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1. Computational Analysis of Complex Amorphization/Crystallization Dynamics in Large Phase Change Memory Devices

   Kashem, M. T.; Muneer, S.; Noor, N.; Scoggin, J.; Silva, H.; Gokirmak, A. (April 2019, Materials Research Society symposia proceedings)

   Phase change memory devices become practical for non-volatile storage at small dimensions due to reduced power and predictable device operation. In larger scale cells, devices can be locally melted due to filament formation and liquid filaments can be retained in parts of the cell for a long time even if most or all of the cells are initially amorphized during long fall-times. The complex amorphization and crystallization dynamics make these large cells more unpredictable and enable their applications as physically unclonable functions (PUF) [1,2]. Computational analysis of the complex amorphization-crystallization dynamics in phase change memory devices with large geometries is important to understand the evolution of phase distributions and temperature profiles during programming of these devices. In this work, we conduct electrothermal finite element simulations of reset operation on a large Ge2Sb2Te5 (GST) cell using the framework we have developed in COMSOL multiphysics [3]-[9] and analyze the complex dynamics of amorphization, nucleation and growth during electrical stress. We input voltage waveforms measured from electrical characterization of on-oxide GST line cells with bottom metal contact pads and Si3N4 capping. A 2D polycrystalline model of the experimentally measured cells (~360 nm wide, ~400 nm long and ~50 nm thick) is constructed in the simulations. Access devices are modeled using the spice models. The simulations capture some of the interplay between changes in the device resistance due to heating and phase changes and current fluctuations. 

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2. On Convergence of Federated Averaging Langevin Dynamics

   Deng, Wei; Zhang, Qian; Ma, Yian; Song, Zhao; Lin, Guang (April 2024, UAI Publisher)

   We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of models. We develop theoretical guarantees for FA-LD for strongly log-concave distributions with non-i.i.d data and study how the injected noise and the stochastic-gradient noise, the heterogeneity of data, and the varying learning rates affect the convergence. Such an analysis sheds light on the optimal choice of local updates to minimize the communication cost. Important to our approach is that the communication efficiency does not deteriorate with the injected noise in the Langevin algorithms. In addition, we examine in our FA-LD algorithm both independent and correlated noise used over different clients. We observe that there is a trade-off between the pairs among communication, accuracy, and data privacy. As local devices may become inactive in federated networks, we also show convergence results based on different averaging schemes where only partial device updates are available. In such a case, we discover an additional bias that does not decay to zero. 

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3. Bending fluctuations in semiflexible, inextensible, slender filaments in Stokes flow: Toward a spectral discretization

   https://doi.org/10.1063/5.0144242  

   Maxian, Ondrej; Sprinkle, Brennan; Donev, Aleksandar (April 2023, The Journal of Chemical Physics)

   Semiflexible slender filaments are ubiquitous in nature and cell biology, including in the cytoskeleton, where reorganization of actin filaments allows the cell to move and divide. Most methods for simulating semiflexible inextensible fibers/polymers are based on discrete (bead-link or blob-link) models, which become prohibitively expensive in the slender limit when hydrodynamics is accounted for. In this paper, we develop a novel coarse-grained approach for simulating fluctuating slender filaments with hydrodynamic interactions. Our approach is tailored to relatively stiff fibers whose persistence length is comparable to or larger than their length and is based on three major contributions. First, we discretize the filament centerline using a coarse non-uniform Chebyshev grid, on which we formulate a discrete constrained Gibbs–Boltzmann (GB) equilibrium distribution and overdamped Langevin equation for the evolution of unit-length tangent vectors. Second, we define the hydrodynamic mobility at each point on the filament as an integral of the Rotne–Prager–Yamakawa kernel along the centerline and apply a spectrally accurate “slender-body” quadrature to accurately resolve the hydrodynamics. Third, we propose a novel midpoint temporal integrator, which can correctly capture the Ito drift terms that arise in the overdamped Langevin equation. For two separate examples, we verify that the equilibrium distribution for the Chebyshev grid is a good approximation of the blob-link one and that our temporal integrator for overdamped Langevin dynamics samples the equilibrium GB distribution for sufficiently small time step sizes. We also study the dynamics of relaxation of an initially straight filament and find that as few as 12 Chebyshev nodes provide a good approximation to the dynamics while allowing a time step size two orders of magnitude larger than a resolved blob-link simulation. We conclude by applying our approach to a suspension of cross-linked semiflexible fibers (neglecting hydrodynamic interactions between fibers), where we study how semiflexible fluctuations affect bundling dynamics. We find that semiflexible filaments bundle faster than rigid filaments even when the persistence length is large, but show that semiflexible bending fluctuations only further accelerate agglomeration when the persistence length and fiber length are of the same order. 

