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The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…

The majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag compared with the…

Patterns are quotidian in nature. Distinct multiscale patterns are generally a consequence of nonequilibrium dynamical processes associated with mechanical or hydrodynamic instabilities. In this thesis, I report experimental investigations…

We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any…

Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here we use a perturbation approach to study the flow around oscillating sharp edges in a microchannel. This work…

Pulsatile flow through compressed or defective blood vessels is a topic of fundamental importance in hemodynamics, particularly in cardiovascular research. This study examines flow dynamics within a tube with a bipolar cross section,…

Oscillatory flow in confined spaces is central to understanding physiological flows and rational design of synthetic periodic-actuation based micromachines. Using theory and experiments on oscillating flows generated through a laser-induced…

It is shown that initiated by action of molecular viscosity impulse flow, directed usually from the moving fluid to limiting it solid surface, can, under certain conditions, turn to zero and get negative values in the case of non-stationary…

For low enough flow rates, turbulent channel flow displays spatial modulations of large wavelengths. This phenomenon has recently been interpreted as a linear instability of the turbulent flow. We question here the ability of linear…

Structural and functional heterogeneity are hallmarks of cortical circuits, from broad degree distributions in the mouse connectome to diverse intrinsic neuronal timescales. Yet a mechanistic link between connectivity heterogeneity and…

The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…

We examine the dynamical properties of a single-layer convolutional recurrent network with a smooth sigmoidal activation function, for small values of the inputs and when the convolution kernel is unitary, so all eigenvalues lie exactly at…

The linear dynamics and instability mechanisms of double-layered weakly viscoelastic fluid flowing over an inclined plane are analyzed in the presence of insoluble surfactant at both the free surface and interface. The constitutive equation…

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…

The overall traffic of droplets in a network of microfluidic channels is strongly influenced by the liquid properties of the moving droplets. In particular, the effective hydrodynamic resistance of individual droplets plays a key role in…

We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and intersticial fluid flows. Oxygen obeys a…

The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity…

We study emergent oscillatory behavior in networks of diffusively coupled nonlinear ordinary differential equations. Starting from a situation where each isolated node possesses a globally attracting equilibrium point, we give, for an…

A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…

It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when…