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We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i)…
Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback…
We introduce finite ramified self-affine substrates in two dimensions with a set of appropriate hopping rates between nearest-neighbor sites, where the diffusion of a single random walk presents an anomalous {\it anisotropic} behavior…
We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where…
In these lecture notes I describe some of the main theoretical ideas emerged to explain the aging dynamics. This is meant to be a very short introduction to aging dynamics and no previous knowledge is assumed. I will go through simple…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
Dynamics of a classical particle in a one-dimensional, randomly driven potential is analysed both analytically and numerically. The potential considered here is composed of two identical spatially-periodic saw-tooth-like components, one of…
A continuum (Mullins-type) model is formulated for the isotropic evolution of a solid surface on which the mass transport occurs by oscillatory surface diffusion. The time-space oscillations of diffusivity are assumed to be induced by…
We show that the scale (conformal) anomaly in field theories leads to new anomalous transport effects that emerge in an external electromagnetic field in an inhomogeneous gravitational background. In inflating geometry the QED scale anomaly…
We present new simulation results on a hard sphere system at high densities. Using three-time correlations, we can account for the anomalous diffusion, which results from a homogeneous back-dragging effect. Furthermore, we calculate the…
The renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by the Gaussian self-similar velocity field with finite, and not small, correlation time. The inertial-range energy…
Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of…
Oscillatory flow patterns have been observed in many different driven many-particle systems. The conventional assumption is that the reason for emergent oscillations in opposing flows is an increased efficiency (throughput). In this…
Aging changes including age spots and atherosclerotic plaques develop in an inhomogeneous and accelerated manner. For understanding this phenomenon, some aging changes are analyzed by Misrepair mechanism, a mechanism proposed in…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…
Using experimental longitudinal and transverse velocities data for very high Reynolds number turbulence, we study both anisotropy and asymmetry of turbulence. These both seem to be related to small scale turbulent structures, and to…
We consider one-dimensional asymmetric exclusion processes with a simple attractive interaction, where the distance between consecutive particles is not allowed to exceed a certain limit and investigate the consequences of this coupling on…
The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by a non-Gaussian velocity field with finite correlation time. The velocity is governed by the…