Related papers: Analysis of the Correlation Dimension for Inertial…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
Understanding the dynamics of material objects advected by turbulent flows is a long standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting…
We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic…
We investigate stochastic resetting in coupled systems involving two degrees of freedom, where only one variable is reset. The resetting variable, which we think of as hidden, indirectly affects the remaining observable variable through…
A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of…
We investigate non-perturbative results of inviscid forced Burgers equation supplemented to continuity equation in three-dimensions. The exact two-point correlation function of density is calculated in three-dimensions. The two-point…
We present an analytic study of the density fluctuation of a Newtonian self-gravity fluid in the expanding universe with $\Omega_\Lambda+\Omega_m=1$, which extends our previous work in the static case. By use of field theory techniques, we…
The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of…
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these…
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert particle increases due to the influence of an external…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
We investigate the spread of correlations carried by an excitation in a 1-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\propto r^{-\mu}$). The increase…
We have developed a theory for inhomogeneous systems that allows for incorporation of effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess $\phi({\bf…
A new description of strange attractor systems through three geometrical and dynamical invariants is provided. They are the correlation dimension ($\mathcal{D}$) and the correlation entropy ($\mathcal{K}$), both having attracted attention…
To better understand the collisionless dark matter flow on different scales, statistical theory involving kinematic and dynamic relations must be developed for different types of flow, e.g. incompressible, constant divergence, and…
We examine the effect of Dean number on the inertial focusing of spherical particles suspended in flow through curved microfluidic ducts. Previous modelling of particle migration in curved ducts assumed the flow rate was small enough that a…
The dynamical evolution of collisionless particles in an expanding background is described. After discussing qualitatively the key features, the gravitational clustering of collisionless particles in an expanding universe is modelled using…
We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
We revisit the global existence of solutions with some large perturbations to the incompressible, viscous, and non-resistive MHD system in a three-dimensional periodic domain, where the impressed magnetic field satisfies the Diophantine…