相关论文: Canards and curvature: nonsmooth approximation by …
Canards are special solutions of slow/fast systems which are ubiquitous in neuroscience and electrical engineering. Two distinct classes of canard solutions have been identified and carefully studied: folded singularity canards and torus…
We propose a novel non-linear manifold learning from snapshot data and demonstrate its superiority over Proper Orthogonal Decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap (Tenenbaum…
Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed.…
We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimension…
Disordered solids respond to quasistatic shear with intermittent avalanches of plastic activity, an example of the crackling noise observed in many nonequilibrium critical systems. The temporal power spectrum of activity within disordered…
We use blowup to study the regularization of codimension one two-fold singularities in planar piecewise smooth (PWS) dynamical systems. We focus on singular canards, pseudo-equlibria and limit cycles that can occur in the PWS system. Using…
This thesis is devoted to the study of some aspects of perturbative QCD, and in particular to the development of high-precision techniques for the extraction of physical parameters such as structure functions, parton distributions, and the…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
We study the dynamics of waves in a system of diffusively coupled discrete nonlinear sources. We show that the system exhibits burst waves which are periodic in a traveling-wave reference frame. We demonstrate that the burst waves are…
We discuss fattening phenomenon for the evolution of planar curves according to their nonlocal curvature. More precisely, we consider a class of generalized curvatures which correspond to the first variation of suitable nonlocal perimeter…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
Volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang…
We use a master equation to study the dynamics of two coupled macroscopic quantum systems (e.g.\ a Josephson junction made of two Bose-Einstein condensates or two spin states of an ensemble of trapped ions) subject to a weak continuous…
We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized…
Cascades are self-reinforcing processes underlying the systemic risk of many complex systems. Understanding the universal aspects of these phenomena is of fundamental interest, yet typically bound to numerical observations in ad-hoc models…
The main goal of this paper is to give a complete fractal analysis of piecewise smooth (PWS) slow-fast Li\'{e}nard equations. For the analysis, we use the notion of Minkowski dimension of one-dimensional orbits generated by slow relation…
The one-dimensional Kardar-Parisi-Zhang (KPZ) equation is becoming an overarching paradigm for the scaling of nonequilibrium, spatially extended, classical and quantum systems with strong correlations. Recent analytical solutions have…
To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For…
The dynamics of an M-dimensional extended object whose M+1 dimensional world volume in M+2 dimensional space-time has vanishing mean curvature is formulated in term of geometrical variables (the first and second fundamental form of the…
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing…