Related papers: A Path Integral Approach to Effective Non-Linear M…
The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are…
Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an…
Composites are ideally suited to achieve desirable multifunctional effective properties since the best properties of different materials can be judiciously combined with designed microstructures. Here we establish cross-property relations…
Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects.…
In this study we consider perturbative series solution with respect to a parameter {\epsilon} > 0. In this methodology the solution is considered as an infinite sum of a series of functional terms which usually converges fast to the exact…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
We develop a new approach to recurrence and the existence of non-constant harmonic functions on infinite weighted graphs. The approach is based on the capacity of subsets of metric boundaries with respect to intrinsic metrics. The main tool…
We introduce a data-based approach to estimating key quantities which arise in the study of nonlinear control systems and random nonlinear dynamical systems. Our approach hinges on the observation that much of the existing linear theory may…
In this paper, we introduce a weak maximum principle-based approach to input-to-state stability (ISS) analysis for certain nonlinear partial differential equations (PDEs) with boundary disturbances. Based on the weak maximum principle, a…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this…
Given a set of well-formed terminal pairs on the external face of an undirected planar graph with unit edge weights, we give a linear-time algorithm for computing the union of non-crossing shortest paths joining each terminal pair, where…
The method of the factorization of the path integral measure, based on a nonlinear filtering equation, is extended to the case of a nonfree isometric action of the compact semisimple unimodular Lie group on a smooth compact Riemannian…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
Representation of the elastic scattering amplitude in the form of the path integral is obtained using the stationary Schroedinger equation. A few methods of evaluation of path integrals for large coupling constants are formulated. The…
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic…
In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we…
Existing online continuous-time parameter estimation laws provide exact (asymptotic/exponential or finite/fixed time) identification of dynamical linear/nonlinear systems parameters only if the external perturbations are equaled to zero or…
We investigate the optimal tradeoff between information gained about an unknown coherent state and the state disturbance caused by the measurement process. We propose several optical schemes that can enable this task, and we implement one…