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Thomas Gilbert

Publications and source records attributed to Thomas Gilbert.

At least 19 recordsLinked to original sources
arXiv2024

The Future of HCI-Policy Collaboration

Policies significantly shape computation's societal impact, a crucial HCI concern. However, challenges persist when HCI professionals attempt to integrate policy into their work or affect policy outcomes. Prior research considered these challenges at the ``border'' of HCI and policy. This paper asks: What if HCI considers policy integral to its intellectual concerns, placing system-people-policy interaction not at the border but nearer the center of HCI research, practice, and education? What if HCI fosters a mosaic of methods and knowledge contributions that blend system, human, and policy expertise in various ways, just like HCI has done with blending system and human expertise? We present this re-imagined HCI-policy relationship as a provocation and highlight its usefulness: It spotlights previously overlooked system-people-policy interaction work in HCI. It unveils new opportunities for HCI's futuring, empirical, and design projects. It allows HCI to coordinate its diverse policy engagements, enhancing its collective impact on policy outcomes.

cs.HC↗
arXiv2020

What mathematical billiards teach us about statistical physics?

We survey applications of the theory of hyperbolic (and to a lesser extent non hyperbolic) billiards to some fundamental problems of statistical physics and their mathematically rigorous derivations in the framework of classical Hamiltonian systems.

cond-mat.stat-mech↗
arXiv2018

A Broader View on Bias in Automated Decision-Making: Reflecting on Epistemology and Dynamics

Machine learning (ML) is increasingly deployed in real world contexts, supplying actionable insights and forming the basis of automated decision-making systems. While issues resulting from biases pre-existing in training data have been at the center of the fairness debate, these systems are also affected by technical and emergent biases, which often arise as context-specific artifacts of implementation. This position paper interprets technical bias as an epistemological problem and emergent bias as a dynamical feedback phenomenon. In order to stimulate debate on how to change machine learning practice to effectively address these issues, we explore this broader view on bias, stress the need to reflect on epistemology, and point to value-sensitive design methodologies to revisit the design and implementation process of automated decision-making systems.

cs.LG↗
arXiv2017

Absence of correlations in the energy exchanges of an exactly solvable model of heat transport with many degrees of freedom

A process based on the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice cells share their energies among many identical degrees of freedom while, in each cell, only two of them are associated with energy exchanges connecting neighbouring cells. It is shown that, up to dimensional constants, the heat conductivity is half the interaction rate, regardless of the degrees of freedom. Moreover, as this number becomes large, correlations between the energy variables involved in the exchanges vanish. In this regime, the process thus boils down to the time-evolution of the local temperatures which is prescribed by the discrete heat equation.

cond-mat.stat-mech↗
arXiv2017

Heat conduction and the nonequilibrium stationary states of stochastic energy exchange processes

I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different temperatures, a systematic characterization of their non-equilibrium stationary states. These arguments avoid resorting to the analysis of a dual process and yield a straightforward derivation of Fourier's law, as well as higher-order static correlations, such as the covariant matrix. The transposition of these results to families of gradient models generalizing the KMP model is established and specific cases are examined.

cond-mat.stat-mech↗
arXiv2016

Dynamical contribution to the heat conductivity in stochastic energy exchanges of locally confined gases

We present a systematic computation of the heat conductivity of the Markov jump process modeling the energy exchanges in an array of locally confined hard spheres at the conduction threshold. Based on a variational formula [Sasada M. 2016, {\it Thermal conductivity for stochastic energy exchange models}, arXiv:1611.08866], explicit upper bounds on the conductivity are derived, which exhibit a rapid power-law convergence towards an asymptotic value. We thereby conclude that the ratio of the heat conductivity to the energy exchange frequency deviates from its static contribution by a small negative correction, its dynamic contribution, evaluated to be $-0.000\,373$ in dimensionless units. This prediction is corroborated by kinetic Monte Carlo simulations which were substantially improved compared to earlier results.

cond-mat.stat-mech↗
arXiv2015

On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas

We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a `piston', i.e. a line-segment, which moves back and forth along a one-dimensional interval partially intersecting the cell. This model can be considered as the elementary building block of a spatially extended high-dimensional billiard modeling heat transport in a class of hybrid materials exhibiting the kinetics of gases and spatial structure of solids. Using heuristic arguments and numerical analysis, we argue that, in a regime of rare interactions, the billiard process converges to a Markov jump process for the energy exchanges and obtain the expression of its generator.

