Related papers: Free-Energy Functional Method for Inverse Problem …
A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…
The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical…
We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target…
We propose the concept of autonomous self-damaging in "smart" composite materials, controlled by activation of added nanosize "damaging" capsules. Percolation-type modeling approach earlier applied to the related concept of self-healing…
We simulate crystallisation of hard spheres with short-ranged attractive potentials, as a model self-assembling system. We show how measurements of correlation and response functions during assembly can be used to tune the interaction…
A binary mixture of particles interacting with spherically-symmetric potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume…
In classical analysis, the convergence behavior of power series solutions to differential or recurrence equations is generally assumed to be invariant under internal rearrangement. This paper challenges that belief by proving that, for…
We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
We have identified the ground state configurations of soft particles (interacting via inverse power potentials) confined between two hard, impenetrable walls. To this end we have used a highly reliable optimization scheme at {\it vanishing}…
The past decade has witnessed the advances of artificial intelligence with various applications in engineering. Recently, artificial neural network empowered inverse design for metasurfaces has been developed that can design on-demand…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
The self-energy functional theory (SFT) is generalized to describe the real-time dynamics of correlated lattice-fermion models far from thermal equilibrium. This is achieved by means of a reformulation of the original equilibrium theory in…
Approximate exchange-correlation functionals built by modeling in a non-linear way the adiabatic connection (AC) integrand of density functional theory have many attractive features, being virtually parameters-free and satisfying different…
We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a "cage" is Gaussian, which is not…
The free energy of ion solvation can be decomposed into enthalpic and entropic contributions. This helps to understand the connection between the dielectric properties and the underlying forces. We present a simple linear-response model of…
We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a…
Thanks to a constant energy input, active matter can self-assemble into phases with complex architectures and functionalities such as living clusters that dynamically form, reshape and break-up, which are forbidden in equilibrium materials…
We present a variational free-energy formulation for distributionally robust decision-making with ambiguity in the generative model. The formulation, related to a broad range of learning and control frameworks, yields a minimax optimal…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…