Related papers: A new nonlinear instability for scalar fields
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy…
A stochastic PDE, describing mesoscopic fluctuations in systems of weakly interacting inertial particles of finite volume, is proposed and analysed in any finite dimension $d\in\mathbb{N}$. It is a regularised and inertial version of the…
We examine in this article the one-dimensional, non-local, singular SPDE \begin{equation*} \partial_t u \;=\; -\, (-\Delta)^{1/2} u \,-\, \sinh(\gamma u) \,+\, \xi\;, \end{equation*} where $\gamma\in \mathbb{R}$, $(-\Delta)^{1/2}$ is the…
We introduce a multifield dark energy model with a nonflat field-space metric, in which one field is dynamical while the others have constant spatial gradients. The model is predictive at the background level, leading to an early dark…
All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…
The incompressible Toner-Tu (ITT) partial differential equations (PDEs) are an important example of a set of active-fluid PDEs. While they share certain properties with the Navier-Stokes equations (NSEs), such as the same scaling…
We investigate the dark energy phenomenology in an extended parameter space where we allow the curvature density of our universe as a free-to-vary parameter. The inclusion of the curvature density parameter is motivated from the recently…
In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…
Einstein's field equations with a background source term that induces perturbations and the applications of this new formalism to a compact dense matter relativistic star are presented. We introduce a new response kernel in the field…
A new method to remove the stiffness of partial differential equations is presented. Two terms are added to the right-hand-side of the PDE : the first is a damping term and is treated implicitly, the second is of the opposite sign and is…
We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
The gauge-independent invariant approach to investigation of the linear scalar perturbations of inflaton and gravitational fields is developed in self-consistent way. This approach allows to compare various gauges used by other researchers…
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…
We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in…
In this thesis, we explore several related topics broadly regarding the symmetry and geometric properties of nonlocal partial differential equations (PDE). This thesis is split into three parts. In the first part, we study two…
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more…
We study stochastically forced semilinear parabolic PDE's of the Ginzburg-Landau type. The class of forcings considered are white noises in time and colored smooth noises in space. Existence of the dynamics in $L^\infty$, as well as…
The evolution of weak discontinuity is investigated in the flat FRW universe with a single scalar field and with multiple scalar fields. We consider both massless scalar fields and scalar fields with exponential potentials. Then we find…