $\sim 1/f$ in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than $10$ s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times $\tau$ displays a power-law decay, likely due to persistent collective fluctuations of the host medium., Comment: 5 pages + 4 page of supplemental material, 6 figures, to be published on Phys. Rev. Lett

This paper is concerned with the determination of credit risk premia of defaultable contingent claims by means of indifference valuation principles. Assuming exponential utility preferences we derive representations of indifference premia of credit risk in terms of solutions of Backward Stochastic Differential Equations (BSDE). The class of BSDEs needed for that representation allows for quadratic growth generators and jumps at random times. Since the existence and uniqueness theory for this class of BSDEs has not yet been developed to the required generality, the first part of the paper is devoted to fill that gap. By using a simple constructive algorithm, and known results on continuous quadratic BSDEs, we provide sufficient conditions for the existence and uniqueness of quadratic BSDEs with discontinuities at random times.

This article focuses on the mathematical problem of existence and uniqueness of BSDE with a random terminal time which is a general random variable but not a stopping time, as it has been usually the case in the previous literature of BSDE with random terminal time. The main motivation of this work is a financial or actuarial problem of hedging of defaultable contingent claims or life insurance contracts, for which the terminal time is a default time or a death time, which are not stopping times. We have to use progressive enlargement of the Brownian filtration, and to solve the obtained BSDE under this enlarged filtration. This work gives a solution to the mathematical problem and proves the existence and uniqueness of solutions of such BSDE under certain general conditions. This approach is applied to the financial problem of hedging of defaultable contingent claims, and an expression of the hedging strategy is given for a defaultable contingent claim or a life insurance contract.

The valuation of counterparty risk for single name credit derivatives requires the computa- tion of joint distributions of default times of two default-prone entities. For a Merton-type model, we derive some formulas for these joint distribu- tions. As an application, closed formulas for counterparty risk on a CDS or for a first-to-default swap on two underlyings are obtained.