Related papers: A Path Integral Approach to Effective Non-Linear M…
It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the…
A theory is developed for evaluation of nonlinear elastic moduli of composite materials with nonlinear inclusions dispersed in another nonlinear material (matrix). We elaborate a method aimed for determination of elastic parameters of a…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
We demonstrate that the nonlinear optimisation of a finite-amplitude disturbance over a freely evolving and possibly even turbulent flow, can successfully identify subcritical dynamo branches as well as the structure and amplitude of their…
We introduce a new approach for measuring both the effective medium and the transport properties of light propagation in heterogeneous media. Our method utilizes the conceptual equivalence of frequency variation with a change in the…
We develop an effective theory of pulse propagation in a nonlinear {\it and} disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena…
In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel…
In this work, we rigorously derive effective dynamics for light from within a limited frequency range propagating in a photonic crystal that is modulated on the macroscopic level; the perturbation parameter $\lambda \ll 1$ quantifies the…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…
We apply the linear $\delta$-expansion (LDE), originally developed as a nonperturbative, analytical approximation scheme in quantum field theory, to problems involving noninteracting electrons in disordered solids. The initial idea that the…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
We discuss several features of the propagation of perturbations in nonlinear scalar field theories using the effective metric. It is shown that the effective metric can be classified according to whether the gradient of the scalar field is…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
In the path integral formulation of the partition function of quantum spin models, most current treatments employ the so-called static approximation to simplify the process of summing over all possible paths. Although sufficient for…
We introduce and analyze a new quantity, the path integral ideal, governing the flow of generic discrete theories to the continuum limit and greatly increasing their convergence. The said flow is classified according to the degree of…
The non-linear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n + 1 theorem…
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…