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This study presents the numerical models used for the simulation of the large viscoplastic deformations that aluminium undergoes during the extrusion process in order to obtain industrial profiles. This study also gives examples of results…
The goal of this article is to introduce the Hamiltonian Monte Carlo (HMC) method -- a Hamiltonian dynamics-inspired algorithm for sampling from a Gibbs density $\pi(x) \propto e^{-f(x)}$. We focus on the "idealized" case, where one can…
We introduce the Hamming Ball Sampler, a novel Markov Chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction…
We develop an algorithm for sampling from the unitary invariant random matrix ensembles. The algorithm is based on the representation of their eigenvalues as a determinantal point process whose kernel is given in terms of orthogonal…
We present a multiscale modeling approach that concurrently couples quantum mechanical, classical atomistic and continuum mechanics simulations in a unified fashion for metals. This approach is particular useful for systems where chemical…
Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice however, sampling of the complete configuration space is often hindered by high energy barriers between different regions…
Tool condition monitoring (TCM) systems can improve productivity and ensure workpiece quality, yet, there is a lack of reliable TCM solutions for small-batch or one-off manufacturing of industrial parts. TCM methods which include the…
There exist two formulations for quantum heat engine that models an energy transfer between two microscopic systems. One is semi-classical scenario, and the other is full quantum scenario. The former is formulated as a unitary evolution for…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
We introduce and compare three different Monte Carlo determinantal algorithms that allow one to compute dynamical quantities, such as the self-energy, of fermionic systems in their thermodynamic limit. We show that the most efficient…
We propose a change of style for numerical estimations of physical quantities from measurements to inferences. We estimate the most probable quantities for all the parameter region simultaneously by using the raw data cooperatively.…
In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that,…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…
We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces…
A new method is proposed for integrating the equations of motion of an elastic filament. In the standard finite-difference and finite-element formulations the continuum equations of motion are discretized in space and time, but it is then…
Enforcing exact conservation laws instead of average ones in statistical thermal models for relativistic heavy ion reactions gives raise to so called canonical effect, which can be used to explain some enhancement effects when going from…
The Hamiltonian Monte Carlo (HMC) algorithm is a powerful Markov Chain Monte Carlo (MCMC) method that uses Hamiltonian dynamics to generate samples from a target distribution. To fully exploit its potential, we must understand how…
Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining…