Related papers: Dynamics with Infinitely Many Derivatives: Variabl…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
We study the properties of cosmological density perturbations in a multi-component system consisting of a scalar field and a perfect fluid. We discuss the number of degrees of freedom completely describing the system, introduce a full set…
In this paper, a high-order nonlinear continuous integral-derivative observer is presented based on finite-time stability and singular perturbation technique. The proposed integral-derivative observer can not only obtain the multiple…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
We apply topological methods to obtain global continuation results for harmonic solutions of some periodically perturbed ordinary differential equations on a $k$-dimensional differentiable manifold $M \subseteq \mathbb{R}^m$. We assume that…
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of {\em arbitrary order}, posed on the domain $\{t>0, 0<x<L\}$. We first show that by analysing…
We address several concerns related to the derivation of drift-ordered fluid equations. Starting from a fully Galilean invariant fluid system, we show how consistent sets of perturbative drift-fluid equations in the case of a isothermal…
In this paper we introduce the topological state derivative for general topological dilatations and explore its relation to standard optimal control theory. We show that for a class of partial differential equations, the shape dependent…
L-infinity morphisms are studied from the point of view of perturbative quantum field theory, as generalizations of Feynman expansions. The connection with the Hopf algebra approach to renormalization is exploited. Using the coalgebra…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
In inflationary cosmology, the form of the potential is still an open problem. In this work, second-order effects of the inflationary potential are evaluated and related to the known formula for the primordial perturbations at a wide range…
Exponential integrators based on contour integral representations lead to powerful numerical solvers for a variety of ODEs, PDEs, and other time-evolution equations. They are embarrassingly parallelizable and lead to global-in-time…
We investigate the issue of coordinate redefinition invariance by carefully performing nonlinear transformations in the discretized quantum mechanical path integral. By resorting to hamiltonian path integral methods, we provide the first…
In Physics, we are generally interested in real solutions involving natural phenomena, where knowledge of real functions of real variables is sufficient to obtain physically relevant results. However, the complexity of phenomena associated…
The quantum theory of cosmological perturbations in single field inflation is formulated in terms of a path integral. Starting from a canonical formulation, we show how the free propagators can be obtained from the well known…
Precise understanding of nonlinear evolution of cosmological perturbations during inflation is necessary for the correct interpretation of measurements of non-Gaussian correlations in the cosmic microwave background and the large-scale…
For a field theory that is invariant under diffeomorphisms there is a subtle interplay between symmetries, conservation laws and the phase space of the theory. The natural language for describing these ideas is that of differential forms…
For simple inflationary models, we provide a consistent and complete scheme by which the macro-physical details of early universe inflation may be determined explicitly from the underlying micro-physical theory. We examine inflationary…