Related papers: Universal square-root-log scaling for slender-body…
Small-scale mechanical behaviour shows significant departures from classical elastic-plastic theory. In a remarkable number of instances, the strength of a material appears to scale as the reciprocal square root of the smallest length…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
Recent scaling results for the AC conductivity of ionic glasses by Roling et al. [Phys. Rev. Lett. vol 78, 2160 (1997)] and Sidebottom [Phys. Rev. Lett. vol 82, 3653 (1999)] are discussed. It is shown that Sidebottom's version of scaling is…
Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation…
We describe recent attempts to extract the shear viscosity of the dilute Fermi gas at unitarity from experiments involving scaling flows. A scaling flow is a solution of the hydrodynamic equations that preserves the shape of the density…
In mechanical engineering W\"ohler plots serve to measure the average number of load cycles before materials break, as a function of the maximal stress in each cycle. Although such plots are prevalent in engineering for more than 150 years,…
The three-body scattering problem in Coulombic systems is widespread, however yet unresolved problem by the mathematically rigorous methods. In this work this long term challenge has been undertaken by combining distorted waves and…
We probe the two-scale factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar field theories with…
We investigate percolation in mixtures of nanorods in the presence of external fields that align or disalign the particles with the field axis. Such conditions are found in the formulation and processing of nanocomposites, where the field…
We study universal aspects of polymer conformations and transverse fluctuations for a single swollen chain characterized by a contour length $L$ and a persistence length $\ell_p$ in two dimensions (2D) and in three dimensions (3D) in the…
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…
For percolating systems, we propose a universal exponent relation connecting the leading corrections to scaling of the cluster size distribution with the dynamic corrections to the asymptotic transport behaviour at criticality. Our…
The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its…
The static and dynamic properties of dendrimers in semidilute solutions of linear chains of comparable size are investigated using Brownian dynamics simulations. The radius of gyration and diffusivity of a wide variety of low generation…
In many-body systems with U(1) global symmetry, the charge fluctuations in a subregion reveal important insights into entanglement and other global properties. For subregions with sharp corners, bipartite fluctuations have been predicted to…
Increase in viscosity under increasing shear stress, known as shear thickening (ST), is one of the most striking properties of dense particulate suspensions. Under appropriate conditions, they exhibit discontinuous shear thickening (DST),…
We study the global, i.e. radially averaged, high Reynolds number (asymptotic) scaling of streamwise turbulence intensity squared defined as ${I^2=\overline{u^2}/U^2}$, where $u$ and $U$ are the fluctuating and mean velocities, respectively…
Mode conversion and resonant absorption are crucial mechanisms for wave transport and absorption. Scaling behavior of mode conversion or resonant absorption is well-known for electromagnetic and MHD waves in planar geometry. Our recent…
We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $\Delta \phi$ relative to the critical jammed state, the shear strain $\epsilon$,…
Experiments on field electron emission from single-tip nanoemitters have typically been carried out using a counter-electrode with a finite curvature radius $R$, positioned at a distance $d_{\rm{gap}}$ from the emitter's apex. The effects…