Related papers: The Mesoscopic Partition Function:A Combined Spati…
Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…
The optimization of the conversion of thermal energy into work and the minimization of dissipation for nano- and mesoscopic systems is a complex challenge because of the important role fluctuations play on the dynamics of small systems. We…
In this paper, we analyze the effects of expansion on large scale structure formation in our Universe. We do that by incorporating a cosmological constant term in the gravitational partition function. This gravitational partition function…
Gradient metasurface, formed by a set of subwavelength unit cells with different phase modulation, is widely used in polarized beam splitting (BS) in the classical and quantum optics. Specifically, its phase gradient allows the path and…
Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to…
We present the path integral representation of the generating function for classical exclusive particle systems. By introducing hard-core bosonic creation and annihilation operators and appropriate commutation relations, we construct the…
We investigate the use of extended phase-space symplectic integration for simulating two different classes of electron dynamics. The first one, with one and a half degrees of freedom, comes from plasma physics and describes the classical…
A general-purpose, self-adapting Monte Carlo (MC) algorithm implemented in the program {\tt Foam} is described. The high efficiency of the MC, that is small maximum weight or variance of the MC weight is achieved by means of dividing the…
The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while…
In this paper, we show that geometric functionals (e.g., excursion area, boundary length) evaluated on excursion sets of sphere-cross-time long memory random fields can exhibit fractional cointegration, meaning that some of their linear…
Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…
Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into…
Over the last two decades, scientific literature has been blooming with various means of simulating epithelial cell colonies. Each of these simulations can be separated by their respective efficiency (expressed in terms of consumed…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
Phase-field methods offer a versatile computational framework for simulating large-scale morphological evolution. However, the applicability and predictability of phase-field models are inherently limited by their ad hoc nature, and there…
The present thesis shows that Quantum Information concepts can be used to better understand the quantum-to-classical boundary in mesoscopic and macroscopic systems. Our findings suggest a way to push this boundary towards the macroscopic…
A mesoscopic multi-particle collision model for fluid dynamics is generalized to incorporate the chemical reactions among species that may diffuse at different rates. This generalization provides a means to simulate reaction-diffusion…
We develop the spacetime aspects of the computation of partition functions for string/M-theory on AdS(3) xM. Subleading corrections to the semi-classical result are included systematically, laying the groundwork for comparison with CFT…
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and L\"owdin method such that…
In the quantum theory, using the notion of partial supersymmetry, in which some, but not all, operators have superpartners we derive the Euler theorem in partition theory. The paraferminic partition function gives another identity in…