math.DS↗
arXiv2015

L\'evy walks on lattices as multi-state processes

Continuous-time random walks combining diffusive scattering and ballistic propagation on lattices model a class of L\'evy walks. The assumption that transitions in the scattering phase occur with exponentially-distributed waiting times leads to a description of the process in terms of multiple states, whose distributions evolve according to a set of delay differential equations, amenable to analytic treatment. We obtain an exact expression of the mean squared displacement associated with such processes and discuss the emergence of asymptotic scaling laws in regimes of diffusive and superdiffusive (subballistic) transport, emphasizing, in the latter case, the effect of initial conditions on the transport coefficients. Of particular interest is the case of rare ballistic propagation, in which case a regime of superdiffusion may lurk underneath one of normal diffusion.

cond-mat.stat-mech↗
arXiv2014

Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards

We study diffusion on a periodic billiard table with infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a L\'evy walk combining exponentially-distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [Phys. Rev. Lett. 50, 1959 (1983)].

cond-mat.stat-mech↗
arXiv2014

Transport properties of L\'evy walks: an analysis in terms of multistate processes

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker, we are led to a description of such L\'evy walks in terms of multistate processes whose time-evolution is shown to obey a set of coupled delay differential equations. Using simple arguments, we obtain asymptotic solutions to these equations and rederive the scaling laws for the mean squared displacement of such processes. Our calculation includes the computation of all relevant transport coefficients in terms of the parameters of the models.

cond-mat.stat-mech↗
arXiv2014

Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of super-diffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time-range accessible to numerical simulations. We compare our simulations to the known analytical results for the variance of the anomalously-rescaled limiting normal distributions.

cond-mat.stat-mech↗
arXiv2011

A two-stage approach to relaxation in billiard systems of locally confined hard spheres

We consider the three-dimensional dynamics of systems of many interacting hard spheres, each individually confined to a dispersive environment, and show that the macroscopic limit of such systems is characterized by a coefficient of heat conduction whose value reduces to a dimensional formula in the limit of vanishingly small rate of interaction. It is argued that this limit arises from an effective loss of memory. Similarities with the diffusion of a tagged particle in binary mixtures are emphasized.

cond-mat.stat-mech↗
arXiv2010

Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases

We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study a billiard model, namely a three-dimensional periodic Lorentz gas. The geometry of the model is studied in order to find the regimes in which it exhibits normal diffusion. In this regime, we calculate numerically the transition probabilities between cells to compare the persistent random-walk approximation with simulation results for the diffusion coefficient.

cond-mat.stat-mech↗
arXiv2010

Stable and unstable regimes in higher-dimensional convex billiards with cylindrical shape

We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by models of particles interacting via a string-type mechanism, and confined by hard walls. The combination of these elements may give rise to a defocusing mechanism, similar to that in two dimensions, which allows large chaotic regions in phase space. The remaining part of phase space is associated with marginally stable behaviour. In fact periodic orbits in these systems generically come in continuous parametric families, sociated with a pair of parabolic eigen-directions: the periodic orbits are unstable in the presence of a defocusing mechanism, but marginally stable otherwise. By performing the stability analysis of families of periodic orbits at a nonlinear level, we establish the conditions under which families are nonlinearly stable or unstable. As a result, we identify regions in the parameter space of the models which admit non-linearly stable oscillations in the form of whispering gallery modes. Where no families of periodic orbits are stable, the billiards are completely chaotic, i.e.\ the Lyapunov exponents of the billiard map are non-zero.

nlin.CD↗
arXiv2009

Chaos in cylindrical stadium billiards via a generic nonlinear mechanism

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder and several planes; the combination of these elements may give rise to defocusing, allowing large chaotic regions in phase space. By studying families of marginally-stable periodic orbits that populate the residual part of phase space, we identify conditions under which a nonlinear instability mechanism arises in their vicinity. For particular geometries, this mechanism rather induces stable nonlinear oscillations, including in the form of whispering-gallery modes.

nlin.CD↗
arXiv2009

Diffusion coefficients for multi-step persistent random walks on lattices

We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with two-step memory on different classes of one-, two- and higher-dimensional lattices.

cond-mat.stat-mech↗