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4. Breaking Reversibility Accelerates Langevin Dynamics for Non-Convex Optimization

   Xuefeng Gao, Mert Gurbuzbalaban (January 2020, Proceedings of Machine Learning Research)

   null (Ed.)

   Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minima while eventually visiting a global minimum on longer time-scales. LD is based on the first-order Langevin diffusion which is reversible in time. We study two variants that are based on non-reversible Langevin diffusions: the underdamped Langevin dynamics (ULD) and the Langevin dynamics with a non-symmetric drift (NLD). Adopting the techniques of Tzen et al. (2018) for LD to non-reversible diffusions, we show that for a given local minimum that is within an arbitrary distance from the initialization, with high probability, either the ULD trajectory ends up somewhere outside a small neighborhood of this local minimum within a recurrence time which depends on the smallest eigenvalue of the Hessian at the local minimum or they enter this neighborhood by the recurrence time and stay there for a potentially exponentially long escape time. The ULD algorithm improves upon the recurrence time obtained for LD in Tzen et al. (2018) with respect to the dependency on the smallest eigenvalue of the Hessian at the local minimum. Similar results and improvements are obtained for the NLD algorithm. We also show that non-reversible variants can exit the basin of attraction of a local minimum faster in discrete time when the objective has two local minima separated by a saddle point and quantify the amount of improvement. Our analysis suggests that non-reversible Langevin algorithms are more efficient to locate a local minimum as well as exploring the state space. 

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5. Exact solution for the Anisotropic Ornstein–Uhlenbeck process

   https://doi.org/10.1016/j.physa.2021.126526  

   de Almeida, Rita M.C.; Giardini, Guilherme S.Y.; Vainstein, Mendeli; Glazier, James A.; Thomas, Gilberto L. (February 2022, Physica A: Statistical Mechanics and its Applications)

   Active-Matter models commonly consider particles with overdamped dynamics subject to a force (speed) with constant modulus and random direction. Some models also include random noise in particle displacement (a Wiener process), resulting in diffusive motion at short time scales. On the other hand, Ornstein–Uhlenbeck processes apply Langevin dynamics to the particles’ velocity and predict motion that is not diffusive at short time scales. Experiments show that migrating cells have gradually varying speeds at intermediate and long time scales, with short-time diffusive behavior. While Ornstein–Uhlenbeck processes can describe the moderate-and long-time speed variation, Active-Matter models for over-damped particles can explain the short-time diffusive behavior. Isotropic models cannot explain both regimes, because short-time diffusion renders instantaneous velocity ill-defined, and prevents the use of dynamical equations that require velocity time-derivatives. On the other hand, both models correctly describe some of the different temporal regimes seen in migrating biological cells and must, in the appropriate limit, yield the same observable predictions. Here we propose and solve analytically an Anisotropic Ornstein–Uhlenbeck process for polarized particles, with Langevin dynamics governing the particle’s movement in the polarization direction and a Wiener process governing displacement in the orthogonal direction. Our characterization provides a theoretically robust way to compare movement in dimensionless simulations to movement in experiments in which measurements have meaningful space and time units. We also propose an approach to deal with inevitable finite-precision effects in experiments and simulations. 

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