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We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $\mathbb Z^d$. In particular, we provide an oscillation decay assuming only…
In this Series, we study the weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion. In this part, we focus on steady solutions and develop an `adjoint method' for deriving the nonlinear amplitude…
Nonlocal problems for higher-order elliptic operators in dihedral and plane angles are considered. The Green formula is obtained, which leads to adjoint problems that take the form of nonlocal transmission problems in dihedral and plane…
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
This paper introduces significant advancements in fractional neural operators (FNOs) through the integration of adaptive hybrid kernels and stochastic multiscale analysis. We address several open problems in the existing literature by…
In the present paper in the assumption of the slowness of variation of the vertically stratified medium parameters in the horizontal direction within the time we have analyzed the evolution of the non-harmonic wave trains of the internal…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
We discuss the use of differential sampling method to image local perturbations in anisotropic periodic layers, extending earlier works on the isotropic case. We study in particular the new interior transmission problem that is associated…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model…
This paper presents an algorithm for computing inner estimates of the regions of attraction of limit cycles of a nonlinear hybrid system. The basic procedure is: (1) compute the dynamics of the system transverse to the limit cycle; (2) from…
A general method to determine covariant Lyapunov vectors in both discrete- and continuous-time dynamical systems is introduced. This allows to address fundamental questions such as the degree of hyperbolicity, which can be quantified in…
Nonlocal Hamiltonians are used widely in first-principles quantum calculations; the nonlocality stems from eliminating undesired degrees of freedom, e.g. core electrons. To date, attempts to couple nonlocal systems to external…
We extend unsteady thin aerofoil theory to model aerofoils with generalised chordwise porosity distributions. The analysis considers a linearised porosity boundary condition where the seepage velocity through the aerofoil is related to the…
We consider the nonlinear wave modulation of arbitrary amplitude periodic traveling wave solutions of the Ostrovsky equation, which arises as a model for the unidirectional propagation of small-amplitude, weakly nonlinear surface and…
Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined…
We explain the topology of the space, so called, Fredholm-Lagrangian-Grassmannain and the quantity ``Maslov index'' for paths in this space based on the standard theory of Functional Analysis. Our standing point is to define the Maslov…
A Koopman decomposition of a complex system leads to a representation in which nonlinear dynamics appear to be linear. The existence of a linear framework with which to analyse nonlinear dynamical systems brings new strategies for…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…